Abstract: Based on the nonlinear geometric theory of extensible rods, an exact mathematical model of thermal post-buckling behavior of uniformly heated elastic rods with axially immovable ends is developed, in which the arc length s(x) of axial line and the longitudinal displacement u(x) are taken as the basic unknown functions. This is a two point boundary value problem of first order ordinary differential equations with strong non-linearity. By using shooting method and analytical continuation, the nonlinear boundary value problems are numerically solved. The thermal post-buckled states of the rods with transversely simply supported and clamped ends are obtained respectively and the corresponding numerical data tables and characteristic curves are also given.

Key words: elastic straight rod, thermal post-buckling, nonlinear mathematical model, shooting method, numerical solution