Postbuckling Analysis of Slender Elastic Rods Subjected to Uniform Thermal Loads

Formulation and analytical solution for the postbuckling behavior of slender rods subjected to uniform temperature variations and constrained by double-hinged nonmovable boundary condition are presented. The material is assumed linear elastic and its thermal strain-temperature relationship is nonlinear. Large displacements are considered, hence the formulation is geometrically nonlinear. The governing equations are derived from geometrical compatibility, equilibrium of forces and moments, constitutive equations, and strain-displacement relation, yielding a set of six first-order nonlinear ordinary differential equations with boundary conditions specified at both ends, which constitute a complex boundary value problem. A closed-form analytical solution found via complete elliptic integral is derived from the governing equations defining the shape of the postbuckled rod (elastica). The results are presented in nondimensional graphs for a range of temperature gradients and different values of slenderness ratios.