This paper presents a three-dimensional beam element for stability analysis of elastic thin-walled open-section beams in multibody systems. The beam model is based on the generalized strain beam formulation. In this formulation, a set of independent deformation modes is defined which are related to dual stress resultants in a co-rotational frame. The deformation modes are characterized by generalized strains or deformations, expressed as analytical functions of the nodal coordinates referred to the global coordinate system. A nonlinear theory of non-uniform torsion of open-section beams is adopted for the derivation of the elastic and geometric stiffness matrices. Both torsional-related warping and Wagner’s stiffening torques are taken into account. Second order approximations for the axial elongation and bending curvatures are included by additional second order terms in the expressions for the deformations. The model allows to study the buckling and post-buckling behaviour of asymmetric thin-walled beams with open cross-section that can undergo moderately large twist rotations. The inertia properties of the beam are described using both consistent and lumped mass formulations. The latter is used to model rotary and warping inertias of the beam cross-section. Some validation examples illustrate the accuracy and computational efficiency of the new beam element in the analysis of the buckling and post-buckling behaviour of thin-walled beams under various loads and (quasi)static boundary conditions. Finally, applications to multibody problems are presented, including the stability analysis of an elementary two-flexure cross-hinge mechanism.

本文提出了三维梁单元，用于多体系统中弹性薄壁开口截面梁的稳定性分析。梁模型基于广义应变梁公式。在此公式中，定义了一组独立的变形模式，这些模式与同向旋转框架中的双应力合力有关。变形模式的特征在于广义应变或变形，表示为参考全局坐标系的节点坐标的解析函数。推导非线性弹性理论的开放截面梁用于弹性和几何刚度矩阵的推导。扭转相关的翘曲和瓦格纳的加强扭矩都被考虑在内。轴向伸长率和弯曲曲率的二阶近似值包含在变形表达式中的其他二阶项中。该模型允许研究具有开放横截面的非对称薄壁梁的屈曲和后屈曲行为，该屈曲可以承受适度的大扭转旋转。使用一致的和集总的质量公式来描述梁的惯性特性。后者用于模拟梁横截面的旋转和翘曲惯性。一些验证示例说明了在各种载荷和（准）静态边界条件下分析薄壁梁的屈曲和后屈曲行为时，新梁单元的准确性和计算效率。最后，介绍了对多体问题的应用，