基于相对自由度壳的非线性动态分析

为了简便有效地解决板壳结构的大变形问题 ,针对16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。利用 Hu- Washinzu变分原理 ,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。算例表明 :该文针对相对自由度壳单元提出的方法及推导的公式 ,能够解决壳的弹塑性大变形动力分析问题

Nonlinear dynamic analysis of shell elementwith a relative degree of freedom

A 16 node shell element with relative degrees of freedom was developed for large deformation analysis of plate and shell structures. The element does not include rotation parameters, but the displacement of the shell element is represented by the displacement at the shell mid surface together with the relative displacement of the shell top surface. The model is based on the complete three dimensional field equations for displacement, stress and strain. The Hu Washinzu variational principle and the assumed strain method were used to develop a scheme with enhanced accuracy for large displacement analyses. Wilson's incompatible mode was used to construct strain fields for large deformation analysis. The finite element formulation is then developed for the shell element. Numerical examples show that the proposed methodology achieves good performance for a range of problems which exhibit large deformation, elastic plastic dynamic response.