求解摩擦接触问题的一个非内点光滑化算法  

Non-Interior Smoothing Algorithm for Frictional Contact Problems

作　　者：张洪武[1] 何素艳[1] 李兴斯[1] 

机构地区：[1]大连理工大学工业装备结构分析国家重点实验室,大连116024

出　　处：《应用数学和力学》2004年第1期42-52,共11页Applied Mathematics and Mechanics

基　　金：国家基础性研究专项基金(G1999032805)

摘　　要：给出了一个求解三维弹性有摩擦接触问题的新算法,即基于NCP函数的非内点光滑化算法。首先通过参变量变分原理和参数二次规划法,将三维弹性有摩擦接触问题的分析归结为线性互补问题的求解;然后利用NCP函数,将互补问题的求解转换为非光滑方程组的求解;再用凝聚函数对其进行光滑化,最后用NEWTON法解所得到的光滑非线性方程组。方法具有易于理解及实现方便等特点。通过线性互补问题的数值算例及接触问题实例证实了该算法的可靠性与有效性。A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming methods wwe applied to the analysis of three-dimensional factional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.

关 键 词：三维摩擦接触 参数二次规划法 线性互补问题 NCP函数 凝聚函数 非内点光滑化算法 

分 类 号：O221[理学—运筹学与控制论] O242.21[理学—数学]