2nd Edition

Theory and Analysis of Elastic Plates and Shells

By J. N. Reddy Copyright 2007
    568 Pages 154 B/W Illustrations
    by CRC Press

    Because plates and shells are common structural elements in aerospace, automotive, and civil engineering structures, engineers must understand the behavior of such structures through the study of theory and analysis. Compiling this information into a single volume, Theory and Analysis of Elastic Plates and Shells, Second Edition presents a complete, up-to-date, and unified treatment of classical and shear deformation plates and shells, from the basic derivation of theories to analytical and numerical solutions.

    Revised and updated, this second edition incorporates new information in most chapters, along with some rearrangement of topics to improve the clarity of the overall presentation. The book presents new material on the theory and analysis of shells, featuring an additional chapter devoted to the topic. The author also includes new sections that address Castigliano's theorems, axisymmetric buckling of circular plates, the relationships between the solutions of classical and shear deformation theories, and the nonlinear finite element analysis of plates. The book provides many illustrations of theories, formulations, and solution methods, resulting in an easy-to-understand presentation of the topics.

    Like the previous edition, this book remains a suitable textbook for a course on plates and shells in aerospace, civil, and mechanical engineering curricula and continues to serve as a reference for industrial and academic structural engineers and scientists.

    PREFACE TO THE SECOND EDITION
    PREFACE
    ABOUT THE AUTHOR

    VECTORS, TENSORS, AND EQUATIONS OF ELASTICITY
    Introduction
    Vectors, Tensors, and Matrices
    Equations of Elasticity
    Transformation of Stresses, Strains, and Stiffnesses

    ENERGY PRINCIPLES AND VARIATIONAL METHODS
    Virtual Work
    Energy Principles
    Castigliano's Theorems
    Variational Methods

    CLASSICAL THEORY OF PLATES
    Introduction
    Assumptions of the Theory
    Displacement Field and Strains
    Equations of Motion
    Boundary and Initial Conditions
    Plate Stiffness Coefficients
    Stiffness Coefficients of Orthotropic Plates
    Equations of Motion in Terms of Displacements

    ANALYSIS OF PLATE STRIPS
    Introduction
    Governing Equations
    Bending Analysis
    Buckling under Inplane Compressive Load
    Free Vibration
    Transient Analysis

    ANALYSIS OF CIRCULAR PLATES
    Introduction
    Governing Equations
    Axisymmetric Bending
    Asymmetrical Bending
    Free Vibration
    Axisymmetric Buckling

    BENDING OF SIMPLY SUPPORTED RECTANGULAR PLATES
    Introduction
    Navier Solutions
    Lévy's Solutions

    BENDING OF RECTANGULAR PLATES WITH VARIOUS BOUNDARY CONDITIONS
    Introduction
    Lévy Solutions
    Approximate Solutions by the Ritz Method

    GENERAL BUCKLING OF RECTANGULAR PLATES
    Buckling of Simply Supported Plates under Compressive Loads
    Buckling of Plates Simply Supported along Two Opposite Sides and Compressed in the Direction Perpendicular to Those Sides
    Buckling of Rectangular Plates Using the Ritz Method

    DYNAMIC ANALYSIS OF RECTANGULAR PLATES
    Introduction
    Natural Vibration of Simply Supported Plates
    Natural Vibration of Plates with Two Parallel Sides Simply Supported
    Natural Vibration of Plates with General Boundary Conditions
    Transient Analysis

    SHEAR DEFORMATION PLATE THEORIES
    First-Order Shear Deformation Plate Theory
    The Navier Solutions of FSDT
    The Third-Order Plate Theory
    The Navier Solutions of TSDT
    Relationships between Solutions of Classical and Shear Deformation Theories

    THEORY AND ANALYSIS OF SHELLS
    Introduction
    Governing Equations
    Analytical Solutions of Thin Cylindrical Shells
    Analytical Solutions of Shells with Double Curvature
    Vibration and Buckling of Circular Cylinders

    FINITE ELEMENT ANALYSIS OF PLATES
    Introduction
    Finite Element Models of CPT
    Finite Element Models of FSDT
    Nonlinear Finite Element Models

    REFERENCES
    SUBJECT INDEX

    Summaries and Problems appear in every chapter.

    Biography

    J. N. Reddy

    Praise for the previous edition
    "This new book by J.N. Reddy digests more than two decades of research by him in plate theories (specially for thick plates and laminated composites), variational methods, and finite elements into an excellent textbook, which can be used very well by beginning or advanced graduate students, or by many engineers who deal with aerospace, automotive, and civil engineering structures. That is, the material is presented carefully and reasonably thoroughly in language that is easy to follow. This is the best textbook that this reviewer has seen for understanding the most important aspects of plate theory, and containing modern, important aspects of plate theory, which Timoshenko hardly could touch upon at all (in some cases they were not yet recognized topics), especially thick plates, laminated composites, and finite elements. And yet Reddy's book accomplishes good, useful introductions to all these topics in a mere 540 pages. Theory and Analysis of Elastic Plates is a textbook that clarifies the important aspects of plate theory, emphasizing its most important modern ones. For this purpose it is the best book available, in this reviewer's experience. As such it belongs on the bookshelves of every technical library, and every graduate student or engineer seriously interested in plates, and should become a widely used textbook in graduate-level courses."
    —Arthur W. Leissa, Ohio State University, Applied Mechanics Reviews