变分不等原理的优化解法及应用

The Direct Optimization Method of Sloving Variational Inequalities Principle and its Application

将变分不等原理应用到塑性成形速度场的近似求解中,通过近似速度场,得到塑性成形过程中所需要的外力.为了避开直接求解变分不等式的困难,使用优化方法对塑性成形问题的能量泛函求极小值来得到相应的近似解.为了证明方法的有效性,计算了平面应变镦粗的成形问题,并与解析解及实验结果进行了比较.

In this paper,variational inequalities principle has been applied to approximate calculation of velocity field of plastic forming.Through the calculation of approximate velocity field of plastic forming,we can get the force of plastic forming.In order to avoid the difficulty of direct solving the variational inequalities,the optimization method has been applied to solving the energy function of the generalized variational inequalities principle.Through making a comparison between the results of the plastic forming processes of plane upsetting by the method between the theory and experiment,the method is effective.