基于带面内转角自由度四节点平板壳单元的板壳非线性分析

4-node flat shell element with drilling degrees of freedom for nonlinear analysis of plates and shells

针对矩形平板壳单元在工程结构,例如大跨度桥梁数值分析实践中的广泛应用,采用具有给定位移模式的纵、横向离散条带描述单元整体位移场。该位移场由2个部分构成,即单元中面膜位移和横向挠曲变位,其中面内位移由包含节点转角自由度在内的节点位移参数沿纵、横向条带顺次插值得到,而横向变位表示为双3次Hermite多项式乘积形式。单元模型确保位移及应变分量在单元内部和相邻单元之间连续,物理概念明确,提高分析精度与可靠性。通过选取受弯方形薄板弹塑性分析及圆柱壳体大变形、大转动2个经典算例,发现本文计算结果与经典解析解以及其他数值解十分接近。提出的板壳单元位移模型可以有效地解决复杂板式结构稳定极限承载力分析问题。

Nowadays, various kinds of rectangular plate/shell elements have found wide applications for numerical analysis of engineering structures, such as long-span bridges. Some typical discrete strips in both longitudinal and transverse directions with presumed displacement modes were employed to describe more reasonably the displacement field of the element. Such a displacement field consists of two parts, namely the membrane action in the middle plane of the element and lateral deflection perpendicular to the middle plane. The in-plane displacement components were given through consecutive interpolations along perpendicular strips of nodal parameters, which in particular include the drilling degrees of fi＇eedom, while the out-of-plane deflection is simply expressed as third-order Hermitian interpolations of nodal parameters sequentially in perpendicular strip directions. The present model is capable of ensuring the continuity of displacement and strain components both in the element domain and at the interface of interconnected elements, thereby the underlying physical meaning is clear and the improvement of analysis accuracy can be satisfied. By selecting two benchmark problems, namely the elasto-plastic analysis of a thin plate and large deformation/large rotation problem of a thin cylindrical shell, good agreements can be achieved between analytical, solution and/or numerical results obtained by other researchers and present predictions. Meanwhile, these examples demonstrate efficiency and robustness of the 4-node flat shell element for determining the maximum load carrying capacity of complicated plate structures.