A thermo-mechanical stress prediction improvement of using the classical lamination theory via Saint-Venant’s principle for laminated composite plates

Abstract

Saint-Venant’s principle was introduced as the principle of the stress resultant equivalence for one dimensional structures, such as beams, cylindrical and prismatic structures. According to the principle, the stress distributions may be different around the area where forces are applied, but their resultants are invariant. In this paper, we apply the Saint-Venant’s principle to improve the thermomechanical stresses calculated by the Classical lamination theory (CLT). First we solve the CLT for laminated composite plates, calculate the transverse shear stresses using three-dimensional stress equilibrium equations, and obtain the improved displacement field with perturbation terms via transverse shear constitutive equations. At this point, these perturbation terms are unknown, which can be determined by applying the stress resultant equivalence (or the Saint-Venant’s principle). Once the terms are calculated, the improved displacements and stresses are obtained. To verify the accuracy of the proposed approach, simply-supported plates under mechanical and/or thermal loadings are taken as a test-bed, in which symmetric and anti-symmetric cross-ply layups are considered. The results obtained are compared to those of three-dimensional elasticity as well as first-order shear deformation theory. Finally the errors induced by the present approach are systematically analyzed in terms of the stress resultants.