STEADY-STATE THERMAL BENDING OF THICK RECTANGULAR-PLATES

An analysis of the steady-state thermal bending of a thick rectangular plate is carried out by a tenth-order theory of moderately thick plat es. The boundary conditions for a temperature field are considered to be a partially prescribed constant temperature on the top face, zero t emperature at the bottom face and two edges, and no flux at the two ed ges. The temperature field is rigorously analyzed by the theory of thr ee-dimensional heat conduction. The mechanical boundary conditions of the plate are considered traction-free at the top and bottom faces, th e two opposite edges are simply supported, and the other two edges are free. The displacement and stress field is analyzed exactly by a part icular solution deduced from part of a three-dimensional elasticity so lution and a homogeneous solution consisting of three solutions to pla ne stress, generalized plane stress, and antisymmetric stress. Numeric al results for thermal stresses and displacements are presented. One o f the normal stresses at the top face becomes discontinuous at the bou ndary of the prescribed surface temperature.