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.
Bibliographical noteFunding Information:
This work was partially supported by NSF DMS 98-03752 (JC,PH,IGK), and a Humboldt prize (IGK). We thank Dr. Harm Hinrich Rotermund and Mr. Janpeter Wolff, of the Fritz-Haber-Institut in Berlin for sharing their unpublished results on reaction-heating induced buckling, for performing experiments on laser-heating induced buckling, and for many helpful discussions regarding the modeling of their experiments. We also thank Professors Alberto Cuitino and Fehmi Cirak for advice and comments.
- Applied heat sources
- Laser beam heating
- Thermoelastic buckling