工程接触问题的罚优化方法与罚因子的选取

A Penalty Optimized Method of Contact Problem in Engineering and Selection of penalty Factor

工程中接触问题普遍存在；经典的数学工具解决接触问题可以得到精确解，但适用范围有限．本文采用一种数值计算法罚函数法，从优化的角度求解接触问题．通过将接触边界的互不嵌入条件引入系统总势能；弹性接触的约束变分问题转化为优化问题．并进一步推导出了罚优化法的有限元迭代控制方程，给出了求解过程，并讨论了罚困子的选取，通过算例验证了该方法的有效性．

Contact problems are common in engineering. Classical mathematics tools can get exact solution in solving contact problems but be finite to use. A numerical method, penalty function method, isutilized to solve contact problems in optimized point of view in this article. Elastic contact problems of restrictedvariation are transformed into optimized problems as the non-penetration condition of contact boundary is introduced in the total potential energy of the system. Furthemore, iterative control equations of penalty optimizedmethod are deduced and the solving process is given. At last, a example proves the validity.