几何非线性复合材料层合固体壳单元

COMPOSITE LAMINATED SOLID SHELL ELEMENT FOR GEOMETRICALLY NONLINEAR ANALYSIS

通过定义广义应力,提出了一个改进的刚度矩阵,以克服固体壳元的厚度自锁问题,并能保证沿复合材料层合结构厚度方向上的连续应力分布;将应力插值函数分为低阶和高阶两部分,建议了一个新的非线性变分泛函,推导了一个用于几何非线性分析的九节点固体壳单元,该单元的计算精度和效率基本上与九节点减缩积分单元相当,与同类型其他单元相比,该单元显著提高了计算效率。

Starting from defining generalized stress, this paper presents a modified stiffness matrix method to overcome the thickness locking of solid shell elements and guarantee the continuous distribution of the transverse normal stress of composite laminate shell structures. By splitting the stress into lower order term and higher order term, a nonlinear variation principle is developed and a 9-node solid shell element with 6 DOF per node is derived for the geometrically nonlinear analysis of composite laminated shells. The higher order assumed stress modes are judiciously selected to 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 accuracy of the present element is virtually identical to that of the uniformly reduced integration (URI) element yet with a little additional computational cost for the stabilization matrix. The stabilization matrix is of prime importance as the global tangential stiffness matrices resulting from the URI elements often become singular after a few iterations.