任意边界形状的二维刚塑性成形过程的无网格分析方法

Rigid-plastic meshless method for two-dimensional metal forming problems with arbitrarily shaped dies

将无网格伽辽金方法引入到塑性成形过程模拟,结合刚塑性材料假设,提出了基于刚塑性理论的无网格伽辽金方法,推导了其刚度矩阵方程和求解列式,给出了模具形状任意的二维塑性成形问题摩擦力边界条件的施加方法以及无网格方法应用于任意边界形状的塑性成形问题时的坐标转换关系,建立了无网格方法模拟任意边界形状的塑性成形问题的步骤,并编写了相应的计算程序。应用建立的方法对典型塑性成形过程进行了无网格方法分析,通过与刚塑性有限元方法分析结果的比较,验证了本文所建立方法的可行性。

The meshless method is introduced into the analysis of the metal forming processes. Under the hypothesis of the rigid-plastic material, the rigid-plastic meshless method is developed and the stiffness matrix equation is established. The imposing method of the arbitrarily shaped frictional boundary condition is solved and the transformation matrix between the global coordinate system and the local coordi- nate system is given. The procedure for analyzing metal forming problems is given, the program for the rigid-plastic meshless method is written. A typical forging process is simulated. The results are compared with those of finite element analysis. The effectiveness and accuracy of the rigid-plastic meshless method developed in this paper is demonstrated.