THE BISECTION METHOD FOR FINDING SWITCHING POINTS IN DYNAMICAL CONTACT PROBLEMS
The article represents the algorithm for analysis of multi-degree-of- freedom systems with unilateral constraints subjected to dynamical loads. The unilateral contact leads to a non-linear problem. Dynamic response of structures with unilateral supports can be evaluated using time discretization. The system is considered to be linear within a single time step (or structural model). It is convenient to use direct integration methods for the problem solution. At this an accuracy of time-stepping method depends on time interval Dt. The bisection method is applied to find switching points, i.e. time instants at which a unilateral contact closes or opens.At the first step structural model is defined according to initial conditions. Then displacement, velocity and acceleration are computed for each mass using Newmark’s method and new structural model is determined by static analysis. If structural model doesn’t change go to next step. In other case (unilateral contact closes or opens) time interval is divided by two and previous step is repeated. The process is continued until the interval is sufficiently small. The algorithm was implemented in MathCAD and the results of its application are shown using the test problem.