A Meshless Projection Iterative Algorithm For Signorini Problems

Many physical phenomena such as beach percolation, electropainting, free boundary problems and seepage problems can be modeled as Signorini problems. In Signorini problems, Dirichlet and Neumann boundary conditions alternate on a known or unknown portion of the boundary in conjunction with certain nonlinear complementary Signorini conditions. Besides, the solution of Signorini problems is further complicated by the fact that the number and the position of the points where the change from one type of boundary condition to the other occurs are unknown.This first chapter reviews the recent developments of Signorini problems and the meshfree method. Then, we introduce the construction process for the meshfree shape functions in the Section two. The third chapter is the core part of this paper; in this Section we describe a new explicit projection iterative algorithm with the improved interpolating boundary element-free method for Signorini problems using boundary integral equations(BIEs). At last, some numerical examples are also given to further illustrate the efficiency and reliability of the algorithm.In this dissertation, a meshless projection iterative algorithm is proposed for Signorini problems. Firstly, a new explicit projection iterative scheme is developed based on the fixed point equation. Then, the original Signorini problem is transformed into a sequence of mixed elliptic boundary value problems and finally solved using the improved interpolating boundary element-free method at each iterative step.