An efficient, fully coupled beam model is developed to analyse laminated composite thin-walled structures with arbitrary cross-sections. The Euler–Lagrangian equations are derived from the kinematic relationships for a One-Dimensional (1D) beam representing Three-Dimensional (3D) deformations that take into account the cross-sectional stiffness of the composite structure. The formulation of the cross-sectional stiffness includes all the deformation effects and related elastic couplings. To circumvent the problem of shear locking, exact solutions to the approximating Partial Differential Equations (PDEs) are obtained symbolically instead of by numerical integration. The developed locking-free composite beam element results in an exact stiffness matrix and has super-convergent characteristics. The beam model is tested for different types of layup, and the results are validated by comparison with experimental results from literature.

中文翻译：

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用于分析任意截面层合复合结构的超收敛薄壁 3D 梁单元

开发了一种有效的全耦合梁模型来分析具有任意横截面的层压复合薄壁结构。欧拉-拉格朗日方程是从代表三维 (3D) 变形的一维 (1D) 梁的运动学关系导出的，其中考虑了复合结构的横截面刚度。截面刚度的公式包括所有的变形效应和相关的弹性耦合。为了规避剪切锁定问题，近似偏微分方程 (PDE) 的精确解是通过符号而不是通过数值积分获得的。开发的无锁定复合梁单元产生精确的刚度矩阵并具有超收敛特性。梁模型针对不同类型的铺层进行了测试，