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首页> 外文期刊>Applied Mathematical Modelling >Non-linear in-plane multiple equilibria and buckling of pin-ended shallow circular arches under an arbitrary radial point load
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Non-linear in-plane multiple equilibria and buckling of pin-ended shallow circular arches under an arbitrary radial point load

机译：任意径向点载荷下销端浅圆拱的非线性面内多重平衡和屈曲

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This paper analytically investigates effects of the load location on the non-linear in-plane multiple equilibria, limit points, stationary points of inflexion, cusp, and buckling behavior of a pin-ended elastic shallow circular arch under a radial point load at an arbitrary location along the arch length. Theoretical solutions for the non-linear response of the arch to the arbitrary radial point load including the limit points, stationary points of inflexion, cusp and multiple equilibria are derived. The major findings are: (1) there exists special modified slenderness corresponding to an arch, whose non-linear equilibrium path has stationary point of inflexion or a cusp and which can distinguish the number of multiple limit points and equilibria; (2) criteria distinguishing multiple limit points and equilibria are developed by relating the special modified slenderness to the load location; (3) theoretical solutions for the load, axial force and displacement at stationary points of inflexion and at cusps are also deduced; (4) the load location and the modified slenderness of an arch significantly influence the non-linear multiple equilibria of the arch; and (5) the load location has significant influence on the buckling pattern of an arch, and when the point load is applied at a location away from the apex of the arch, the arch can buckle only in a limit point instability pattern, but not in a bifurcation pattern. (C) 2019 Elsevier Inc. All rights reserved.
机译：本文分析性地研究了载荷位置对任意径向点载荷作用下的端部弹性浅圆拱的非线性平面内多重平衡，极限点，屈曲的固定点，尖点和屈曲行为的影响。沿弓长度的位置。推导了拱对任意径向点载荷的非线性响应的理论解，包括极限点，弯曲的固定点，尖点和多重平衡。主要发现是：（1）存在对应于弓形的特殊修长度，其非线性平衡路径具有固定的拐点或拐点，并且可以区分多个极限点的数量和平衡点。 （2）通过将特殊修改的细长度与载荷位置相关联来制定区分多个极限点和平衡的标准； （3）推导了在弯曲的固定点和尖点处的载荷，轴向力和位移的理论解； （4）拱的载荷位置和修正的细长度显着影响拱的非线性多重平衡； （5）载荷位置对拱形结构的屈曲模式有很大的影响，当点载荷施加在远离拱形顶点的位置时，拱形结构只能以极限点失稳模式屈曲，而不会弯曲分叉模式。 （C）2019 Elsevier Inc.保留所有权利。

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