Nonlinear in-plane elastic buckling of shallow circular arches under uniform radial and thermal loading

This paper presents a nonlinear in-plane elastic buckling analysis of circular shallow arches that are subjected both to a uniform temperature field and to a uniform radial load field. A virtual work method is used to establish nonlinear equilibrium equations and buckling equilibrium equations, and analytical solutions for the limit instability and bifurcation buckling loads are obtained. It is found that the temperature influences the limit instability, bifurcation buckling and postbuckling behaviour of shallow arches significantly. The limit instability and bifurcation buckling loads increase with an increase of the temperature. A maximum temperature is shown to exist for the occurrence of bifurcation buckling of shallow arches, and when the temperature is higher than this value, bifurcation buckling of an arch is not possible. h geometric parameter is introduced to define switches between the limit instability and bifurcation buckling modes, and between buckling and no buckling. Formulae and methods for the calculation of the limiting values of the arch geometric parameter are developed. It is also found that the limiting values of the arch geometric parameter decrease with an increase of the temperature.