The element-free Galerkin method for the variational-hemivariational inequality of the dynamic Signorini-Tresca contact problems with friction in elastic materials

The element-free Galerkin method is presented for the variational-hemivariational inequality of the dynamic Signorini-Tresca contact problems with friction in elastic materials. The Dirichlet boundary conditions and the constrained conditions are imposed by the penalty method. The error estimates of the element-free Galerkin method indicate that the convergence order depends on the spatial step, the time step, the largest degree of basis functions in the moving least-squares approximation and the penalty factor. Numerical examples verify our theoretical results. (C) 2022 Elsevier B.V. All rights reserved.

Automated summary

The element-free Galerkin method is proposed for the variational-hemivariational inequality of the dynamic Signorini-Tresca contact problems with friction in elastic materials. The Dirichlet boundary conditions and the constrained conditions are imposed by the penalty method. The error estimates of the element-free Galerkin method indicate that the convergence order depends on various factors, including the spatial step, the time step, the largest degree of basis functions in the moving least-squares approximation, and the penalty factor. Numerical examples confirm the validity of our theoretical results.