可计算厚度方向应力的壳单元

在板料成形数值模拟中通常使用壳单元,然而,传统的壳单元在计算“回弹”(弹性恢复)变形时精度很差,其原因之一是由于这些壳单元忽略了厚度方向的应力而代之为平面应力条件。为了改善这个缺陷,本文提出的壳单元,通过构造厚度方向的二次形函数引入厚度方向的变形,使得三维本构关系可以不经任何改变被直接使用,并且壳上、下表面的载荷对厚度方向应力的影响也能较好地表现出来。通过几个数值算例证明该壳单元对弹塑性大变形问题分析是有效的。

A shell element accounting for through thickness stress

The conventional shell elements yield poor accuracy in some problems analysis because their stress in thickness direction is neglected.The element proposed in this paper introduces the through thickness deformation by constructing the quadratic shape function in thickness direction.3D constitutive relation can be employed directly without any change and the load can be applied on bottom and top surface of the shell element simultaneously.Several numerical examples show the shell element effective for large elasto-plastic deformation problems.