Abstract

The nonlinear in-plane buckling behaviour of pinned-pinned shallow circular arches made of functionally graded material (FGM) is investigated using a one-dimensional Euler–Bernoulli model. The effect of the bending moment on the membrane strain is included. The material properties vary along the thickness of the arch. The external load is a radial concentrated force at an arbitrary position. The pre-buckling and buckled equilibrium equations are derived using the principle of virtual work. Analytical solutions are given for both bifurcation and limit point buckling. Comprehensive studies are performed to find the effect of various parameters on the buckling load and on the behaviour. The major findings: (1) arches have multiple stable and unstable equilibria; (2) when the load is at the crown, the lowest buckling load is related to bifurcation buckling for most geometries and material compositions but when the external force is replaced, only limit point buckling is possible; (3) the position of the load has huge influence on the buckling load; (4) such arches are sensitive to small loading imperfections when loaded in the vicinity of the crown. The paper intends to improve and extend the existing knowledge about the behaviour of pinned-pinned shallow FGM arches under arbitrary concentrated radial load.

中文翻译：

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任意集中径向力作用下FGM浅拱的非线性稳定性分析

摘要

使用一维Euler–Bernoulli模型研究了功能梯度材料（FGM）制成的销钉固定式浅圆拱的非线性面内屈曲行为。包括弯矩对膜应变的影响。材料特性沿弓的厚度变化。外部载荷是在任意位置的径向集中力。利用虚功原理推导了预屈曲和屈曲的平衡方程。给出了分叉和极限点屈曲的解析解。进行了全面的研究，以发现各种参数对屈曲载荷和性能的影响。主要发现：（1）足弓具有多个稳定和不稳定的平衡点；（2）当负载在表冠上时，对于大多数几何形状和材料成分，最小的屈曲载荷与分叉屈曲有关，但是当替换外力时，只能进行极限点屈曲；（3）载荷的位置对屈曲载荷影响很大；（4）当在拱顶附近加载时，这种拱对较小的加载缺陷敏感。本文旨在改进和扩展有关在任意集中径向载荷下钉扎浅FGM拱的行为的现有知识。