刚塑性成形模拟中有限元和无网格迦辽金法的自动耦合算法

ALGORITHMS AUTOMATICALLY COUPLED ELEMENT FREE GALERKIN INTO RIGID PLASITIC FINITE ELEMENT

利用有限元法分析金属的刚塑性问题时,在变形的高梯度区域单元容易严重畸变,这极大地降低了分析精度。在刚塑性有限元方法的框架中,文中根据计算增量步的网格质量,提出金属刚塑性有限元和无网格迦辽金法的自动耦合算法,在单元严重畸变的区域转换为无网格迦辽金法进行计算。数值实例表明:算法在很大程度上既保持了有限元法的计算效率,又能够发挥无网格迦辽金法分析金属刚塑性问题的计算精度,而且能够抑制金属刚塑性有限元法在变形的高梯度区域容易产生网格畸变、无网格迦辽金法计算效率低的缺点。

The analysis for rigid plastic forming problems with finite element method can lose considerable accuracy due to severely distortional meshes.Based on the analysis frame of rigid plastic finite element methods,automatically coupling algorithms for rigid plastic problems have been proposed,which converts the FE（finite element） analysis into the EFG（element free Galerkin） computation to preserve the accuracy in the region where meshes have been severely distorted.Numerical example shows that the present algorithms exploit the respective advantages of both the FE method whose computational efficiency is high and the EFG method which can throws out mesh distortions and be suitable for rigid plastic forming analysis.