Steady-State Thermal Bending of Thick Rectangular Plates

Abstract

An analysis of the steady-state thermal bending of a thick rectangular plate is carried out by a tenth-order theory of moderately thick plates. The boundary conditions for a temperature field are considered to be a partially prescribed constant temperature on the top face, zero temperature at the bottom face and two edges, and no flux at the two edges. The temperature field is rigorously analyzed by the theory of three-dimensional heat conduction. The mechanical boundary conditions of the plate are considered traction-free at the top and bottom faces, the two opposite edges are simply supported, and the other two edges are free. The displacement and stress field is analyzed exactly by a particular solution deduced from part of a three-dimensional elasticity solution and a homogeneous solution consisting of three solutions to plane stress, generalized plane stress, and antisymmetric stress. Numerical results for thermal stresses and displacements are presented. One of the normal stresses at the top face becomes discontinuous at the boundary of the prescribed surface temperature.