In-plane elastic buckling of shallow parabolic arches under an external load and temperature changes

This paper studies the in-plane stability of rotationally restrained shallow arches subjected to a vertical uniform load and temperature changes below 100°C. The virtual work principle method was used to establish the nonlinear equilibrium and buckling equations. Analytical solutions for the nonlinear in-plane symmetric snap-through and asymmetric bifurcation critical loads are obtained. Then the effects of the uniform temperature field and temperature gradients on the in-plane stability for arches are studied. The influence of temperature variations on the critical loads for both the symmetric snap-through and asymmetric bifurcation modes was significant. The critical loads increase with an increase of the uniform temperature field and a decrease of temperature gradients. Furthermore, the effect of temperature changes on the critical load increases with the span-rise ratio m of arches. Increasing the stiffness of the rotational springs will increase the effect of the uniform temperature field but reduce the effect of the temperature gradients.