Buckling in response to applied heat sources

We consider the problem of thermoelastic buckling of slender rods and thin plates subject to specified heat sources on their surfaces. The situation arises in experiments in which the heat sources are either distributed in space (heat produced by exothermic heterogeneous chemical reactions catalyzed on the surface of a thin elastic crystal) or are more localized (laser beam heating of the crystal). The steady heat balance equation is solved for the unbuckled rod (plate), taking into account conduction and radiation losses. The resulting temperature fields induce buckling, which is studied analytically and numerically as a bifurcation problem in the appropriate nonlinear elastostatic equilibrium equations.