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SHEAR DEFORMABLE BEAMS AND PLATES (RELATIONSHIP WITH CLASSICAL
C.M. Wang, J.N. Reddy, K.H. Lee
Most books on the theory and analysis of beams and plates deal with the classical (Euler-Bernoulli/Kirchoff) theories but few include shear deformation theories in detail. The classical beam/plate theory is not adequate in providing accurate bending, buckling, and vibration results when the thickness-to-length ratio of the beam/plate is relatively large. This is because the effect of transverse shear strains, neglected in the classical theory, becomes significant in deep beams and thick plates. This book illustrates how shear deformation theories provide accurate solutions compared to the classical theory.
Equations governing shear deformation theories are typically more complicated than those of the classical theory. Hence it is desirable to have exact relationships between solutions of the classical theory and shear deformation theories so that whenever classical theory solutions are available, the corresponding solutions of shear deformation theories can be readily obtained. Such relationships not only furnish benchmark solutions of shear deformation theories but also provide insight into the significance of shear deformation on the response. The relationships for beams and plates have been developed by many authors over the last several years. The goal of this monograph is to bring together these relationships for beams and plates in a single volume.
The book is divided into two parts. Following the introduction, Part 1 consists of Chapters 2 to 5 dealing with beams, and Part 2 consists of Chapters 6 to 13 covering plates. Problems are included at the end of each chapter to use, extend, and develop new relationships.
Part and chapter headings: Preface. Introduction. An overview of plate theories. Beams. Bending of Beams. Beam theories. Relationships between EBT and TBT. Relationships between EBT and RBT. Shear-Flexural Stiffness Matrix. Summary of relationships. Stiffness matrix. Buckling of Columns. Relationship between Euler-Bernoulli and Timoshenko columns. Relationship between Euler-Bernoulli and Reddy-Bickford columns. Tapered Beams. Stress resultant-displacement relations. Deflection and force relationships. Symmetrically laminated beams. Plates. Theories of Plate Bending. Classical (Kirchhoff) plate theory (CPT). First-order shear deformation plate theory (FSDT). Third-order shear deformation plate theory (TSDT). Bending Relationships for Simply Supported Plates. Relationships between CPT and FSDT. Relationships between CPT and TSDT. Bending Relationships for Lévy Solutions. Governing equations. Bending relationships. Bending Relationships for Circular and Annular Plates. Relationships between CPT and FSDT. Relationships between CPT and TSDT. Bending Relationships for Sectorial Plates. Formulation. Exact bending relationships. Buckling Relationships. Polygonal plates. Circular plates. Sectorial mindlin plates. Free Vibration Relationships. Relationships between CPT and FSDT. Relationships between CPT and TSDT. Relationships for Inhomogeneous Plates. Deflection relationships for sandwich plates. Deflection relationships for functionally graded circular plates. Buckling load relationships for sandwich mindlin plates. Free vibration relationships for sandwich plates. Subject index.