Lemke’s algorithm with parameter change of external forces for finding switching points in dynamical contact problems
The article represents the algorithm for analysis of multi-degree-offreedom systems with unilateral constraints subjected to dynamical loads. The unilateral contact leads to a non-linear problem because of structural alteration (open and close contact). However, system is considered linear within a single structural model. Dynamic response of structures with unilateral supports can be evaluated using
time discretization. Displacement, velocity and acceleration are computed for each mass using Newmark’s method. Current structural model and switching points, i.e. time instants at which contact closes or opens, is determined by Lemke’s algorithm with parameter change of external forces p . Structural model changes if 0 < p <1. The algorithm was implemented and tested in MathCAD for beams. But it can be applied to other structures if contact stiffness matrix is calculated using any of the known methods.