第二类混合变分不等式的MRM-边界元分析  

MRM-Boundary Element Analysis for the Mixed Variational Inequality with Second Kind

作　　者：武震东[1] 丁睿[1] 

机构地区：[1]苏州大学数学科学学院,苏州215006

出　　处：《应用数学学报》2007年第4期719-728,共10页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10201026;1067211号);苏州大学优秀青年骨干教师基金(R2317131号)资助项目.

摘　　要：本文以弹性力学中的摩擦问题为背景,采用多重互易方法(MRM方法),边界元方法,将摩擦问题中的第二类混合变分不等式化解为MRM-边界混合变分不等式,给出了MRM-边界混合变分不等式解的存在唯—性,通过引入变换将原MRM-边界混合变分不等式化解为标准的凸极值问题,采用正则化方法处理后,给出了MRM-边界混合变分不等式的迭代分解方法。文末给出了数值算例。Using the friction problem in elasticity as the background, the mixed variational inequality of the second kind in friction problem is reduced to an MRM-boundary mixed variational inequality by the multiple reciprocity method （MRM）. The existence and uniqueness for the solution of the MRM-boundary mixed variational inequality are obtained. Introducing the transformation, the MRM-boundary mixed variational inequality is reduced to a standard convex optimization problem. Applying regularization, the iterative decomposition methods for the regularized problem are presented. Finally the numerical experiment is given.

关 键 词：MRM方法 混合边界变分不等式 摩擦问题 

分 类 号：O175.2[理学—数学]