Meshless projection iterative analysis of Signorini problems using a boundary element-free method

This paper presents a meshless method based on coupling a boundary element-free method (BEFM) with a new projection iterative scheme for Signorini problems. Using the new iterative scheme, the nonlinear complementary Signorini boundary conditions are transformed into Neumann boundary conditions. Then, mixed elliptic problems are formed and are solved by the BEFM. In this method, only a nodal data structure on the boundary is required, and the coefficient matrices of the discrete system equations only have to be computed once in the whole iterative process. Convergence of the iterative scheme is discussed theoretically. Numerical examples involving beach percolation and an electropaint process are given to illustrate the convergence rate and high computational efficiency of the method.