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

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.