金属刚粘塑性变形的能量泛函与动力显式算法有限元分析

ENERGY FUNCTIONAL AND RIGID VISCOPLASTIC DYNAMIC EXPLICIT FEA OF METAL FORMING PROCESS

设计出刚粘塑性动态变形场的能量泛函，采用罚函数法和Ｌａｇｒａｎｇｉａｎ乘子法取消对运动容许速度场满足体积不可压缩的约束条件，运用虚功原理和广义变分原理，推导出刚粘塑性变形的动力分析显式算法有限元方程，以及速率形式的中心差分求解的时间积分显式，给出了两个金属变形的算例．

This paper studies the technique of rigid viscoplastic dynamic explicit finite element analysis (FEA). Two new energy functionals of rigid viscoplastic dynamic deformation are proposed, and the relevant variation equations and formulations of FEA are devised using the virtual work principle and generalized variation approach. The penalty method is introduced to remove the restraint of incompressibility. The central difference method of the rate type explicit formulations is given. A code of 3 D rigid viscoplastic dynamic explicit FEA is developed. Two metal forming examples are given using different methods: rigid viscoplastic dynamic explicit, elastic plastic dynamic explicit, and rigid viscoplastic implicit FEA. The results by the code are in good agreement with those of the other methods.