Assessment of plate theories for treating the thermomechanical response of layered plates

Abstract

The analytical solution of thermally induced cylindrical bending of layered elastic plates is obtained for a sinusoidal temperature distribution along the span and constant and linear variations across the thickness of the plate. The result is used to assess the accuracy of shear-deformable plate theories in predicting thermal deformation. Two shear-deformable composite plate theories are examined. They are characterized by their kinematics of: (1) the linear variation of in-plane displacements across the entire thickness of the plate without transverse normal strain, and (2) the cubic variation of in-plane displacements across the entire thickness of the plate with nonzero transverse normal strain. Comparisons of the predicted thermal displacements with the exact solution revealed that the plate theories considered experience limitations in accurately predicting the rapid variation of transverse displacement in each layer. The results indicate the need for adopting a plate theory with a cubic variation of in-plane displacements in each layer to improve the prediction of transverse normal displacement.