A scaled boundary finite element based node-to-node scheme for 2D frictional contact problems

This paper proposes a new node-to-node (NTN) scheme for modeling two-dimensional contact problems within a scaled boundary finite element method (SBFEM) framework. The analysis is formulated and solved directly as a mathematical programming problem known as a mixed complementarity problem (MCP). Polygon elements with arbitrary number of edges and nodes are constructed in the SBFEM modeling. Only the edges of these polygon elements are discretized thereby accommodating highly non-uniform discretization. Non-matching meshes are easily converted into matching meshes by appropriate node insertions, thereby allowing the use of the advantageous node-to-node contact scheme. Contact constraints of non-penetration and friction are described directly in a complementarity format that enables, for instance, the satisfaction of non-penetration without having to resort to user-specified control parameters. Numerical examples using 1st and 2nd order scaled boundary elements are presented to highlight the quality of the elements used through satisfaction of various patch tests, and the accuracy and robustness of the overall approach.