Analysis of dynamic frictional contact problems using variational inequalities

This investigation is concerned with the development, implementation and ap plication of variational inequalities (VI) to treat the general elastodynam ic contact problem. Two VI algorithms are used to treat the general frictio nal contact formulation and to identify the candidate contact surface and c ontact stresses. The first algorithm, which decomposes the proposed into tw o sub-problems, is based upon the iterative use of mathematical programming and Lagrange multipliers. The second algorithm treats the VI formulation i n a single step, using nondifferentiable optimization algorithm. In order to ensure that the dynamic contact problem is modeled accurately, a generalized-cx method is adopted for time marching. The selected time int egration parameters significantly reduce the spurious high-frequency modes, which are present in the traditional Newmark method in impact and dynamic frictional problems. In order to demonstrate the versatility and accuracy o f the proposed FE algorithms, a number of numerical examples are examined. (C) 2001 Elsevier Science B.V. All rights reserved.