基于拟应变法的壳单元大变形分析及在冲击动力问题中的应用

Large deformation study of shell with assumed strain and its application in impact dynamic analysis

为了简便有效地解决板壳结构的大变形问题,本文针对八节点相对自由度壳单元进行研究。该单元的位移场由壳的中面节点位移和上表面节点的相对位移组成,不带有转动变量。所有的研究都是基于完全的三维位移、应力、应变场。采用拟应变法,对应变场另行假设,能够改善该单元在大变形情况下的计算精度。通过引入Wilson非协调模式,构造了大变形情况下的拟应变场表达式,给出了该单元用于解决非线性动力分析问题的有限元求解方程。通过算例表明,本文针对相对自由度壳单元提出的方法及推导的公式,能够解决冲击动力问题中的大变形问题。

A 8-nodes shell element with the relative degree of freedom has been developed for the large deformation analysis of the plate and shell structure. Without the rotation parameters, the displacement field of the shell element is represented by the displacement on the shell mid-surface together with the relative displacement on the shell top surface. The development is based upon the complete three dimensional field equation of displacement, stress and strain. With the aid of assumed strain method, a scheme to enhance the accuracy of the element for large displacement analysis is described. Resorting to the Wilson's incompatible mode, the assumed strain fields are constructed for the large deformation analysis. The finite element formulation of shell element with the relative degree of freedom is derived. The numerical examples show that the proposed methodology achieves good performance for the impact problems which exhibit large deformation, elastic-plastic dynamic response.