| High-order Shear Deformation Theories 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 so-called Generalized Zigzag Theory, is presented. It has two layer-dependent variables in the zeroth- and first-order terms. Due to its success in laminate analysis, the feasibility of assigning the two layer-dependent variables in the second- and third-order terms is examined, resulting in the Quasi-layerwise Theories. Unfortunately, a physical absurdity--coordinate dependency, takes place. It then requires a technique, the so-called Global-Local Superposition Technique, to formulate the laminate theory to be coordinate-independent for the numerical advantage. The recursive expressions presented in this study, though somewhat tedious, are necessary to achieve the numerical advantage. By examining the results based on the Superposition Theories, it is concluded that the completeness of the terms is meant two fold: not only can no low-order term be skipped, but more high-order terms are preferred.; The objective of completeness seems to conflict with the fundamental of two continuity conditions in each coordinate direction. In order to satisfy both aspects, a special technique called the Hypothesis for Double Superposition is proposed. Several three-term theories, the so-called Double Superposition Theories, are examined. They give excellent values for in-plane displacement, in-plane stress, and transverse shear stress. However, because w is considered as constant in the examples, both transverse displacement and transverse normal stress are not as good as the remaining components.; Among all the theories examined in this thesis, it seems that the Generalized Zigzag Theory, with up to seventh-order terms, and the third-order Double Superposition Theories give the best agreement with Pagano's solution in all ranges of layer number for both symmetric and unsymmetrical laminates. Although they both are layer-number independent theories, the former has seven degrees-of-freedom while the latter has only three, provided w is considered to be constant through the laminate thickness. As a consequence, the Double Superposition Theories are concluded as the best selection for laminate analysis in this thesis. |
