Numerical Methods And Application For Elasto-Plastic Contact Problems

Elasto-plastic contact problems is of great importance to engineering and one of important subject in computational solid mechanics. Surrounding the reliability, precision and efficiency of their numerical methods, the work completed in this paper is as follows:1.Analyzing and comparing the existing algorithms on contact problems,a new algorithm--mixed variable method is proposed. It reduces, to the maximum extent, basic unknown variables, and consideribly raises the computational efficiency of contact problems. It is implemented in 2-D problems and extended to 3-D problems.2.Based on analyzing the initial condition of contact problem, the correctness of contact and check conditions adopted in this paper is proved and a method of automatic loading is suggested.3. Based on analyzing the path-dependence for elasto-plastic contact problems with or without friction, the difference between contact probing and elasto-plastic iterations is cleared and the strategy rationally combining with them is proposed.4. Positive-Nagetive Sequence Modification Method (in short PNSM) and PNSM with prescribed displacements proposed by Wang Xucheng et al. are combined to condense the finite element equations. This is also a main step of raising the computational efficiency of elasto-plastic contact problems.5. The analytical integration of constitutive equations of real materials proposed by Wang Xucheng and writer is extended to plane stress and cycle elasto-plastic problems. It, combined with the total strain increment schem in stress calculation, raises the precision and efficiency to calculate stress.Using above schemes, a 2-D finite element program for elasto-plastic contact problems is developed. This program has about 6000 sentences and is able to solve moving elasto-plastic contact problems with or without friction. By using this program, Hertz problem and several practical examples are solved. These examples not only can verify the efficiency and precision of the numerical schemes but also themselves have important engineering value.In this paper 2-D elastic contact problems are also solved by Boundary Element Method. The contact algorithm combining a mixed reference frame with FEM condensing technique is suggested and Hertz problem are solved.It vertifies that BEM has the advantage over FEM in higher presion and less preparation of data for elastic contact problems.The simple method to derive fundamental solutions and the formula of the analytical integration for 2-D isoparametric element are proposed in this paper.