A Domain Decomposition Method For Dynamic Elasto-plastic Torsion Problem

The dynamic elasto-plastic torsion problem is applied widely in physics, mechanics and engine. In this paper, it constructs domain decomposition method (DDM) for the evolutionary variational inequality described by dynamic elasto-plastic torsion problem. This thesis is composed of the following three sections:In the chapter two, it considers DDM for the elliptic problem of Helmholtz equation and constructs the algorithm for Helmholtz equation. Two numerical examples are implemented, it shows the efficiency of the method.In the chapter three, DDM for the parabolic equation is discussed. First, backward Euler time scheme is used to transform the original parabolic equation into an elliptic equation; then we solve two numerical examples by DDM. Comparing the results of FEM and DDM, it shows that DDM is efficiency for parabolic equation.In the chapter four, it presents the overlapping DDM and convergence for the dynamic elasto-plastic torsion problem. For the parabolic variational inequality described by dynamic elasto-plastic torsion problem, first, backward Euler time scheme is used to transform the original parabolic variational inequality into an elliptic variational inequality; then we solve it by overlapping DDM and yields the algorithm. Finally, two numerical examples prove the efficiency of the method.