Both the initial geometrical imperfections and material nonlinearity have great influence on the stability of the struts. In this paper, an analytical approximate solution of the post-buckling behavior of the geometrically imperfect struts with pinned–pinned ends under axial compression is obtained. The struts are made of aluminum alloys, and its constitutive relation conforms to the Ramberg–Osgood law. The Ramberg–Osgood type constitutive relation is extended by Taylor series to facilitate its application. A theory based on Euler–Bernoulli hypothesis is applied to establish the nonlinear equilibrium equations of the aluminum alloy struts. The analytical approximate solutions of the nonlinear equilibrium equations are derived by the harmonic balance method for the first time. Moreover, numerical solutions are obtained by finite element analysis for comparison. By comparing with the numerical solution, the accuracy of the analytical approximate solution proposed in this paper is verified in the case of small strain. The effects of material nonlinearity and initial geometrical imperfections on the post-buckling equilibrium path of the aluminum alloy struts are analyzed by the proposed analytical approximate solution.

中文翻译：

初始几何缺陷和材料非线性对支柱的稳定性都有很大影响。在本文中，获得了具有销钉销端的几何缺陷支柱在轴向压缩下的后屈曲行为的解析近似解。支柱由铝合金制成，其本构关系符合 Ramberg-Osgood 定律。Ramberg-Osgood 型本构关系通过 Taylor 级数进行扩展，以方便其应用。应用基于欧拉-伯努利假设的理论来建立铝合金支柱的非线性平衡方程。首次采用调和平衡法推导出非线性平衡方程的解析近似解。而且，数值解是通过有限元分析得到的，用于比较。通过与数值解的比较，验证了本文提出的解析近似解在小应变情况下的准确性。通过所提出的解析近似解，分析了材料非线性和初始几何缺陷对铝合金支柱屈曲后平衡路径的影响。