端对端压缩下拱形和蛇形结构的屈曲后分析

Zheng Zhang, Fuhua Ye, Yuhang Dong, Fan Zhang, Zhichao Fan
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引用次数: 0

摘要

拱形结构和蛇形结构是两种基本的结构形式,在各个领域都有重要应用。当两端承受压缩荷载时,这些结构会发生挠曲-扭转后屈曲,从而产生复杂的变形模式,这些模式很难用基本函数来描述,这给寻找分析解决方案带来了巨大挑战。在本研究中,我们提出了一种解决这一问题的新方法。通过用三角级数展开来表示横向位移,并利用平衡方程,用称为马修函数的特殊函数来表示角位移。此外,还采用了能量法来获得屈曲扭转后屈曲变形成分的解析解。实验和有限元分析(FEA)验证了理论结论。根据理论结果,得出了结构的最大主应变和弯曲扭转比的明确分析表达式,为实际应用中拱形和蛇形结构的设计提供了宝贵的见解。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Post-Buckling Analysis of Arch and Serpentine Structures under End-to-End Compression
Arch and serpentine structures are two fundamental structural forms with significant applications in various fields. When subjected to compressive loading at both ends, these structures undergo flexural-torsional post-buckling, resulting in complex deformation modes that are challenging to describe using basic functions, posing significant challenges in finding analytical solutions. In this study, we propose a novel approach to address this issue. By representing the lateral displacement with a trigonometric series expansion and utilizing the equilibrium equation, the angular displacement is expressed in terms of special functions known as Mathieu functions. Furthermore, the energy method is employed to obtain analytical solutions for the flexural-torsional post-buckling deformation components. The theoretical findings are validated through experiments and finite element analysis (FEA). Based on theoretical results, explicit analytical expressions for the maximum principal strain and the bending-torsion ratio of the structures are derived, offering valuable insights for the design of arch and serpentine structures in practical applications.
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