Nonlinear Instability Behavior and Buckling of Shallow Arches Under Gradient Thermo-Mechanical Loads

Abstract

This paper investigates the nonlinear behavior and buckling of shallow arches under gradient thermal and mechanical loading. The gradient temperature varies continuously along the thickness of the cross section of the arch but uniformly distributes over the entire length of the arch. The principle of virtual work and mid-plane plane formulations are employed to derive analytical solutions for the structural responses, internal force and critical buckling loads of the arch. Subsequently, the phenomenon of the buckling mode switching are also identified and discussed. It is found that the fixed arch under gradient thermo-mechanical loading can buckle in a symmetric instability mode or an anti-symmetric instability mode, namely limit point buckling or bifurcation buckling, which depend on its geometric parameter and the gradient temperature. The effects of the gradient temperature change on the radial displacement, axial displacement, axial compressive force and bending moment as well as critical buckling loads of the arch are investigated through parametric studies comprehensively.