The Virtual Element Method for the Dam Foundation With Joint

Abstract

The contact is a typical non-linear problem that exists in various projects. For traditional three-node triangular mesh and four-node quadrilateral mesh, the accuracy and convergence of the calculation results are affected by the quality of the mesh. The test space and trial space in the virtual element method (VEM) do not need to be accurately calculated, avoiding mesh dependence. In this paper, the formulation of linear elasticity and the formulation of the frictionless node-to-segment (NTS) contact model via VEM are shown. There are four numerical simulations. The sensitivity of the virtual element method to mesh distortion is studied in the first numerical simulation. The exactness and convergence of the algorithm are investigated by the second numerical example. The second numerical example simultaneously explores the penalty factor’s effect on the results. The third example investigated the impact of mesh shape and number of Voronoi mesh elements on the results by comparing normal contact stresses. The fourth numerical example studies the application of the method to engineering. Those numerical examples show that the virtual element method is insensitive to mesh distortion and could solve the joint contact in engineering.