Analysis of thermal post-buckling of heated elastic rods

Based on the nonlinear geometric theory of extensible rods, an exact mathem atical model of thermal post-buckling behavior of uniformly heated elastic rods with axially immovable ends is developed, in which the are length s(x) of axial line and the longitudinal displacement u(x) are taken as the basi c unknown functions. This is a two point boundary value problem of first or der ordinary differential equations with strong nonlinearity. By using shoo ting method and analytical continuation, the nonlinear boundary value probl ems are numerically solved. The thermal post-buckled states of the rods wit h transversely simply supported and clamped ends are obtained respectively and the corresponding numerical data tables and characteristic curves are a lso given.