In this paper, a weak form quadrature element formulation of a geometrically nonlinear shell model is proposed and applied for analysis of laminated composite shell structures. Thickness stretch parameters of the shell are incorporated for introducing 3D constitutive relations in the formulation. A drilling rotation constraint on the basis of polar decomposition of a modified deformation gradient is enforced by the Lagrange multiplier method and employed for implementing spatial finite rotations. The present formulation is shown to be feasible to model complex structures and circumvent locking problems naturally. A series of numerical benchmark examples are presented to demonstrate the validity of the formulation.

中文翻译：

---

包含厚度拉伸和钻孔旋转的几何非线性层压复合壳的正交单元公式

在本文中，提出了几何非线性壳模型的弱形式正交单元公式，并将其应用于层合复合壳结构的分析。结合壳的厚度拉伸参数以在公式中引入 3D 本构关系。通过拉格朗日乘子法实施基于修正变形梯度极坐标分解的钻井旋转约束，并用于实现空间有限旋转。目前的公式被证明是可行的，可以模拟复杂的结构并自然地避免锁定问题。提供了一系列数值基准示例来证明公式的有效性。