MATHEMATICAL MODELING FOR COMPUTER PROCESSING OF SCANS OF DEFORMABLE SOLIDS UNDER CONSTRUCTION AND ANALYSIS OF THEIR FINITE ELEMENT MODELS
PURPOSE. The modern practice of engineering calculations of part material strength uses averaged mechanical characteristics obtained through the standard tests of samples. In real conditions, it is strongly advised to avoid this averaging in order to minimize the errors when constructing the mathematical models of deformable solids using a finite element method. METHODS. In this paper, we propose a new approach based on the scanning of deformable solids using computed tomography. However, a series problem hinders the implementation of this approach: accurate identification of the scanned deformable solid relative to a real object by geometry and mechanical properties of material require an extremely large amount of data (information). RESULTS AND THEIR DISCUSSION. This problem is solved through the use of mathematical modeling and an algorithm for processing bitmap images of deformable solid sections enabling to construct the variations of mechanical characteristics of its material and geometry. The key algorithm of the presented mathematical modeling is the use of pixel characteristics of computed tomography images. Also, the necessary component of the algorithm is the use of data obtained via full-scale testing of samples. Assuming the wide use of computed tomography for medical purposes the fragments of human femur and jaw have been chosen as the objects of the study. This choice is determined by the specificity of their geometry and explicit heterogeneity of the bone material. CONCLUSION. A finite element model of a deformable solid with a real distribution of mechanical characteristics of material and individual geometry has been developed. The stress-strain state has been analyzed on the basis of the model.