接触问题有限元分析方法综述

从直接迭代法、接触约束法和数学规划法等方面综述接触问题有限元分析的基本方法 .直接迭代法是一种“试验误差”方法 ,概念清楚 ,实施方便 ,但计算工作量较大 ,而且不能保证迭代一定收敛 .接触约束法主要利用罚函数方法或Lagrange乘子法将接触问题转化为无约束问题求解 .数学规划法利用接触问题的互补条件、非穿透条件等 ,将其归结为二次规划 (线性互补 )问题求解 ,这是一种非迭代类解法 ,收敛平稳、迅速 ,计算工作量较小 .文末简单介绍接触问题研究的一些新趋势

A Summary of Finite Element Analysis for Contact Problems

Contact problems are very common in engineering. The FE methods for contact problems, i.e. the iterative method, the contact constraint method, and the mathematical programming method are discussed. The iterative method is a “trial and error" method with a clear concept and convenient implementation, but the amount of computation is large and convergence cannot be ensured. The contact constraint method can convert a contact problem to a unconstrained optimization problem by use of the penalty method of the Lagrange multiplier. The mathematical programming method solves a contact problem as a quadratic programming (linear complementarity) problem based on its complementarity condition and non-penetration condition, and the method is a non-iterative method with rapid stable convergence and little amount of computation. Finally trends of the research on contact problems are introduced briefly.