text:
# Free Online Course on Computational Investing

I came across this free course on Computational Investing at Coursera.com. It's a great course for anyone interested in investing in stock markets.

What you will learn?

Here's a brief of what you learn in this course: Why do the prices of some companies’ stocks seem to move up and down together while others move separately? What does portfolio “diversification” really mean and how important is it? What should the price of a stock be? How can we discover and exploit the relationships between equity prices automatically? We’ll examine these questions, and others, from a computational point of view. You will learn many of the principles and algorithms hedge funds and investment professionals use to maximize return and reduce risk in equity portfolios.

Introduction Video

Get our R Programming - Data Science for Finance Bundle for just $29$39.


text:
My Math Forum Probability of Choosing Boys & Girls

 Probability and Statistics Basic Probability and Statistics Math Forum

 February 24th, 2014, 04:43 PM #1 Newbie   Joined: Feb 2014 Posts: 9 Thanks: 0 Probability of Choosing Boys & Girls I'm very confused on this particular test question and how my teacher got the answer. Was hoping someone could walk me through the problem. Refer to a family with 5 children; assume that it is equally probable for a boy to be born as it is for a girl to be born. What is the probability that there are at Least three girls given there are at least two boys? The answer is C(5,2)/26. I understand the sample space is 2^5 = 32, but I have no clue where he deducted the 6 from and I'm assuming the C(5,2) is because we stated we had at least 3 girls of the 5 so we need to choose 2 more spots? Any help or "Baby Steps" through this problem would be most appreciated.
 February 24th, 2014, 05:07 PM #2 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,538 Thanks: 920 Math Focus: Elementary mathematics and beyond Re: Probability of Choosing Boys & Girls $\frac{\binom{5}{2}}{\binom{5}{2}\,+\,\binom{5}{3}\ ,+\,\binom{5}{4}\,+\,\binom{5}{5}}\,=\,\frac{10}{2 6}\,=\,\frac{5}{13}$ Make sense now?
 February 24th, 2014, 07:29 PM #3 Newbie   Joined: Feb 2014 Posts: 9 Thanks: 0 Re: Probability of Choosing Boys & Girls So I take it that because we used the term "at least" we then add up the probabilities of each possible Sample Space is what I'm thinking?
 February 24th, 2014, 07:45 PM #4 Global Moderator     Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,538 Thanks: 920 Math Focus: Elementary mathematics and beyond Re: Probability of Choosing Boys & Girls Close. The sample space is the number of ways that the family can have at least two boys.
 February 24th, 2014, 09:17 PM #5 Newbie   Joined: Feb 2014 Posts: 9 Thanks: 0 Re: Probability of Choosing Boys & Girls Sorry, that's what I meant. I noticed there was no C(5,0) or C(5,1) for the sample space and "At least 2" could mean 2,3,4,5. Thank you for your clarification!
 February 25th, 2014, 08:34 PM #6 Global Moderator   Joined: Dec 2006 Posts: 17,702 Thanks: 1353 Given that there are at least two boys, the only way there can be at least three girls is for there to be exactly three girls and two boys. Hence the numerator is C(5,2) (or, equivalently, C(5,3)).

 Tags boys, choosing, girls, probability

,

probability of choosing a girl and is a junior

Click on a term to search for related topics.
 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Puzzled16 Algebra 13 March 6th, 2014 04:05 PM rnck Advanced Statistics 5 July 2nd, 2013 02:41 PM jon1 Probability and Statistics 3 December 12th, 2011 03:18 PM warqzaka Algebra 4 July 5th, 2011 10:06 AM Majestic_Q Algebra 3 December 21st, 2008 12:46 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top

format: plain


text:
You may discuss homework problems with other students, but you have to prepare the written assignments yourself. Late homework will be penalized 10% per day.

Please combine all your answers, the computer code and the figures into one file, and submit a copy in your dropbox on coursework.

Due March 19, 11:59PM.

Grading scheme: 10 points per question, total of 20.

# Question 1 (Based on RABE 12.3)¶

The O-rings in the booster rockets used in space launching play an important part in preventing rockets from exploding. Probabilities of O-ring failures are thought to be related to temperature. The data from 23 flights are given in this file

For each flight we have an indicator of whether or not any O-rings were damaged and the temperature of the launch.

1. Fit a logistic regression, modeling the probability of having any O-ring failures based on the temperature of the launch. Interpret the coefficients in terms of odds ratios.

2. From the fitted model, find the probability of an O-ring failure when the temperature at launch was 31 degrees. This was the temperature forecast for the day of the launching of the fatal Challenger flight on January 20, 1986.

3. Find an approximate 95% confidence interval for the coefficient of temperature in the logistic regression using both the summary and confint. Are the confidence intervals the same? Why or why not?

# Question 2 (Based on RABE 12.5)¶

Table 1.12 of the textbook describes variables in a study of health care in 52 health care facilities in New Mexico in the year 1988. The variables collected are:

Variable Description
RURAL Is hospital in a rural or non-rural area?
BED Number of beds in facility.
MCDAYS Annual medical in-patient days (hundreds).
TDAYS Annual total patient days (hundreds).
PCREV Annual total patient care revenue (\$100). NSAL Annual nursing salaries (\$100).
FEXP Annual facilities expenditures (\$100). NETREV PCREV - NSAL - FEXP 1. Using a logistic regression model, test the null hypothesis that the measured covariates have no power to distinguish between rural facilities and than non-rural facilities. Use level$\alpha=0.05\$.

2. Use a model selection technique based on AIC to choose a model that seems to best describe the outcome RURAL based on the measured covariates.

3. Repeat 2. but using BIC instead. Is the model the same?

4. Report estimates of the parameters for the variables in your final model. How are these to be interpreted?

5. Report confidence intervals for the parameters in 4. Do you think you can trust these intervals?

# Question 3¶

The data set below contains data on a sample of female horseshoe crabs, collecting their weight, width, a categorical variables for their color and the size of their spine. We are interested in understanding how the number of male satellites satell is predicted by these features.

1. Fit a log-linear Poisson regression model with satell as outcome and the remaining variables as predictors.

2. Use step to build a model in a forward fashion for satell starting with just an intercept.

3. Report estimates of the parameters for the variables in your final model. How are these to be interpreted?

4. Report confidence intervals for the parameters in 3. Do you think you can trust these intervals?

In [1]:
crabs = read.table('http://www.ics.uci.edu/~staceyah/111-202/data/horseshoe.txt', header=TRUE)


text:
# Mutually Catalytic Super Branching Random Walks: Large Finite Systems and Renormalization Analysis

Paperback (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $6.35 Usually ships in 1-2 business days (Save 89%) Other sellers (Paperback) • All (4) from$6.35
• New (3) from $53.00 • Used (1) from$6.35
Close
Sort by
Page 1 of 1
Showing All
Note: Marketplace items are not eligible for any BN.com coupons and promotions
$53.00 Seller since 2007 Feedback rating: (471) Condition: New — never opened or used in original packaging. Like New — packaging may have been opened. A "Like New" item is suitable to give as a gift. Very Good — may have minor signs of wear on packaging but item works perfectly and has no damage. Good — item is in good condition but packaging may have signs of shelf wear/aging or torn packaging. All specific defects should be noted in the Comments section associated with each item. Acceptable — item is in working order but may show signs of wear such as scratches or torn packaging. All specific defects should be noted in the Comments section associated with each item. Used — An item that has been opened and may show signs of wear. All specific defects should be noted in the Comments section associated with each item. Refurbished — A used item that has been renewed or updated and verified to be in proper working condition. Not necessarily completed by the original manufacturer. New Brand new. We distribute directly for the publisher. We study features of the longtime behavior and the spatial continuum limit for the diffusion limit of the following particle ... model. Consider populations consisting of two types of particles located on sites labeled by a countable group. The populations of each of the types evolve as follows: Each particle performs a random walk and dies or splits in two with probability$\frac{1}{2}$and the branching rates of a particle of each type at a site$x$at time$t$is proportional to the size of the population at$x$at time$t$of the other type. The diffusion limit of "small mass, large number of initial particles" is a pair of two coupled countable collections of interacting diffusions, the mutually catalytic super branching random walk.Consider now increasing sequences of finite subsets of sites and define the corresponding finite versions of the process. We study the evolution of these large finite spatial systems in size-dependent time scales and compare them with the behavior of the infinite systems, which amounts to establishing the so-called finite system scheme. A dichotomy is known between transient and recurrent symmetrized migrations for the infinite system, namely, between convergence to equilibria allowing for coexistence in the first case and concentration on monotype configurations in the second case. Correspondingly we show (i) in the recurrent case both large finite and infinite systems behave similar in all time scales, (ii) in the transient case we see for small time scales a behavior resembling the one of the infinite system, whereas for large time scales the system behaves as in the finite case with fixed size and finally in intermediate scales interesting behavior is exhibited, the system diffuses through the equilibria of the infinite system which are indexed by the pair of intensities and this diffusion process can be described as mutually catalytic diffusion on$(\R^+)^2$.At the same time, the above finite system asymptotics can be applied Read more Show Less Ships from: Boonsboro, MD Usually ships in 1-2 business days • Canadian • International • Standard, 48 States • Standard (AK, HI) • Express, 48 States • Express (AK, HI)$53.10
Seller since 2010

Feedback rating:

(26)

Condition: New
MASS MARKET PAPERBACK New 0821835424 **NEW**Factory sealed. Number 809. Book is in excellent condition, binding tight, pages crisp & clean. No remainder marks. Shipped with ... delivery confirmation inside US. *p/$WP1-91 Fast shipping and great customer service! Read more Show Less Ships from: Niagara Falls, NY Usually ships in 1-2 business days • Canadian • International • Standard, 48 States • Standard (AK, HI) • Express, 48 States • Express (AK, HI)$110.72
Seller since 2014

Feedback rating:

(7)

Condition: New
2004 Paperback NEW 9780821835425 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. *****PLEASE NOTE: This item ... is shipping from an authorized seller in Europe. In the event that a return is necessary, you will be able to return your item within the US. To learn more about our European sellers and policies see the BookQuest FAQ section***** Read more Show Less

Ships from: Stroud, Glos, United Kingdom

Usually ships in 1-2 business days

• Standard, 48 States
• Standard (AK, HI)
Page 1 of 1
Showing All
Close
Sort by

### Overview

We study features of the longtime behavior and the spatial continuum limit for the diffusion limit of the following particle model. Consider populations consisting of two types of particles located on sites labeled by a countable group. The populations of each of the types evolve as follows: Each particle performs a random walk and dies or splits in two with probability $\frac{1}{2}$ and the branching rates of a particle of each type at a site $x$ at time $t$ is proportional to the size of the population at $x$ at time $t$ of the other type. The diffusion limit of ''small mass, large number of initial particles'' is a pair of two coupled countable collections of interacting diffusions, the mutually catalytic super branching random walk. Consider now increasing sequences of finite subsets of sites and define the corresponding finite versions of the process. We study the evolution of these large finite spatial systems in size-dependent time scales and compare them with the behavior of the infinite systems, which amounts to establishing the so-called finite system scheme. A dichotomy is known between transient and recurrent symmetrized migrations for the infinite system, namely, between convergence to equilibria allowing for coexistence in the first case and concentration on monotype configurations in the second case. Correspondingly we show (i) in the recurrent case both large finite and infinite systems behave similar in all time scales, (ii) in the transient case we see for small time scales a behavior resembling the one of the infinite system, whereas for large time scales the system behaves as in the finite case with fixed size and finally in intermediate scales interesting behavior is exhibited, the system diffuses through the equilibria of the infinite system which are indexed by the pair of intensities and this diffusion process can be described as mutually catalytic diffusion on $(\mathbb{R}^+)^2$. At the same time, the above finite system asymptotics can be applied to mean-field systems of $N$ exchangeable mutually catalytic diffusions. This is the building block for a renormalization analysis of the spatially infinite hierarchical model and leads to an association of this system with the so-called interaction chain, which reflects the behavior of the process on large space-time scales. Similarly we introduce the concept of a continuum limit in the hierarchical mean field limit and show that this limit always exists and that the small-scale properties are described by another Markov chain called small scale characteristics. Both chains are analyzed in detail and exhibit the following interesting effects. The small scale properties of the continuum limit exhibit the dichotomy, overlap or segregation of densities of the two populations, as a function of the underlying random walk kernel. A corresponding concept to study hot spots is presented. Next we look in the transient regime for global equilibria and their equilibrium fluctuations and in the recurrent regime on the formation of monotype regions. For particular migration kernels in the recurrent regime we exhibit diffusive clustering, which means that the sizes (suitably defined) of monotype regions have a random order of magnitude as time proceeds and its distribution is explicitly identifiable. On the other hand in the regime of very large clusters we identify the deterministic order of magnitude of monotype regions and determine the law of the random size. These two regimes occur for different migration kernels than for the cases of ordinary branching or Fisher-Wright diffusion. Finally we find a third regime of very rapid deterministic spatial cluster growth which is not present in other models just mentioned. A further consequence of the analysis is that mutually catalytic branching has a fixed point property under renormalization and gives a natural example different from the trivial case of multitype models consisting of two independent versions of the fixed points for the one type case.

## Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

(0)

(0)

(0)

(0)

### 1 Star

(0)

Your Name: Create a Pen Name or

### Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

### Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

### What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

### Reviews should not contain any of the following:

• - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
• - Time-sensitive information such as tour dates, signings, lectures, etc.
• - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
• - Comments focusing on the author or that may ruin the ending for others
• - Phone numbers, addresses, URLs
• - Pricing and availability information or alternative ordering information

### Reminder:

• - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
• - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
Search for Products You'd Like to Recommend

### Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

If you find inappropriate content, please report it to Barnes & Noble
Why is this product inappropriate?


text:
• 论文 •

### 多斜孔火焰筒壁冷却结构的数值模拟

1. 北京航空航天大学 航空发动机气动热力重点实验室, 北京 100191
• 收稿日期:2007-10-18 出版日期:2008-10-30 发布日期:2010-09-16
• 作者简介:李志强(1970-),男,山西长治人,副教授,lizhiqiang@buaa.edu.cn.

### Numerical simulations of flame tube cooling structure with multi-jet holes

Li Zhiqiang, Tian Tao, Chen Qin

1. National Key Laboratory on Aero-Engines, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
• Received:2007-10-18 Online:2008-10-30 Published:2010-09-16

Abstract: The numerical simulation was used to study the film cooling effectiveness of plate with multi-inclined jet hole. The effect of the blowing ratio, oblique angle of the hole, array way of the hole, compound angle and shape of jet holes was investigated for increasing cooling efficiency. The computational results show that the blowing ratio and the oblique angle of the hole have important influence for the cooling efficiency. With the increase of the blowing ratio, the cooling efficiency increases, but the trend of increase is decreasing. And with the decrease of the oblique angle of the hole, the high cooling efficiency can be gained. The array way of the holes has a certain effect on the cooling efficiency, i.e. long diamond distribution is better than the regular diamond distribution. Also, the computational results show the introduction of the hole offset angle in the y direction is unfavorable for cooling. In addition, compared with cylinder holes, when the holes with the cone contractive entrance and the cone outspread exit are used, it is found that the cooling efficiency can be improved with low blowing ratio, and the cooling efficiency is inferior with high blowing ratio.


text:
# Quartic curve constructor¶

sage.schemes.plane_quartics.quartic_constructor.QuarticCurve(F, PP=None, check=False)

Returns the quartic curve defined by the polynomial F.

INPUT:

• F – a polynomial in three variables, homogeneous of degree 4
• PP – a projective plane (default:None)
• check – whether to check for smoothness or not (default:False)

EXAMPLES:

sage: x,y,z=PolynomialRing(QQ,['x','y','z']).gens()
sage: QuarticCurve(x**4+y**4+z**4)
Quartic Curve over Rational Field defined by x^4 + y^4 + z^4


text:
# Sequence of non-prime naturals

Regarding the question of finding a sequence of non-prime natural numbers, I have consistently found an answer that states that have a 'proper' starting point, say (n+1)!+2; and then all the consecutive n numbers will be non-prime. I am unable to understand that why we need a 'proper' starting point. Is it not that any factorial (n!) will suffice as a starting point, and the number of values in the sequence will be decided by the value of n.

A case in point is an example that shows that 101!+2 is a starting point for the next 100 values, till 101!+101 being non-prime natural number. For this particular case, the logic being offered is that the value 101! and 2 have a common factor, and so on till 101! and 101.

• What is your question? For any $n>2$, the number $n!$ is composite. It may also happen that $n!+1$ is composite, in which case we see that the $n+1$ consecutive numbers $n!, n!+1,n!+2,\ldots, n!+n$ are composite. However, it may also happen that $n!+1$ is prime (e.g., when $n=3$ or when $n=11$ or when $n=154$). – Hagen von Eitzen Nov 5 '17 at 11:39
• It is that what is significance of 'proper' starting point; or any n!, for any natural n, is a starting point. – jiten Nov 5 '17 at 11:42
• A "proper" starting point $N$ is one for which it can be readily established that $N,N+,\ldots, N+n-1$ are composite. Instead of $N=(n+1)!+2$, you could take some smaller $N$, say let $N$ be $2$ plus the product of all primes $\le n+1$. – Hagen von Eitzen Nov 5 '17 at 11:45
• $n!+2$ is prime for $n<2$. – Hagen von Eitzen Nov 5 '17 at 11:46
• @jiten In PARI/GP, you can simply try isprime(154!+1) (or even isprime(1477!+1) – Hagen von Eitzen Nov 5 '17 at 13:11

$99!+1$ is divisible by $199$ while $100!+1$ is divisible by $101$ and $101!+1$ is divisible by $137$, but for example $116!+1$ is prime (see OEIS A002981 for more examples, including $154!+1$)
So if you wanted $116$ or $117$ consecutive composite numbers, you could not take the sequence $116!, 116!+1, 116!+2, \ldots, 116!+116$ since exactly one of those is prime, but you could take the sequences $117!+2, 117!+3, 117!+4, \ldots, 117!+117$ or $118!+2, 118!+3, 118!+4, \ldots, 118!+118$ depending on how many you wanted, since $n!+k$ is composite for $1 \lt k \lt n$ since it is divisible by $k$
And this is why in general $(n-1)!$ or $n!$ are not good starting points to be certain of $n$ consecutive composite numbers, but $(n+1)!+2$ is a good starting point


text:
Change search
Refine search result
1234567 1 - 50 of 507
CiteExportLink to result list
Cite
Citation style
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf
Rows per page
• 5
• 10
• 20
• 50
• 100
• 250
Sort
• Standard (Relevance)
• Author A-Ö
• Author Ö-A
• Title A-Ö
• Title Ö-A
• Publication type A-Ö
• Publication type Ö-A
• Issued (Oldest first)
• Issued (Newest first)
• Created (Oldest first)
• Created (Newest first)
• Last updated (Oldest first)
• Last updated (Newest first)
• Disputation date (earliest first)
• Disputation date (latest first)
• Standard (Relevance)
• Author A-Ö
• Author Ö-A
• Title A-Ö
• Title Ö-A
• Publication type A-Ö
• Publication type Ö-A
• Issued (Oldest first)
• Issued (Newest first)
• Created (Oldest first)
• Created (Newest first)
• Last updated (Oldest first)
• Last updated (Newest first)
• Disputation date (earliest first)
• Disputation date (latest first)
Select
The maximal number of hits you can export is 250. When you want to export more records please use the Create feeds function.
• 1.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
A Study of Automotive Composites and Optimisation for Chassis Implementation2013Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

In the quest of reducing emissions of passenger cars a trend in the car industry has recently been tointroduce lightweight composite materials to replace steel which has been the otherwise main materialto use. In this report the weight-optimising of a structural underbody for a passenger car using twodifferent manufacturing methods is described. The two methods are Advanced Sheet MouldingCompound (A-SMC) and Resin Transfer Moulding (RTM). A-SMC is characterised by a low cycle time andfast layup of the material resulting in lower cost. RTM is slower and thus more expensive but has bettermaterial properties which results in lower weight. The novel approach is to use A-SMC to construct thecomplete underbody as one piece which has not been done before. The geometry is FEM -optimised forminimum material thickness under a standard load case for torsional stiffness.The simulations showed that the underbody was not possible to be manufactured using A-SMC in itsoriginal shape without being reinforced. When reinforcing the structure it met the design constraintsand the weight was optimised to 53.9 kg with the possibility for further improvements. The RTMmethod resulted in 25.83 kg without any reinforcements but showed potential for further weightreduction by changing the geometrical design. A final analysis of the underbody combined the twomanufacturing methods and the weight was here optimised to 25.27 kg without any reinforcements.

• 2.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Mechanical Properties of Resistance Spot Welds in Lightweight Applications2013Licentiate thesis, comprehensive summary (Other academic)

This licentiate thesis is concerned with residual stresses in aluminum alloy 6061-T6 resistance spot welded joint. Several topics related to mechanical strength of welded structures are treated such as; nugget size and microhardness and microstructures of weld zone and their influence on mechanical strength of welded structure, failure load measurement using tensile-shear test, resistance spot welding simulation, residual stress measurement by X-ray diffraction method and analysis effect of welding parameters on the mechanical strength and the residual stresses.

To investigate the effect of resistance spot weld parameters on mechanical strength of welded structures, various welding parameters e.g. welding current, welding time and electrode force are selected to produce welded joints with different quality. According to the failure mode, the empirical equation was used to prediction of failure load base on nugget size and hardness of failure line. Microstructure study has been carried out to investigate microstructural changes in the welded joints. Microhardness tests are done to find hardness profiles due to microstructural changes and determine the minimum hardness.

In addition, an electro-thermal-structural coupled finite element model and X-ray diffraction residual stress measurement have been utilized to analyze residual stresses distribution in weld zone. The electrical and thermal contact conductance, as mandatory factors are applied in contact area between electrode-workpiece and workpiece-workpiece to resolve the complexity of the finite element model. The physical and mechanical properties of the material are defined as thermal-dependent in order to improve the accuracy of the model. Furthermore, the electrodes are removed after holding cycle using the birth and death elements method. Moreover, the effect of welding parameters on maximum residual stress is investigated and a regression model is proposed to predict maximum tensile residual stresses in terms of welding parameters.

The results obtained from the finite element analysis have been used to build up two back-propagation artificial neural network models for the residual stresses and the nugget size prediction. The results revealed that the neural network models created in this study can accurately predict the nugget size and the residual stresses produced in resistance spot weld. Using a combination of these two developed models, the nugget size and the residual stresses can be predicted in terms of spot weld parameters with high speed and accuracy.

• 3.
Univ Zanjan, Zanjan 4537138791, Iran..
Univ Zanjan, Zanjan 4537138791, Iran.. KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Residual Stresses in Resistance Spot Welded AZ61 Mg Alloy2019In: CMES - Computer Modeling in Engineering & Sciences, ISSN 1526-1492, E-ISSN 1526-1506, Vol. 118, no 2, p. 275-290Article in journal (Refereed)

The use of magnesium alloys has been rapidly increased due to their ability to maintain high strengths at light weights. However weldability of steels and aluminum alloys by using resistance spot weld (RSW) process is a major issue, because it cannot be directly utilized for magnesium alloys. In this study, a structural-thermal-electrical finite element (FE) model has been developed to predict the distribution of residual stresses in RSW AZ61 magnesium alloy. Thermophysical and thermomechanical properties of AZ61 magnesium alloy have been experimentally determined, and have been used in FE model to increase the accuracy of the model. X-ray diffraction (XRD) technique has been utilized to measure the residual stresses in welded samples, and its results have been used to validate the FE model. Comparison study shows that the results obtained by using FE model have a good agreement with the experimental XRD data. In specific, the results show that the maximum tensile residual stress occurs at the weld center while decreases towards the nugget edge. In addition, the effects of welding parameters such as electrical current, welding time, and electrode force have been investigated on the maximum tensile residual stress. The results show that the tensile residual stress in welded joints rises by increasing the electrical current; however, it declines by prolonging the welding time as well as increasing the electrode force.

• 4.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Iran Univ Sci & Technol, Tehran, Iran. KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures. Linkoping Tech Univ, Linkoping, Sweden .
An approach in prediction of failure in resistance spot welded aluminum 6061-T6 under quasi-static tensile test2012In: Proceedings of the Institution of mechanical engineers. Part B, journal of engineering manufacture, ISSN 0954-4054, E-ISSN 2041-2975, Vol. 226, no B6, p. 1026-1032Article in journal (Refereed)

The aim of this article is to predict the failure load in resistance spot welded aluminum 6061-T6 sheets with 2mm thickness under quasi-static tensile test. Various welding parameters, e. g. welding current, welding time and electrode force are selected to produce welded joints with different quality. The results show that for all the samples in this study only interfacial failure mode was observed in tensile-shear test and no pull-out mode was observed. According to the failure mode, an empirical equation was used for the prediction of failure load based on nugget size and hardness of failure line. Microstructure study has been carried out to investigate microstructural changes in the welded joints. For determination of the minimum hardness, microhardness tests have been carried out to find hardness profiles. The minimum hardness value was observed for a thin layer around the nugget with large and coarse grains. The results show that by using the presented empirical equation, the failure can be predicted with a good agreement only by measuring nugget size.

• 5.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Iran Univ Sci & Technol, Tehran, Iran. KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
On Residual Stresses in Resistance Spot-Welded Aluminum Alloy 6061-T6: Experimental and Numerical Analysis2013In: Journal of materials engineering and performance (Print), ISSN 1059-9495, E-ISSN 1544-1024, Vol. 22, no 12, p. 3612-3619Article in journal (Refereed)

In this study, an electro-thermal-structural-coupled finite element (FE) model and x-ray diffraction residual stress measurements have been utilized to analyze distribution of residual stresses in an aluminum alloy 6061-T6 resistance spot-welded joint with 2-mm-thickness sheet. Increasing the aluminum sheet thickness to more than 1 mm leads to creating difficulty in spot-welding process and increases the complexity of the FE model. The electrical and thermal contact conductances, as mandatory factors are applied in contact areas of electrode-workpiece and workpiece-workpiece to resolve the complexity of the FE model. The physical and mechanical properties of the material are defined as thermal dependent to improve the accuracy of the model. Furthermore, the electrodes are removed after the holding cycle using the birth-and-death elements method. The results have a good agreement with experimental data obtained from x-ray diffraction residual stress measurements. However, the highest internal tensile residual stress occurs in the center of the nugget zone and decreases toward nugget edge; surface residual stress increases toward the edge of the welding zone and afterward, the area decreases slightly.

• 6.
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran .
Iran Univ Sci & Technol, Tehran, Iran. KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Prediction of the nugget size in resistance spot welding with a combination of a finite-element analysis and an artificial neural network2014In: Materiali in tehnologije, ISSN 1580-2949, E-ISSN 1580-3414, Vol. 48, no 1, p. 33-38Article in journal (Refereed)

The goal of this investigation is to predict the nugget size for a resistance spot weld of thick aluminum 6061-T6 sheets 2 mm. The quality and strength of spot welds determine the integrity of the structure, which depends thoroughly on the nugget size. In this study, the finite-element method and artificial neural network were used to predict the nugget size. Different spot welding parameters such as the welding current and the welding time were selected to be used for a coupled, thermal-electrical-structural finite-element model. In order to validate the numerical results a series of experiments were carried out and the nugget sizes were measured. The results obtained with the finite-element analysis were used to build up a back-propagation, artificial-neural-network model for the nugget-size prediction. The results revealed that a combination of these two developed models can accurately and rapidly predict the nugget size for a resistance spot weld.

• 7. Alam, M M
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Influence of defects on fatigue crack propagation in laser hybrid welded eccentric fillet joint2011In: Engineering Fracture Mechanics, ISSN 0013-7944, E-ISSN 1873-7315, Vol. 78, no 10, p. 2246-2258Article in journal (Refereed)

Fatigue cracking of laser hybrid welded eccentric fillet joints has been studied for stainless steel. Two-dimensional linear elastic fracture mechanics analysis was carried out for this joint geometry for four point bending load. The numerical simulations explain for the experimental observations why the crack propagates from the lower weld toe and why the crack gradually bends towards the root. Lack of fusion turned out to be uncritical for the initiation of cracks due to its compressive stress conditions. The linear elastic fracture mechanics analysis has demonstrated in good qualitative agreement with fatigue test results that lack of fusion slightly (<10%) reduces the fatigue life by accelerating the crack propagation. For the geometrical conditions studied here improved understanding of the crack propagation was obtained and in turn illustrated. The elaborated design curves turned out to be above the standard recommendations.

• 8. Alam, M. M.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
The influence of surface geometry and topography on the fatigue cracking behaviour of laser hybrid welded eccentric fillet joints2010In: Applied Surface Science, ISSN 0169-4332, E-ISSN 1873-5584, Vol. 256, no 6, p. 1936-1945Article in journal (Refereed)

Laser hybrid welding of an eccentric fillet joint causes a complex geometry for fatigue load by 4-point bending. The weld surface geometry and topography were measured and studied in order to understand the crack initiation mechanisms. The crack initiation location and the crack propagation path were studied and compared to Finite Element stress analysis, taking into account the surface macro-and micro-geometry. It can be explained why the root and the upper weld toe are uncritical for cracking. The cracks that initiate from the weld bead show higher fatigue strength than the samples failing at the lower weld toe, as can be explained by a critical radius for the toe below which surface ripples instead determine the main stress raiser location for cracking. The location of maximum surface stress is related to a combination of throat depth, toe radius and sharp surface ripples along which the cracks preferably propagate.

• 9. Alam, Minhaj M
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
The Effects of Surface Topography and Lack of Fusion on The Fatigue Strength of Laser Hybrid Welds2009In: Congress proceedings: ICALEO, 28th International Congress on Applications of Lasers & Electro-Optics, 2009, p. 38-46Conference paper (Refereed)

The geometrical aspects of laser hybrid welds (before, during and after the process) differ from autonomous laser welding and from arc welding. When studying the fatigue behaviour of laser hybrid welded fillet joints we identified that the micro-topography (i.e. the surface ripples) can be more important than the macrogeometry of the weld surface or lack of fusion (LOF), which frequently was detected. The plastic replica method was applied to measure the toe radii at the weld edges while the micro-topography was identified by interferometric profilometry. From metallurgical analysis of the joint interface, the tendency to LOF can be explained. Stress analysis was carried out by Finite element analysis (FEA) for the complex joint geometry and a bending load situation, showing maximum stress on the weld toes, even when including LOF. It was shown that the position and value of the maximum stress depends on a non-trivial combination of the weld geometry, including possible LOF, and the surface micro-topography. Thus it can be explained that at compressive stress conditions LOF does not contribute significantly to the fatigue strength of laser hybrid welds while the surface topography does. Recommendations for defining and in turn avoiding critical geometrical aspects during the welding process are discussed.

• 10. Alam, Minhaj M
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Fatigue behaviour study of laser hybrid welded eccentric fillet joints – Part II: State-of-the-art of fracture mechanics and fatigue analysis of welded joints2009In: 12th NOLAMP proceeding 2009: Nordic Laser Materials Processing Conference / [ed] Erling Dam Mortensen, 2009Conference paper (Other academic)

Simplified fatigue and fracture mechanics based assessment methods are widely used by the industry to determine the structural integrity significance of postulated cracks, manufacturing flaws, service-induced cracking or suspected degradation of engineering components under normal and abnormal service loads. In many cases, welded joints are the regions most likely to contain original fabrication defects or cracks initiating and growing during service operation. The welded joints are a major component that is often blamed for causing a structure failure or for being the point at which fatigue or fracture problems initiate and propagate. Various mathematical models/techniques for various classes of welded joints are developed by analytically or by simulation software's that can be used in fatigue and fracture assessments. This literature survey compiled useful information on fracture and fatigue analysis of various welded joints. The present review is divided into two major sections- fracture mechanics and fatigue analysis with widely used models. A survey table is also introduced to get the outlook of research trend on fatigue and fracture over last 3 decades. Although tremendous research effort has been implemented on fatigue and fracture analysis of conventional welding, research on relatively new welding technology (laser welding, hybrid laser welding) is still limited and unsatisfactory. In order to give guarantee or make welding standard for new welding technology, further research is required in the field of fatigue and fracture mechanics including FEM and multi-scale modeling.

• 11. Alam, Minhaj M
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Geometrical Aspects of The Fatigue Behaviour of Laser Hybrid Fillet Welds2009In: Proceedings of the Fatigue Design Conference, 2009Conference paper (Refereed)
• 12. Alam, Minhaj M
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Fatigue Behaviour Study of Laser Hybrid Welded Eccentric Fillet Joints - Part I2009In: 12th NOLAMP proceeding 2009: Nordic Laser Materials Processing Conference / [ed] Erling Dam Mortensen, 2009Conference paper (Other academic)

Welded joints are a major component that is often responsible for causing a structure failure or for being the point at which fatigue cracking initiates and propagates. Despite tremendous research efforts, the understanding of fatigue behaviour is still limited, particularly for new techniques like laser hybrid welding. Beside a comprehensive state-of-the-art study, the paper presents a fatigue study of laser hybrid welded eccentric fillet joint of stainless steel of 10 mm thickness, with 5 mm displacement. Motivation is to study the influence of the surface geometry shape on fatigue performance under a four point bending test. 13 samples were produced, measuring the toe radii and testing under constant amplitude loading with stress ratio R=0. Different techniques have been used to measure local weld geometry, like plastic replica, a 3D optical profiler and a 3D-digitizer. The influence of the local weld geometry, like the toe radii, on the stress concentration was studied by FE-analysis. Occasionally lack of fusion was observed, which was taken into account in the FE-analysis. Based on the nominal stress approach, SN-curves were designed for laser hybrid welded eccentric fillet joints. Macro hardness tests were carried out and the crack surfaces were observed in order to detect crack initiation and propagation. Correlations between the toe radii, the corresponding stress maxima and crack initiation locations were studied between the different samples and even along the welds.

• 13. Alkhagen, M.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
A triaxial rheometer for soft compressible solids2002In: Journal of Rheology, ISSN 0148-6055, Vol. 46, no 1, p. 31-47Article in journal (Refereed)

The compression and the shear of soft compressible solids were studied using the triaxial rheometer. The sample was fixed between two parallel plates and the deformation was controlled by an x, y, z displacement on one plate while the stress was measured on the other. The triaxial stress transducer eliminates the edge effects by only measuring the stress on an interior region of the plate. The edge effects and the associated measurement errors were analyzed by the simple isotropic elastic theory and were compared to the measurements done on the chloroprene rubber foam.

• 14. Allaoui, Aissa
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
On the compressive response of carbon nanotube tangles2009In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 373, no 35, p. 3169-3173Article in journal (Refereed)

The nonlinear bulk compressibility of entangled multiwalled carbon nanotubes is studied. The analogy with textile fibre assemblies is explored by means of the well established van Wyk model. In view of the small diameter of the nanotubes. the possible effect of adhesive van der Waals interactions at tube-tube contacts is analysed. It is found, however, that the contribution of adhesive contacts to the bulk stress should be negligible. Compression experiments are performed on multi-walled carbon nanotubes and show that van Wyk's model is able to describe the response, although the values of the dimensionless parameter k of van Wyk's model were lower than expected. There is indeed no indication that van der Waals interactions play any significant role.

• 15. Al-Zubaidy, M. N.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Properties of orthotropic glass-polypropylene composites manufactured by weaving of prepreg tapes and other routes2000In: Plastics, Rubber and Composites Processing and Applications, ISSN 09598111 (ISSN), Vol. 29, no 10, p. 520-526Article in journal (Refereed)

This paper reports a study of the melt impregnation and weaving of glass-polypropylene prepreg tapes into sheet for use as a precursor for pressed thermoplastic composite products and a comparison of the properties attainable with those achievable by other comparable routes. Melt impregnation has been used successfully to manufacture well impregnated tapes, with and without internal coupling agent. It appears that weaving could be an economically viable process for converting unidirectional tape into a conformable, press formable prepreg. The properties of glass-polypropylene laminates manufactured by pressing the tape woven product were compared with those of other glass-polypropylene composites, including crossply laminate made from Plytron and samples prepared by film stacking. Quasi-static mechanical properties were found to be comparable with those of Plytron and superior to those of the other materials. In the coupled samples, coupling was somewhat less effective than in Plytron. The impact behaviour of the pressed, tape woven products was impressive and superior to any of the other materials tested. Â© 2000 IoM Communications Ltd.

• 16.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Dynamic Analysis of Sinusoidal, Random and Shock Vibration according to Launch Environment for Small Spacecraft Development to Asteroid 2016-HO32019Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

The investment of space commerce is skyrocketing and it is predicted to be a nascent business in the future. The spacecraft demand has been growing not only for NASA and other space agency’s mission but also collaboration business between small space industries, academia, and scientific community. This glimpse brought an interest to a new investor, government, military, and manufacturing company to deliver their objectives efficiently. Nowadays, many startups compete embracing innovation and pioneering the novelty of space project beyond prodigious vision in an unprecedented way. Many players foresee that decreasing size of the rocket is an important key to survive and succeed in the space business. One of the efficient acts is lowering the launch cost. This can be achieved by designing a small size, lightweight and affordable spacecraft. Within this context, a Beyond Atlas Spacecraft which will be sent to Asteroid 2016-HO3, has achieved a wet mass of 20.85 kg with the size of 24.7 x 42.2 x 40.8 cm in stowed mode and 84 x 399 x 40.8 cm in unstowed mode. However, the drawback being light and small may lead to catastrophic failure due to resonance frequency events. According to past experience, the gyro of the Swedish national satellite was damaged during ground testing and it was suspected due to high amplification when the natural frequency coincides to the main structure resonance. Therefore, this work is focusing on a spacecraft development and a non-destructive structural analysis. The coupled-load analysis of a preliminary spacecraft design including sinusoidal, random vibration and shock analysis are calculated using FEM. This effort can reduce the risk of component destruction before laboratory testing as well as understand better the dynamic behavior of the spacecraft. The critical frequency in each orthogonal axis with base input from launch environment of the LM-3A Launch Vehicle was devised. The maximum stress, amplitude, and acceleration in accordance of qualification test criteria were evaluated and discussed.

• 17.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.), Solid Mechanics (Div.).
Early assessment of composite structures: Framework to analyse the potential of fibre reinforced composites in a structure subjected to multiple load case2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

To meet the need of lightweight chassis in the near future, a technological step of introducing anisotropic materials like Carbon Fibre Reinforced Plastics (CFRP) in structural parts of cars is a possible way ahead. Though there are commercially available tools to find suitability of Fibre Reinforced Plastics (FRPs) and their orientations, they depend on numerical optimization and complexity increases with the size of the model. Nevertheless, the user has a very limited control of intermediate steps. To understand the type of material system that can be used in different regions for a lightweight chassis, especially during the initial concept phase, a more simplified, yet reliable tool is desirable.The thesis aims to provide a framework for determining fibre orientations according to the most-ideal loading path to achieve maximum advantage from FRP-materials. This has been achieved by developing algorithms to find best-fit material orientations analytically, which uses principal stresses and their orientations in a finite element originating from multiple load cases. This thesis takes inspiration from the Durst criteria (2008) which upon implementation provides information on how individual elements must be modelled in a component subjected to multiple load cases. This analysis pre-evaluates the potential of FRP-suitable parts. Few modifications have been made to the existing formulations by the authors which have been explained in relevant sections.The study has been extended to develop additional MATLAB subroutines which finds the type of laminate design (uni-directional, bi-axial or quasi-isotropic) that is suitable for individual elements.Several test cases have been run to check the validity of the developed algorithm. Finally, the algorithm has been implemented on a Body-In-White subjected to two load cases. The thesis gives an idea of how to divide the structure into sub-components along with the local fibre directions based on the fibre orientations and an appropriate laminate design based on classical laminate theory.

• 18.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Concept study for cost and weight reduction of a barge container sized module2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

The intention of this thesis is to develop, evaluate new concepts and look over the current design for a container sized barge module. By request of Group Ocean, a cost and weight reduction is the main improvement criteria along with keeping the strength of the module.Five concepts are developed, analyzed and discussed with the supervisor at Group Ocean, where three are decided to be presented here. The other two are left out, since they are considered way too expensive without giving a satisfying result. The three concepts that are developed throughout this thesis are; changing to high strength steel, changing to sandwich panels and increasing stiffeners with smaller dimensions.A structural optimization is made in the software MATLAB to find out the best dimension to use for the sandwich panels. To determine the local stresses, the finite element method is used in Inventor Professional. It is also where the design and CAD modules are built in, so for simplifications it is used for FEA (Finite Element Analysis) as well. To reduce the amount of elements and nodes, shell elements and other structural constraints are used in the FEA. All the concepts are modelled with the same structural constraints so a practical comparison study can be made.The final designs resulted in a total weight reduction up to 40% with a material cost reduction of 12%. Based on what type of material is chosen, the material cost reduction range is between 3-12% and the weight reduction range is between 13-40%.

• 19.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Utvärdering av infästningar i sandwichkonstruktioner för fordonsapplikationer2011Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

The automotive industry is increasingly studying lightweight solution in their designs, also rational production and low costs in materials and manufacturing methods are of great interest. This thesis consisted in the practical evaluation of anchors for sandwich panels. The object was to study loads of shearing and pull out of the plane. The experiments were carried out on panels made up of 1mm aluminium coatings and 50mm extruded polystyrene (XPS) at its core. As the fasteners used simple methods such as blind rivets, screw and glue. 44 tests were performed. Out of these 32 considered pullout of the plane and 12 considered shearing. The results show that it is possible to have good strength in shearing and pull with simple methods.

• 20.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Pipe-In-Pipe system for offshore applications: Post buckling analysis associated with thermal expansion2014Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

The usage of Pipe-In-Pipe (PIP) solutions for offshore applications has increased during the lastyears. The solution gives high thermal insulation and protects the flow line from environmental impacts. One critical load case is buckling of the pipeline system due to thermal expansions of the inner pipe. This project intends to increase knowledge about PIP systems, investigate the impact of different parameters as well as update parameters in an existing SIMLA model. A FE-model of a PIP system was created in ANSYS with a refined section where pipes and centralizers are modelled with solid elements.The ANSYS-model was tested against a verified FE-model created in SIMLA. The global results obtained from ANSYS and SIMLA did not give a perfect match. The ANSYS model tended to buckle in another way, which is assumed to be related to different modelling of resistance between the pipeline and the seabed as well as unwished properties between the side section and the midsection.Local results obtained from ANSYS showed that there are discontinuities in bending moment and effective axial forces when passing a centralizer. The contact force between centralizer and pipes give rise to high friction forces that acts along the same line as the axial force in the pipes.Increased friction coefficient between centralizer and outer pipe resulted in increased discontinuity in axial force. Selection of a proper friction coefficient thus has significant influence on the results.Centralizer stiffness was evaluated by a local FE-model where a centralizer was compressed between the inner and the outer pipe. Displacement of inner pipe was evaluated as a function of applied force. The result showed that the force-displacement curve describing centralizer stiffness follows

Q (Δ)=($C{1}$ Δ) $\frac{2}{3}$

where $C{1}$     is a constant depending on dimensions and material of the centralizer. Linearized indifferent sections and with a centralizer thickness of 0,1 meter the following expression gave stiffnesses in the range 100-1000 MN/m, which agrees with stiffnesses used in the SIMLA model.displacements up to 0.3 mm the radial stiffness used in SIMLA is still good to use.

• 21. Andre, A.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures. KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures. KTH.
An experimental and numerical study of the effect of some manufacturing defects2013In: ICCM International Conferences on Composite Materials, International Committee on Composite Materials , 2013, p. 4105-4112Conference paper (Refereed)

During the manufacturing process of composite structural parts, layer of fabrics or unidirectional prepreg may have to be cut in order to fulfil production requirements. From a general mechanical point of view, cutting fibres in a composite part has a large negative impact on the mechanical properties. However, such interventions are necessary in particular cases, for example due to draping of complex geometries. A rather extensive test program was launched to investigate the effects of defects that typically could arise during manufacturing. The overall purpose of the test program was to determine knock-down factors on strength for typical manufacturing defects that occasionally arise and sometimes are hard to avoid in production: cuts/gaps and fibre angle deviations. Four types of specimens were tested, reference, intersection of cuts in adjacent layers combined with a bolt hole, cut in a zero degree ply combined with a bolt hole and specimens with misaligned fibres. The specimens with misaligned fibres were tested with three different fibre angles. In addition to the experimental procedure, FE-analyses utilising cohesive elements were conducted, and after mechanical tests, Non Destructive Investigation (NDI) and fractographic investigations were performed. An excellent correlation between analyses and experiments were obtained.

• 22.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Development of a motion platform for the G1X radar2019Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

The Giraffe 1X is a mobile short range 3D radar from Saab used for example to detect threats and create protection in a ground based air defence system. It can also be used on naval platforms for air and surface surveillance. During the development of the radar, the system needs to be tested for both sea and mobile land applications. The most convenient place for testing is on the roof of Saab’s facility in Gothenburg. There elevators can raise the radar to the roof giving an excellent view of for example Landvetter airport and the sea. To aid future verification experiments of the radar system, this project was started in order to develop and construct a motion platform used to simulate sea- and vehicle motions. During a six month period at Saab, the work of the project was started with a thorough research of motions platforms to conduct preliminary concept studies. Furthermore the concepts were drawn as 3D-CAD models in Creo Parametric in order to visualise the different solutions and present them for suppliers. The report also covers the assembly of the produced parts, together with the development of a user interface to control the motion platform.

Lastly, the result of product development is a two-degree of freedom (DOF) motion platform influenced by the gyroscopic gimbal concept. The G1X radar is mounted on a gimbal platform which is made out of two aluminium frames, whereas the outer frame rotates around an horizontal axis while the inner frame rotates around a transversely mounted horizontal axis mounted on the outer frame. Each aluminium frame is attached to a link arm which is mounted on a motor that is used to tilt the frame. The platform can be tilted _ 22 o in pitch and _ 22 o in roll. The gimbal is supported by a steel structure to allow ground clearance and to raise the radar to a comfortable working height.

• 23.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Simultaneous modal adjustment of multiple aircraft configurations using an optimization method2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

When designing an airplane, it is necessary to know precisely the vibration modes of the structure. To do so, the Finite Element model of the airplane is adjusted to ground vibration tests results using optimization. Particularly, for airplanes able to carry several external payloads, this adjustment process must be performed for all payloads configurations. In this Master Thesis, the possibility of adjusting simultaneously different airplane configurations to their respective tests results is explored. Such a method ensures that the final Finite Element model is the same in all configurations. After implementation in the company’s software, this method is subsequently tested over two configurations. The results obtained are compared to those from separate adjustment of the models with the same variable parameters. Comparison shows that simultaneous model adjustment is promising. A better choice of variable parameters is required to improve results.

• 24.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Additive weld manufacturing and material properties effect on structural margins2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

the FE analyses. Traditionally all parts are modeled with isotropic base material. Analyses are made on a part of the nozzle which includes both a butt weld and metal deposition and which is an interface to another part causing loads that has to be sustained by the weld and the MD. As a small part of this thesis was also a fatigue study made to a spot weld test specimen.

In order to strengthen the nozzle to prevent structural damage, an outer layer is added to the already existing metal cone by material deposition, MD, or additive manufacturing. During the manufacturing process the material will indicate some degree of anisotropic properties.

The key purpose of this thesis was to analyze how this anisotropic behaviour might affect the structural stiffener connected to this anisotropic material when exposed to a load at the end of the stiffener. Further analysis due to fatigue was also done to parts of the structure. The procedure was done by building a model and setting up the different anisotropic properties with help of a finite element program, Ansys. The material properties regarding the anisotropy of the material was changed and compared in order to see how it affected stresses and strains in the anisotropic material and it‘s surrounding materials. Further analysis was made to the properties of the weld such as the yield limit.

The result would indicate that for loadings that did not generate plastic deformations, hence elastic deformations, there were no significant difference forthe different trial values of the yield ratios. However, the differences became parent when studying large plastic deformations. Variation of the Young’s modulus would show some differences in the monitored properties for both elastic and plastic deformations. Studies of degrading the welds yield limit would show no diffrences when elastic deformations were present, but would have a big impact when large plastic deformations were present. The J-values variations for the spotweld would indicate huge differences depending on the yield limits for the spotweld and base material.

• 25.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Effect of material grade on fatigue strength and residual stresses in high strength steel welds2012Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

This thesis work is concerned with effect of material grade on fatigue strength of welded joints. Fatigue strength evaluation of welded joints in as welded and post weld treated condition was carried out with effective notch method. Results of peak stress method have also been compared with those of effective notch method for as welded joints. In addition, using the results of effective notch method, the effect of important weld and global geometry factors on notch stress concentration factor has been studied with 2-level design of experiment and a mathematical relation among stress concentration factor and the geometric factors has been proposed. Overall, thickness of the base plate and toe radius is found to be the most important factors determining fatigue strength of the joint.

Welding induced residual stresses have also been predicted using 2D and 3D FEM analysis to see their effect on fatigue strength of the joints. Also, transversal residual stresses were measured using X-ray diffraction method to assess the accuracy of predicted results. Based on simulation results, effect of geometric factors on maximum value of transversal residual stress was also investigated.

• 26.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Load bearing Composite Beam in a Bus Structure2012Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 27. Aygül, M.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures. KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Structural Engineering and Bridges.
Investigation of distortion-induced fatigue cracked welded details using 3D crack propagation analysis2014In: International Journal of Fatigue, ISSN 0142-1123, E-ISSN 1879-3452, Vol. 64, p. 54-66Article in journal (Refereed)

The behaviour of distortion-induced fatigue cracks in welded details in an existing bridge was studied analytically by performing crack propagation analysis based on linear elastic fracture mechanics. The real load history of the bridge was obtained from strain measurements. These loads were utilised to examine the crack growth rate and the residual service life of the cracked detail. Moreover, the effectiveness, accuracy and applicability of the crack propagation analysis on bridge structures were investigated by simulating a complex case of fatigue cracking using several crack propagation analyses. The results of the analyses revealed that the fatigue crack in the studied details had significantly different crack growth characteristics in different directions. In the thickness direction, for instance, the crack was seen to propagate at a certain rate, which increased with the propagated crack from the beginning and, as expected, the crack propagation rate decreased when the crack grew longer. The crack was subsequently arrested half way through the thickness of the plate. In the longitudinal direction, the crack was not, however, arrested in the same way as in the thickness direction and it continued to propagate at a reduced yet constant crack growth rate. The results also revealed that, even though distortion-induced fatigue cracking was usually caused by a mixed-mode condition (i.e. a combination of modes I, II and III), the governing propagation mode is still mode I. Furthermore, it was also observed that the contribution of modes II and III to crack propagation was very little and dependent on the location of the propagated crack front, as well as the geometrical configuration of the cross-beam.

• 28.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
High performance nanocomposite polymer electrolytes2006In: Composite interfaces (Print), ISSN 0927-6440, E-ISSN 1568-5543, Vol. 13, no 4-6, p. 545-559Article in journal (Refereed)

Solid lithium-conducting nanocomposite polymer electrolytes based on poly(oxyethylene) (POE) were prepared using high aspect ratio cellulosic whiskers and lithium imide salt, LiTFSI. The cellulosic whiskers were extracted from tunicate - a sea animal - and consisted of slender parallelepiped rods that have an average length around 1 μm and a width close to 15 nm. High performance nanocomposite electrolytes were obtained. The filler provided a high reinforcing effect, despite the favorable cellulose/POE interactions that were expected to decrease the possibility of interwhisker connection and formation of a percolating cellulosic network, while a high level of ionic conductivity was retained with respect to unfilled polymer electrolytes. Cross-linking and plasticizing of the matrix as well as preparation of the composites from an organic medium were also investigated.

• 29.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures. Université Joseph Fourier, France.
Review of recent research into cellulosic whiskers, their properties and their application in nanocomposite field2005In: Biomacromolecules, ISSN 1525-7797, E-ISSN 1526-4602, Vol. 6, no 2, p. 612-626Article in journal (Refereed)

There are numerous examples where animals or plants synthesize extracellular high-performance skeletal biocomposites consisting of a matrix reinforced by fibrous biopolymers. Cellulose, the world's most abundant natural, renewable, biodegradable polymer, is a classical example of these reinforcing elements, which occur as whiskerlike microfibrils that are biosynthesized and deposited in a continuous fashion. In many cases, this mode of biogenesis leads to crystalline microfibrils that are almost defect-free, with the consequence of axial physical properties approaching those of perfect crystals. This quite "primitive" polymer can be used to create high performance nanocomposites presenting outstanding properties. This reinforcing capability results from the intrinsic chemical nature of cellulose and from its hierarchical structure. Aqueous suspensions of cellulose crystallites can be prepared by acid hydrolysis of cellulose. The object of this treatment is to dissolve away regions of low lateral order so that the water-insoluble, highly crystalline residue may be converted into a stable suspension by subsequent vigorous mechanical shearing action. During the past decade, many works have been devoted to mimic biocomposites by blending cellulose whiskers from different sources with polymer matrixes.

• 30.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Optimeringsmetoder för ASMC-strukturer2015Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

Thin metal sheets have for long been the dominant structural components in automotive bodies, but as environmental concerns mount new materials are needed to reduce mass. Advanced Sheet Moulding Compounds (ASMC) is a carbon fibre composite with short fibres and has been put forward as an alternative. It is both light and has good durability and can be formed in a mould similarly to steel sheets. A distinct advantage is that unlike for steel sheets the thickness in an ASMC component can be varied and stiffeners integrated. This creates great opportunities for optimisation, but as know-how in the industry is scarce a methodology is necessary. This master’s thesis describes a method developed for optimising structural components manufactured in ASMC by analysing a backplate mounted in a Body-In-White (BIW). The optimisation design process was first developed in a simplified model made to mimic a BIW without all the complexities therein. In this thesis free-size optimisation was done individually and coupled with adding uni-directional (UD) fibres and ribs to the backplate. This process was then verified in an accurate car body model and the process translated rather well to a more realistic model as favourable results were obtained. Optimisation resulted in more than 50% decrease in the component’s mass and body torsional stiffness could be increased by up to 7%. A step-by-step guide for this process is presented. Moving forward the design methodology needs to be verified and developed further for different structures and load cases. It is believed that the process detailed works well for many different structures as is, but improvements can be made and are ultimately necessary.

• 31.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Automation of inserts-checking on an Aluminiumsandwich structure2013Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

In space projects, checking inserts can be tedious, even more so for high density of inserts. This paper deals with the development of an automation tool for insert checking. All the principles used to perform inserts calculations are based on the ECSS-Design Handbook [1]. Those principles are summarised and adapted to the tool. The tool requires only a point cloud extracted from a CADmodel giving the position of inserts to be checked and the loads calculated thanks to an FEM-model at those same points to calculate safety margins. This paper details the process followed by the tool to calculate inserts strength and describes possible measures for improvements.

• 32.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Fatigue Life Assessment of Cut Edges in High Strength Steel2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

The interests in more effective and lighter structures have increased the use of high strength steels for higher performances. Plate materials are optimized so thinner structures and higher material strengths are reached, this leads to the cut quality might be a new issue.

In this investigation steel thickness of 6 and 16 mm with minimum yield strength from 355 to 960 MPa are fatigue tested with constant amplitude tensile loading. The specimens were cut using waterjet and also with thermally cut methods such as plasma and oxygen. Before fatigue testing the cut surfaces were measured and roughness Rz values were obtained.

Empirical and analytical results of the surface roughness influencing the fatigue strength for different steel strengths are presented.

Since thermal cutting methods have been developed over the years the FAT values are higher for those IIW are recommending.

When the quality of the cut surface can be kept high the fatigue strength will also be higher than those recommended. This means having a cutting process that provides smooth surfaces such as waterjet and plasma cutting the fatigue life will be longer.

• 33.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Load bearing Composite Beam in a Bus Structure2012Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
• 34.
Khalifa Univ Sci & Technol, Dept Mech Engn, Petr Inst, POB 2533, Abu Dhabi, U Arab Emirates..
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures. Khalifa Univ Sci & Technol, Dept Mech Engn, Petr Inst, POB 2533, Abu Dhabi, U Arab Emirates..
Thermomechanical Evaluation of the Performance and Integrity of a HDPE Stub-End Bolted Flange Connection2019In: Journal of Pressure Vessel Technology-Transactions of the ASME, ISSN 0094-9930, E-ISSN 1528-8978, Vol. 141, no 5, article id 051206Article in journal (Refereed)

In this study, the integrity of a manhole structure made of a 78 in. high density polyethylene (HDPE) stub-end, steel ring, and blind flange, sealed with a compressed nonasbestos fiber (CNAF) gasket is investigated by means of a parametric finite element analysis (FEA). A coupled thermomechanical nonlinear FEA model is built, comprising of a heat transfer and a structural model, which allows modeling the complex thermal and mechanical loads and their interactions present during the operation of the manhole. The temperature-dependent elastic-plastic HDPE material constitutive behavior and the temperature-dependent nonlinear response of the CNAF gasket are accounted for in the model. Factors influencing the performance and integrity of the manhole such as stud-bolt pretorque level (T-b), internal pressure (P-i), and outer temperature (T-o) are considered. Based on the results, the integrity and performance of the structure are assessed in view of a leakage through the gasket criterion and a yielding of the HDPE stub-end criterion. The FEA results reveal that both T-b, P-i, and T-o significantly influence the performance (i.e., leakage) of the gasket and the integrity (i.e., yielding) of the HDPE stubend. At 40 degrees C, it is possible to find a safe operational window for a range of T-b and P-i values, where no leakage through the gasket or yielding of the stub-end occurs. However, as the temperature is increased this safe operational window decreases considerably, and at 80 degrees C safe operation cannot be guaranteed where leakage, yielding, or both simultaneously, will lead to loss in performance and integrity of the manhole structure.

• 35. Barsoum, I.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Analysis of the torsional strength of hardened splined shafts2014In: Materials and Design, ISSN 0261-3069, Vol. 54, p. 130-136Article in journal (Refereed)

The current study presents a finite element modeling framework to determine the torsion strength of hardened splined shafts by taking into account the detailed geometry of the involute spline and the material gradation due to the hardness profile. The aim is to select a spline geometry and hardness depth that optimizes the static torsion strength. Six different spline geometries and seven different hardness profiles including non-hardened and through-hardened shafts have been considered. The results reveal that the torque causing yielding of induction hardened splined shafts is strongly dependent on the hardness depth and the geometry of the spline teeth. The results from the model agree well with experimental results found in the literature and reveal that an optimum hardness depth maximizing the torsional strength can be achieved if shafts are hardened to half their radius.

• 36.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures. Petr Inst, U Arab Emirates.
A procedure to determine the tangential true stress-strain behavior of pipes2015In: International Journal of Pressure Vessels and Piping, ISSN 0308-0161, E-ISSN 1879-3541, Vol. 128, p. 59-68Article in journal (Refereed)

Determining the tangential mechanical properties of a tube is essential for simulation of various manufacturing processes that involve the use of a tubular geometry. The aim of this study is to develop a procedure to determine the tangential true stress-strain behavior of pipes. For this purpose a modified ring test setup is proposed consisting of a ring specimen loaded with two separate D-blocks. Using a finite element model, an optimized ring specimen geometry is obtained. The optimized ring specimen exhibits uniform tangential distribution in the gauge region of the specimen and necking occurs consistently at the center of the gauge length. It is found that friction has a substantial effect on the mechanical response of the ring test for which two different setups to reduce friction are proposed. One using lubricated D-blocks (DB) and one using lubricated D-blocks with needle roller bearing (RB). Assisted by the FE model, the friction during the experiment is account for and a data analysis procedure to determine the tangential stress-strain curve of the pipe is proposed. It is found that the results using this procedure show very good agreement with previously published results.

• 37.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Avancerade metoder för noggrannare dimensionering av svetsade konstruktioner2009In: Svetsen, ISSN 0039-7091, Vol. 68, no 3Article in journal (Other (popular science, discussion, etc.))
• 38.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Fatigue Assessment of Cruciform Joints Welded with Different Methods2005In: IIW Doc. No. XIII-2074-05, 2005Conference paper (Other academic)
• 39.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Fatigue design of welded structures: effect of weld quality and residual stresses, XIII-2312-102010Conference paper (Other academic)
• 40.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Fatigue Strength of cruciform joints fabricated with different welding processes2007In: International Symposium on Integrated Design and Manufacturing of Welded Structures, Eskilstuna, 2007Conference paper (Other academic)
• 41.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
HENRY GRANJON PRIZE COMPETITION 2010 Winner Category C: "Design and Structural Integrity" FATIGUE DESIGN OF WELDED STRUCTURES - SOME ASPECTS OF WELD QUALITY AND RESIDUAL STRESSES2011In: Welding in the World, ISSN 0043-2288, E-ISSN 1878-6669, Vol. 55, no 11-12, p. 2-11Article in journal (Refereed)

The research work reported in this paper aims to increase the accuracy of fatigue life prediction of welded steel structures using local analysis methods by i) establishing a link between weld quality and fatigue life ii) developing simplified engineering methods using finite element routines for prediction of welding residual stresses iii) incorporating the residual stresses into the fatigue life predictions. Acceptance criteria were developed for the weld quality by comprehensive FE-and fracture mechanical analysis and fatigue testing. The results are the foundation for the new weld class system within the Volvo group company. Simplified FE welding simulation routines and procedures for incorporating the predicted residual stresses into crack growth analysis were developed showing good agreement with residual stress measurements and fatigue testing.

• 42.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Local weld geometry and the influence on fatigue strength2010In: Proceedings of the Swedish Conference on Lightweight Optimised Welded Structures: Borlänge, March 24-25, 2009 / [ed] Zubeir Barsoum, Jack Samuelsson, Borlänge, 2010, p. 26-38Conference paper (Other academic)
• 43.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Numerical Analysis and Measurement of Residual Stresses in Multi Pass Welding - Influence on Fatigue Root Crack Propagation2006In: TRENDS IN WELDING RESEARCH, PROCEEDINGS / [ed] David SA; DebRoy T; Lippold JC; Smartt HB; Vitek JM, MATERIALS PARK: ASM INTERNATIONAL , 2006, p. 589-594Conference paper (Refereed)

The purpose of this study is to investigate the residual stresses near the weld root and the weld toe for multi-pass welded tube-to-plates, and the influence of residual stresses on multiaxial fatigue of tubular joints. Two different tubular joint configurations were studied; a three-pass single-U weld groove for maximum weld penetration and a two-pass fillet (no groove) welded tube-to-plates for minimum weld penetration. An axi-symmetric finite element model was developed to calculate the temperature distribution, HAZ, penetration depth and the residual stress distribution for the sequentially coupled thermo-mechanical analysis. The calculated geometry and the temperature distribution of the fusion zone showed good agreement with the micro samples of the welds. The calculated residual stresses was compared with experimental results and showed qualitatively good agreement. The "design root crack" is under compressive stresses in both configuration, -230 MPa for the single-U weld groove and -120 MPa for the fillet weld, respectively. Also the weld toe, transition between weld and tube, is under compressive stresses. Multi-axial fatigue tests were performed in order to study weld root crack propagation. The tube structures were loaded with a static internal pressure in order to separate the design root crack and initiate the crack growth. The fatigue tests show that, depending on the size of the static imposed internal pressure, different crack paths are received.

• 44.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Ny doktorsavhandling: Restspännings- och utmattningsanalyser av svetsade stålkonstruktioner2008In: Svetsen, ISSN 0039-7091, Vol. 67, no 3Article in journal (Other (popular science, discussion, etc.))
• 45.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Prediction of Welding Residual Stresses2007In: International Symposium on Integrated Design and Manufacturing of Welded Structures, Eskilstuna, 2007Conference paper (Other academic)
• 46.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Prediction of welding residual stresses by simplified approaches2010In: Proceedings of the Swedish Conference onLightweight Optimised Welded Structures: Borlänge, March 24-25, 2009 / [ed] Zubeir Barsoum, Jack Samuelsson, Stockholm: KTH Royal Institute of Technology, 2010, p. 39-50Conference paper (Other academic)
• 47.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Residual Stress Analysis and Fatigue Assessment of Welded Steel Structures2008Doctoral thesis, comprehensive summary (Other scientific)

This doctoral thesis is concerned with fatigue life of welded structures. Several topics related to fatigue of welded structures are treated such as; weld defects and their influence on fatigue performance of welded structures, fatigue life prediction using LEFM (Linear Elastic Fracture Mechanics), fatigue testing, welding simulation, residual stress prediction and measurement and their influence on fatigue life.

The work that is reported in this doctoral thesis is part results of the Nordic R&D project QFAB (Quality and Cost of Fabricated Advanced Welded Structures) and the Swedish R&D project LOST (Light Optimized Welded Structures). One of the main objectives is to compare different welding processes for the fatigue performance, weld quality and gain understanding of the weld defects, their appearance in different welding processes and their effect on fatigue life. Another main objective is to study welding residual stresses and their effect on fatigue. The design rules are in some cases conservative and especially on the weld root sides the knowledge about the residual stress field may improve the life prediction. The aim is to develop simplified procedures for analysis of residual stresses, their relaxation and influence on fatigue life.

Fatigue testing of Hybrid Nd: YAG laser/MAG and MAG welded (tandem arc solid wire, flux cored wire, tandem flux cored wire) non-load carrying cruciform joints was carried out. Four batches were produced, tested and the results were compared. The local weld geometry of the cruciform welded joints was measured and analyzed. Residual stress measurement was carried out close to the toe region using X-ray diffraction. Weld defects, in most cases cold laps, in the cracked specimens were measured.

Further fatigue testing, weld defect assessment and residual stress and local weld geometry measurements were carried out on joints welded with flux cored and metal cored arc wires. Two-and three dimensional LEFM crack growth analysis were carried out in order to predict the influence of weld defects, local weld geometry and residual stresses.

Residual stresses in multi-pass welded tube-to-plates were studied for two different tubular joint configurations; a three-pass single-U weld groove for maximum weld penetration and a two-pass fillet (no groove) welded tube-to-plates for minimum weld penetration. Torsion fatigue tests were performed in order to study crack propagation from the weld root. Mode III propagation from the lower and upper weld toe on the same tubular joints was also studied. Some tubes were stress relieved (PWHT) and some were fatigue tested with internal static pressure.

A three dimensional finite element welding simulation of the multi-pass welded tubular joint was carried out. The calculated temperatures in the transient thermal analysis were compared with measured temperatures. The FE predicted residual stresses in the as-welded conditions were verified with hole drilling strain gage measurements. The residual stresses were used as internal stresses in the finite element model for the torsion fatigue simulation in order to study the cycle by cycle relaxation of the residual stresses in constant amplitude torsion loading.

A two dimensional finite element welding simulation procedure was developed in order to predict welding residual stress. The predicted residual stresses were used together with a developed 2D LEFM subroutine to predict the fatigue life, crack path and the effect of residual stresses on weld root defects. The developed simulation subroutines were validated with results found in the literature.

Residual stresses measurement, two-and three dimensional welding simulations were carried out in fillet welded joints in order to study the three dimensional effects of the welding process, boundary conditions and modelling technique on the formation of residual stresses.

• 48.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Residual stress predictin and relaxation in welded tubular joints under constant cyclic loading2006In: Materials Science Forum, ISSN 0255-5476, E-ISSN 1662-9752, Vol. 524-525, p. 323-330Article in journal (Refereed)

In this paper three-dimensional welding simulations were carried out in FE software ANSYS in order to predict transient temperatures and the residual stresses in a three pass welded tubular joints. The thermal analysis and the moving heat source were verified with temperature measurements and the computed residual stresses were verified with hole drilling measurements. Then residual stress relaxation analyses were carried out on the tubular structure, with similar load cases as in earlier fatigue testing on the same tubular joint structures.

• 49.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
Residual stress effects on fatigue life of welded structures using LEFM2008Conference paper (Refereed)
• 50.
KTH, School of Engineering Sciences (SCI), Aeronautical and Vehicle Engineering, Lightweight Structures.
KTH, School of Engineering Sciences (SCI), Solid Mechanics (Dept.).
Residual stress effects on fatigue life of welded structures using LEFM2009In: IIW International Institute of Welding: 62nd AnnualAssembly, 2009Conference paper (Other academic)
1234567 1 - 50 of 507
CiteExportLink to result list
Cite
Citation style
• apa
• ieee
• modern-language-association-8th-edition
• vancouver
• Other style
More styles
Language
• de-DE
• en-GB
• en-US
• fi-FI
• nn-NO
• nn-NB
• sv-SE
• Other locale
More languages
Output format
• html
• text
• asciidoc
• rtf


text:
Thread: dy/dx y=e^(3x)*sin(pi*x)

1. dy/dx y=e^(3x)*sin(pi*x)

How can I figure this out? I feel dumb.

Derivitive of
y= e to the power 3x, times the sin of (pi times x)
y=e^(3x)*sin(pi*x)

2. Originally Posted by Terrible Idiot
How can I figure this out? I feel dumb.

Derivitive of
y= e to the power 3x, times the sin of (pi times x)
y=e^(3x)*sin(pi*x)
You do it by the product rule.

To refresh your memory, the product rule says, if you have two functions a,b multiplied by each other, then their derivative is given by:

d/dx(ab) = a'b + b'a

In other words, it is the derivative of the first function times the second plus the derivative of the second function times the first. (of course the order doesn't matter, you can take the derivative of the second function first and so on...). Note, you also need the chain rule for this, since you have e^(3x) instead of e^x and sin(pi*x) instead of sin(x)

y = y=e^(3x)*sin(pi*x)
=> y' = 3e^(3x)*sin(pi*x) + pi*e^(3x)cos(pi*x)
= e^(3x)*(3sin(pix) + pi*cos(pix))

P.S. Don't call yourself a Terrible Idiot, nothing comes easy the first time around

3. Thanks Jhevon.