An Overall View of Laminate Theories Based on Displacement Hypothesis

Abstract

With the use of a recursive technique, this paper presents an overall comparison of laminate theories based on displacement hypothesis. A generalized polynominal form is used to unify the displacement hypothesis. Both theories available in the literature and inferable from the existing theories are addressed. Firstly, Shear Deformation Theories are recognized to give good results for in-plane stresses but poor results for interlaminar stresses. However, Layerwise Theories give excellent results for both global and local distributions of displacement and stress (both in-plane and out-of-plane). A compromising theory, the Generalized Zigzag Theory, is presented. Due to its success in laminate analysis, a series of Quasi-layerwise Theories are presented. Unfortunately, a physical impossibility-coordinate dependency-takes place. It then requires a Global-Local Superposition Technique to formulate the laminate theories. By examining the results of Superposition Theories, it is concluded that the completeness of the terms is very important. Based on a Hypothesis for Double Superposition, this study presents three Double-Superposition Theories. They are verified to give excellent numerical accuracy, along with computational efficiency, when compared with elasticity solutions.