A Nonlinear Model Study of the Thermal Buckling of Thin Elastic Shells

Abstract

Analysis of the simple model proposed yields equilibrium curves in agreement with those obtained by other investigators for axially compressed, thin-walled, circular cylindrical shells. A rigorous calculation of the stability of the equilibrium of the model indicates that the snap-through phenomenon can be entirely absent when an imperfect shell is heated in a perfectly rigid testing machine. When the testing machine is sufficiently elastic, snap through will occur. It may take place at a temperature smaller than, equal-to, or greater than T = εcr /α, where εcr is the theoretical critical strain of the perfect shell and α is the coefficient of expansion of the material of the shell, but the maximum stress produced in the imperfect shell will always be less than εcr E, where E is Young’s modulus of the material.