带摩擦的弹性接触问题广义变分不等原理的简化证明

On the Generalized Inequalities in Elastic Contact Problem by the Use Simple Method

在弹性摩擦接触问题中 ,从变分原理出发来研究接触问题 ,可以将摩擦力纳入问题的能量泛函 .为了得到摩擦约束弹性接触问题的能量泛函 ,日前大多是用拉格朗日乘子法 ,但拉格朗日方法用在变分不等问题中 ,要利用非线性泛函分析和凸分析来证明 ,证明复杂 .本文利用向量分析的工具及巧妙的变换 ,对带摩擦约束的弹性接触问题的广义变分不等原理进行了严格的证明 ,由于只用到向量分析 ,简化了证明 .

In the case of elastic contact problem with friction, because the friction law on the contact boundary are expressed by inequalities, the variational formulation of the constraints leads to variational inequalities, instead of variational equalities. In general, the energy functional of variational inequalities problem is obtained by use of Lagrange multipliers method. But the Lagrange multipliers method must be proved by nonlinear functional analysis and convex analysis and the process is complicated. In this paper, the proving of the generalized variational functional of elastic contact problem is simplified by use of the vector analysis method.