THERMAL BUCKLING AND POSTBUCKLING CHARACTERISTICS OF EXTENSIONAL SLENDER ELASTIC RODS

Abstract

This paper presents an exact mathematical model for the postbuckling of a uniformly heated slender rod with axially immovable simply supported ends on the basis of geometrically nonlinear theory of extensible rods. The material is assumed linear elastic and its thermal strain-temperature relationship is considered nonlinear. Two approaches have been used in this study. The first approach is based on the extensible elastica theory. The governing equations are derived and solved analytically for the exact closed form solutions that include the equilibrium configurations of the rod, equilibrium paths, and temperature gradients. The exact solutions take the form of elliptic integrals of the first and second kinds. In the second approach, the multisegment integration technique is employed to solve a set of nonlinear differential equations with the associated boundary conditions. The equations are integrated by using the Runge-Kutta algorithm. A comparison study between the analytical elliptic integral solutions and the numerical multisegment integration technique solutions show excellent agreement of results. Special features of the solutions in the form of determination of buckling temperature, effects of slenderness ratio and nonlinear strain-temperature coefficients on the buckling and postbuckling behavior as a function of temperature are also discussed extensively.

Keywords: Thermal postbuckling, elliptic integral, multisegment integration, critical buckling temperature.  

doi: 10.3329/jme.v40i1.3467

Journal of Mechanical Engineering, Vol. ME40, No.1, June 2009 1-8