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.