Non-linear in-plane postbuckling of arches with rotational end restraints under uniform radial loading |
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Authors: | Y-L Pi MA Bradford |
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Affiliation: | aCentre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales, UNSW Sydney, NSW 2052, Australia |
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Abstract: | This paper presents a thorough and comprehensive investigation of non-linear buckling and postbuckling analyses of pin-ended shallow circular arches subjected to a uniform radial load and which have equal elastic rotational end-restraints. The differential equations of equilibrium for non-linear buckling and postbuckling are established based on a virtual work approach. Exact solutions for the non-linear bifurcation, limit point and lowest buckling loads are obtained; in particular, exact solutions for the non-linear postbuckling equilibrium paths are derived. The criteria for switching between fundamental buckling and postbuckling modes are developed in terms of critical values of a geometric parameter for an arch, with exact solutions for these critical values of geometric parameter being obtained. Analytical solutions of non-linear buckling and postbuckling problems for arches with rotational end-restraints are of great interest, since they constitute one of the very few closed-form analyses of buckling and postbuckling behaviour of continuous structural systems. These exact solutions are a contribution to the non-linear structural mechanics of arches, as well as providing useful benchmark solutions for verifying non-linear numerical analyses. |
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Keywords: | Arches Bifurcation Buckling Closed form solutions Elastic Exact analysis Limit point Non-linear Postbuckling Rotational end-restraints Uniform loading Shallow |
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