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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.

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.

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.

THIS tells how once the King of Glory came from heaven to visit us here on earth and live amongst us; how He was born in Bethlehem and brought up in Nazareth; how He went about telling people of the Heavenly Kingdom, and doing good, ministering to the sick and the poor; how He was misunderstood, and disliked, and even hated, till at last they took Him in Jerusalem and nailed Him to a cross so that He died; and how, after that, He came to life again, and went back into heaven, promising to return. (Summary from the Preface of <i>When the King Came</i>)

Though these stories of the lives of twenty saints and heroes of the faith, we have an introduction to the history of the church from 3rd century A.D. to the Reformation. These stories chronicle their lives and sacrifices for the faith. These saints and heroes include: Cyprian, Athanasius, Ambrose, Chrysostom, Jerome, Augustine, Benedict, Gregory the Great, Columba, Charlemagne, Hildebrand, Anselm, Bernard, Becket, Langton, Dominic, Francis, Wycliffe, Hus, and Savonarola. Appropriate for children and adults. - Summary by Maggie Travers

In this second volume, Hodges uses stories of the lives of fourteen well-known saints and heroes of the faith to continue the history of the church from the end of the Reformation through the 1700s. These stories recount their lives and sacrifices for the faith. These saints and heroes include: Luther, More, Loyola, Cranmer, Calvin, Knox, Coligny, William the Silent, Brewster, Laud, Cromwell, Bunyan, Fox, and Wesley. Appropriate and beneficial for children and adults! - Summary by Maggie Travers

4William Penn

By George Hodges

Biography of William Penn - Summary by Richard Vogel

The story of Fountains Abbey, one of England's most famous medieval monasteries, from its foundation in the twelfth century to its suppression at the time of the Reformation; with a description of its various buildings, and an account of the daily life of the monks. Summary by Patrick Randall