摩擦约束有限变形弹塑性广义变分不等原理

GENERALIZED VARIATIONAL INEQUALITY PRINCIPLE OF RATE FORM IN ELASTIO-PLASTIC CONTACTPROBLEM WITH FINITE DISPLACEMENT AND FRICTION

在弹塑性接触问题中,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以便于问题的求解,尤其是数值解。研究了带摩擦约束的有限变形弹塑性接触问题,利用拉格朗日乘子法,证明了有限变形弹塑性接触问题的广义变分不等原理,导出了率形式的能量泛函,为摩擦约束有限变形弹塑性接触问题的数值解提供了理论基础。

In the case of elastic and plastic contact problem with friction, since 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. The research on the elasto-plastic contact problem with friction and finite displacement is done. The gen-eralized variational principle of elasto-plastic contact problem with friction and finite displacement is derived by use of La-grange multiplier method. The energy functional of variational inequalities problem is obtained by use of Lagrange multiplier method. It provides a numerical base for these kinds of problems.