Nonlinear Thermoelastic Buckling of Pin-Ended Shallow Arches under Temperature Gradient

This paper presents a nonlinear thermal buckling analysis of circular shallow pin-ended arches that are subjected to a linear temperature gradient field in the plane of curvature of the arch. The linear temperature gradient produces axial expansion and curvature changes in the arch. The bending action produced by the curvature change and the axial compressive action produced by the restrained axial expansion may lead the arch to buckle suddenly in the plane of its curvature. The end reactions resulting from the restrained axial expansion also produce bending actions that are opposite to that produced by the temperature differential and tend to produce deflections on the convex side of the arch. A geometrically nonlinear analysis for thermoelastic buckling has been carried out based on a virtual work technique, and analytical solutions for the critical temperature gradients for the in-plane limit instability and bifurcation buckling are obtained. It is found that antisymmetric bifurcation is the dominant buckling mode for most shallow arches that are subjected to a linear temperature gradient. The limit instability is possible only for slender and shallow arches. It is also found that a characteristic value of the arch geometric parameter exists and that arches whose geometric parameter is less than this characteristic value show no typical buckling behavior. The formula for this characteristic value of the arch geometric parameter is derived.