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A rigorous theory and corresponding computational algorithms was developed for a variety of problems regarding the analysis of composite beams and plates. The modeling approach is intended to be applicable to both static and dynamic analysis of generally anisotropic, nonhomogeneous beams and plates. Development of a theory for analysis of the local deformation of plates was the major focus. Some work was performed on global deformation of beams. Because of the strong parallel between beams and plates, the two were treated together as thin bodies, especially in cases where it will clarify the meaning of certain terminology and the motivation behind certain mathematical operations.

A rigorous theory and the corresponding computational algorithms were developed for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants of a plate. Additionally, the analysis is used to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. It was decided that the variational-asymptotical method (VAM) would serve as a suitable framework in which to solve these types of problems. Work during this reporting period has progressed along two lines: (1) further evaluation of neo-classical plate theory (NCPT) as applied to shear-coupled laminates; and (2) continued modeling of plates with nonuniform thickness.

The main purpose of this research was to develop a rigorous theory and corresponding computational algorithms for through-the-thickness analysis of composite plates. This type of analysis is needed in order to find the elastic stiffness constants for a plate and to post-process the resulting plate solution in order to find approximate three-dimensional displacement, strain, and stress distributions throughout the plate. This also requires the development of finite deformation plate equations which are compatible with the through-the-thickness analyses. After about one year's work, we settled on the variational-asymptotical method (VAM) as a suitable framework in which to solve these types of problems. VAM was applied to laminated plates with constant thickness in the work of Atilgan and Hodges. The corresponding geometrically nonlinear global deformation analysis of plates was developed by Hodges, Atilgan, and Danielson. A different application of VAM, along with numerical results, was obtained by Hodges, Lee, and Atilgan. An expanded version of this last paper was submitted for publication in the AIAA Journal.