基于刚塑性流动理论的无网格伽辽金方法

为了对金属体积成形过程进行数值模拟，给出基于刚塑性流动理论的无网格伽辽金方法。由于移动最小二乘近似的非插值特征给无网格伽辽金方法的应用带来了一定的困难，将再生核质点法中的完全变换法与无网格伽辽金方法相结合，通过对速度场的移动最小二乘近似进行修正，实现速度边界条件的精确施加；采用罚函数法引入体积不可压缩条件，运用刚塑性材料的不完全广义变分原理，给出基于刚塑性流动理论的无网格伽辽金方法的离散控制方程以及收敛判据和收敛控制方法。数值计算结果表明方法的可行性及有效性。

ELEMENT FREE GARLERKIN METHOD BASED ON FLOW THEORY OF RIGID PLASTIC

The element free Galerkin method based on the flow theory of rigid plastic mechanics is given to simulate the metal bulk forming process. The full transformation method, which proposed in the reproducing kernel particle method, is utilized to implement the velocity boundary conditions directly and exactly at nodes by modifying MLS(moving least squares) approximation to alleviate the difficulty of the implementation of velocity boundary conditions. The modified moving least square appropriation is used to construct the velocity field function. The penalty method is proposed to satisfy the volume incompressibility condition of the rigid plastic material. The discrete control equations of the element free Galerkin method is developed by utilizing the incomplete generalized variational principle of rigid plastic. The control method of convergence is given to improve the proposed method. Numerical simulation of an axisymmetric upsetting process is given to show the effectiveness and feasibility of the present method.