Solution of dynamic frictional contact problems using nondifferentiable optimization

This article is devoted to the development, implementation and application of variational inequalities (VI) to treat the general elastodynamic contact problem. Unlike existing VI algorithms, which rely on the decomposition of the physical problem into two sub-problems, the current study treats the general VI expressions using one-step approach to identify the candidate contact surface and contact stresses. This is accomplished using nondifferentiable optimization algorithm, through a sequence of mathematical programming problems. The dynamic VI formulations are solved using generalized-α time integration scheme. The selected time integration parameters reduce significantly the spurious high-frequency modes, which persist in the traditional Newmark method. In order to demonstrate the versatility and accuracy of the proposed VI and nondifferentiable optimization algorithm, a number of numerical examples are examined. The results show a significant improvement compared with the existing solution techniques.