摩擦约束塑性力学变分不等原理的半反推法

A Semi-inverse Method of Generalized Inequalities in Plastic Contact Problem with Friction

带摩擦约束的弹塑性接触问题,由于摩擦约束条件是一种判别性的条件,它的变分问题的逆问题的研究比较困难。本文对弹塑性接触力学中的变分不等问题的逆问题进行了研究,改进了半反推法并将其应用到弹塑性变分不等原理的研究中,导出了摩擦约束弹塑性增量问题广义变分不等原理中的能量泛函,消除了用拉氏乘子法可能产生的临界变分现象。在证明中,巧妙地处理了增量表示的接触摩擦边界条件,避免了使用非线性泛函分析和凸分析,简化了证明。

In the case of the elastic and plastic contact problem with friction, since the friction law on the contact boundary was 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 was obtained by use of Lagrange multipliers method. But the lagrange multipliers method sometime leads to the variations crisis (some Lagrange multipliers vanished during the variation). In this paper, the research on the inverse problem of contact mechanics was done. The generalized variational functional of elastic and plastic contact problem with friction was derived by the use of a improving semi-inverse method and the variations crisis was eliminated completely. In improving, the difficulty of the friction boundary condition is deal with by an ingenious method and the tool of non-functional analysis is not used.