Higher-order theories for thermal stresses in layered plates

Abstract

First order shear deformation theory renders quite accurate in-plane stresses even for rather thick plates. By means of equilibrium conditions derivatives of the in-plane stresses can be integrated to determine transverse shear and normal stresses. The need to use in-plane derivatives requires at least cubic shape functions. Simplifying assumptions relieve these requirements leading to the extended 2D method. While under mechanical load this method yields excellent results poor transverse normal stresses have been obtained for plates under a sinusoidal temperature distribution. This paper traces back these deficiencies to lentil-like deformations of each separate layer. It is proved that third or fifth order displacement approximations through the plate thickness avoid these deficiencies.