刚塑性无网格方法中体积闭锁问题的缓解算法

RELEASING ALGORITHM FOR VOLUME LOCKING IN RIGID-PLASTIC MESHLESS METHOD

将无网格伽辽金方法引入金属塑性成形过程分析,在给出基于刚塑性理论的无网格伽辽金方法及其基本理论方程的基础上,重点研究应用无网格方法分析金属塑性成形问题时所面临体积闭锁问题的缓解算法,采用体积应变率映射方法,对能量速率泛函中的体积应变率进行修正处理,通过将速度场计算的体积应变率映射到低维空间,降低独立约束方程数目,从而建立体积闭锁现象的缓解算法。应用所建立的方法对典型锻造过程进行了无网格分析,结果表明,该算法能够有效解决体积闭锁问题。

The meshless Galerkin method is introduced to the analysis of the metal forming processes. The fundamental theories and basic equations for the rigid-plastic meshless method are developed. The releasing of the volume locking encountered in the analysis of the metal plastic forming problems is studied and a releasing algorithm is established by modifying the volumetric strain rate in the functional equation. The volumetric strain rate calculated according to velocity field is mapped onto a lower-order space to reduce the number of independent discrete constraint equations. The algorithm can release the volumetric locking without the expense of employing large support size in the rigid-plastic meshless method. A typical metal forming problem is analyzed. The results show that the algorithm can effectively release the volumetric locking problem.