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Postbuckling Behavior Of Symmetrically Laminated Thin shallow Circular Arches

机译：对称层合薄浅圆拱的后屈曲特性

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摘要

The large deflection behavior of a symmetrically laminated thin shallow circular arch subjected to a central concentrated load is studied using the Rayleigh-Ritz finite element method. The shape functions used in the finite element method maintain C~1-continuity of the radial displacement (deflection) and C~0-continuity of the tangential displacement, respectively. The nonlinear algebraic equations of equilibrium are solved to a high degree of accuracy using Taylor's expansion technique in conjunction with the Newton-Raphson method. Nonlinear stability analysis provides accurate solutions for the symmetric and antisymmetric buckling of both pin-ended and fixed shallow arches. The stability of the symmetric deformation path is investigated for both pinned and fixed arches, and a detailed analysis is carried out at the point of bifurcation onto an asymmetric deformation path for a pinned symmetrically laminated shallow arch. The slope of this post-buckled path is also computed, and is shown to be accurate for deformations well beyond the point of bifurcation.
机译：使用瑞利-里兹有限元方法研究了对称叠层的薄浅圆拱在中心集中荷载作用下的大挠度行为。有限元方法中使用的形状函数分别保持径向位移（挠度）的C〜1连续性和切向位移的C〜0连续性。使用泰勒展开技术结合牛顿-拉夫森方法，可以高度精确地求解非线性平衡代数方程。非线性稳定性分析为固定端和固定浅拱的对称和反对称屈曲提供了精确的解决方案。研究了固定和固定拱的对称变形路径的​​稳定性，并在分叉点对固定对称层合的浅拱的不对称变形路径进行了详细分析。还计算了该后屈曲路径的斜率，并且显示出对于远超过分叉点的变形是准确的。

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