The buckling and post-buckling behavior of initially imperfect, sinusoidally curved hinged-hinged beams undergoing very large deflections subjected to lateral concentrated loads acting at the midpoints is investigated via the geometrically nonlinear analysis of the problem. The transverse shear deformation is neglected. The amplitudes of the imperfection are considered to be relatively small. Therefore, the concerning curved beams (or arches) are shallow. The values of the extensional rigidity/length of the beams are assumed to be large enough not to permit considerable amount of change in the lengths of the beams during the deformation. The force-deflection curves corresponding to various amplitudes of the imperfection and the diagrams of the deflections and internal forces corresponding to various stages of the deformation, including those after the buckling, are presented. Not being able to solve the highly nonlinear problem analytically, numerical methods are used.

中文翻译：

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受侧向集中中点荷载作用而受到有限挠曲的铰接铰链最初不完美梁的快速弯折屈曲

通过对该问题进行几何非线性分析，研究了初始不完美的正弦曲线铰接铰链梁的屈曲和后屈曲行为，这些梁经历了很大的挠度，承受了集中在中点处的横向集中载荷。横向剪切变形被忽略。缺陷的幅度被认为是相对较小的。因此，相关的弯曲梁（或拱形）较浅。假定梁的拉伸刚度/长度的值足够大，以至于在变形期间不允许梁的长度发生大量变化。与缺陷的各种幅度相对应的力-挠度曲线以及与变形的各个阶段相对应的挠度和内力图，包括屈曲后的那些。无法解析地解决高度非线性的问题，使用了数值方法。