Two-dimensional Elastic-plastic Contact Problem Free Galerkin - Finite Element Coupling Method

The two-dimensional elasto-plastic contact problems using element-free Galerkin-fmite element (EFG-FE) coupling method are studied. Firstly, the mathematics model of contact problems is introduced. The linear programming method has been studied in detail. Solutions of the contact problems are given. The mixed incremental iteration formulas by a linear programming algorithm for elasto-plastic contact problems are shown. Secondly, main procedures of meshless methods are reviewed and discussed. The approximations of meshless methods and the selection of weight function are carried out. The discontinuous approximations and the approach of boundary conditions are studied. Thirdly, the element-free Galerkin (EFG) method which is based on the moving least-square interpolant is studied. In order to implement EFG method through computer program, the discrete equation from the variational principle (weak form) and the numerical implementation are described. Some numerical examples are carried out by using the EFG method. The imposition of essential boundary conditions by Lagrange multipliers is imperative. The rate of convergence when changing the data of weight function and how to select the data are shown. An EFG-FE coupling method is then presented and implemented. The validity and effectivity of the presented EFG-FE coupling method is also verified through comparing the numerical solutions with theoretical ones. Fourthly, the linear programming technique is combined with EFG-FE coupling method to solve the elasto-plastic contact problems. A cylinder in contact with a rigid plane is implemented to show how to choose some of the parameters of EFG-FE coupling method in solving the contact problems. An elasto-plastic contact of rough surfaces is also carried out. Finally, the main points of the whole paper are sum up and some experiences of the writer are given.