用边界元-数学规划法解弹塑性接触问题

 本文基于塑性增量理论导出一种不显含应变的矩阵增量物理关系及平面应变问题σ_z的表达式,提出解决无摩擦弹塑性接触问题的边界元-数学规划法。据此编写了用边界元法解二维问题的通用程序,并用之解算了两圆柱体的弹性和弹塑性接触问题,将数值解与现有结果进行了比较。

SOLUTION OF ELASTOPLASTIC CONTACT PROBLEM BY BOUNDARY ELEMENT METHOD AND MA- THEMATICAL PROGRAMMING TECHNIQUE

An incremental formulation of the elastoplastic stress-strain relationship is presented, in which the strain terms and the normal stress σ_z for the plane strain problem are not explicitly included. This relationship appears quite suitable for the initial stress expression in the boundary element method （BEM）. The elastoplastic contact problem without friction is investigated by BEM, and the numerical solutions are obtained by virtue of the mathematical programming technique. As numerical examples, the problems of the elastic and elastoplastic contacts of two cylinders are studied. The comparison of the BEM solution with the analytical and the finite element solutions shows that the method developed in this paper is efficient for analysis of the elastoplastic contact problem with small plastic zone.