Shear Deformable Beams and Plates: Relationships with Classical Solutions

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Overview

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.

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

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Editorial Reviews

Booknews
Because the classical Euler-Bernoulli/Kirchoff theories do not provide very good analysis of shear deformity in beams and plates in which the thickness-to-length ratio is relatively large, Wang (civil engineering, National U. of Singapore), J. N. Reddy (mechanical engineering, Texas A&M U.-College Station) and K. H. Lee (mechanical and production engineering, National U. of Singapore) describe shear deformation theories that are much more accurate. However, these theories are also much more complicated, so they, synthesizing the work of researchers over the past few years, also show relationships between the findings of the two approaches, allowing shear deformation results to be obtained from the results of classical theories. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780080437842
  • Publisher: Elsevier Science
  • Publication date: 8/2/2000
  • Pages: 312
  • Product dimensions: 6.00 (w) x 8.90 (h) x 1.00 (d)

Table of Contents

Part and chapter headings: Preface. Introduction. Beams. Bending of Beams. Shear-Flexural Stiffness Matrix. Buckling of Columns. Tapered Beams. Plates. Theories of Plate Bending. Bending Relationships for Simply Supported Plates. Bending Relationships for Lévy Solutions. Bending Relationships for Circular and Annular Plates. Bending Relationships for Sectorial Plates. Buckling Relationships. Free Vibration Relationships. Relationships for Inhomogeneous Plates. Subject index.
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