In this study, an efficient 1D finite element model (FEM) is presented for the axial–flexural buckling, post-buckling and geometrically nonlinear analyses of thin-walled beams. The non-classical effects like transverse shear and normal flexibilities are incorporated in the formulation by adopting a new structural concept called equivalent layered composite cross-sectional (ELCS) modeling. In the framework of ELCS, the original cross section of the thin-walled beam is replaced with a layered composite cross section with equivalent stiffness. A layered global–local shear deformation theory is employed for representing the displacement fields of the beam. A full Green–Lagrange type of geometrically nonlinear FEM is developed to formulate the governing differential equations. The Newton–Raphson linearization approach is adopted for solving the nonlinear equations. The proposed FEM avoids the use of a shear correction factor and has a low number of degrees of freedom (DOFs). For the validation of the proposed model, various buckling, post-buckling and nonlinear bending tests are carried out and the obtained results are compared with the results of classical beam theories and 2D/3D finite element results. Comparisons of the results prove the efficiency and accuracy of the suggested formulation for stability and geometrically nonlinear analysis of thin-walled beams.

在这项研究中，提出了一种有效的一维有限元模型（FEM），用于薄壁梁的轴向-弯曲屈曲，后屈曲和几何非线性分析。通过采用称为等效层状复合截面（ELCS）建模的新结构概念，将非经典效应（如横向剪切力和法向柔韧性）纳入配方中。在ELCS的框架中，薄壁梁的原始横截面被具有等效刚度的分层复合横截面所代替。分层局部-局部剪切变形理论用于表示梁的位移场。开发了完全的Green-Lagrange类型的几何非线性FEM来表达控制微分方程。牛顿-拉夫森线性化方法用于求解非线性方程。所提出的有限元方法避免了使用剪切校正因子，并且自由度（DOF）数量较少。为了验证所提出的模型，进行了各种屈曲，后屈曲和非线性弯曲试验，并将所得结果与经典梁理论和2D / 3D有限元结果进行了比较。结果的比较证明了所建议的公式对于薄壁梁的稳定性和几何非线性分析的效率和准确性。进行了屈曲后和非线性弯曲试验，并将所得结果与经典梁理论和2D / 3D有限元结果进行了比较。结果的比较证明了所建议的公式对于薄壁梁的稳定性和几何非线性分析的效率和准确性。进行了屈曲后和非线性弯曲试验，并将所得结果与经典梁理论和2D / 3D有限元结果进行了比较。结果的比较证明了所建议的公式对于薄壁梁的稳定性和几何非线性分析的效率和准确性。