用于超弹性分析的高效杂交应变——EAS固体壳单元的研究

Research of robust hybrid strain-EAS solid shell element for hyperelastic analysis of shells

提出了一个用于橡胶材料分析的弱变分方程,基于一个可压缩Neo-Hookean模型,将EAS模式和杂交元法有机地结合起来,推导了一个高效、稳定的杂交应变——EAS固体壳单元,通过巧妙地选择应变插值函数和本文中提出的一个精化措施,克服了橡胶材料所表现出的大应变超弹性本构为杂交元正交化法的实施所带来的困难,保证了整个单元列式都仅采用低阶高斯积分,显著提高了计算效率,确保橡胶材料不可压缩性计算的顺利进行,并克服了固体壳元的厚度自锁问题。

A weaker variational procedure is proposed for the large strain analysis of rubber components confining to compressible and incompressible hyperelastic materials of the Neo-Hookean type. The enhanced assumed strain (EAS) modes are incorporated into the hybrid-strain formulation and a robust and stable hybrid strain solid shell element is developed. A refined method is presented and the assumed strain modes are selected, so that the orthogonality between the lower and higher order assumed strain modes is realized. The salient feature of the orthogonality for higher computational efficiency is that the higher order assumed strain modes vanish at the sampling points of the second order quadrature and their energy products with the displacement-derived covariant strain can be programmed without resorting to numerical integration. The whole formulation uses only the second order quadrature, the computational efficiency can be improved and the incompressible locking of hyperelastic materials can be overcome. The formulation overcomes the thickness locking of the solid shell elements, and its efficacy is illustrated by popular benchmark problems.