Introduction to the Theory of Shells

Introduction to the Theory of Shells

Structures and Solid Body Mechanics

1st Edition - January 1, 1974

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  • Author: Clive L Dym
  • eBook ISBN: 9781483136677

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Introduction to the Theory of Shells centers on the foundations of shell theory, and to some of the important problems that can be tackled within the framework of shell theory. Organized into seven chapters, this book begins with an explanation of the elements of the theory of surfaces and the construction of a shell theory. Subsequent chapter describes a class of shells known as membrane shells, or membranes. Other chapters detail the bending of circular cylinders; shells of revolution; and axisymmetric vibrations of circular cylinders. This book will be useful as a text that represents a one-semester beginning for students with a reasonable (first course) background in elasticity theory.

Table of Contents

  • Preface

    I. Preludes

    The Lama Problem

    A Derivation of Beam Theory

    II. The Theory of Surfaces

    The First Fundamental Form

    Curvature and the Second Fundamental Form

    The Gauss-Codazzi Conditions and the Fundamental Form

    The Surface of Revolution

    Some Terminology for Surfaces

    III. The Construction of a Shell Theory

    The Basic Assumptions

    Shell Coordinates

    Strain-Displacement Relations

    Stress Resultants and Strain Energy

    Equations of Equilibrium

    Simplifications of the Strain Energy Functional and the Stress-Strain Relations

    The Kirchoff Boundary Conditions

    Appendix IIIA. Verification of Equation (56)

    Appendix IIIB. Strain-Displacement Relations in Curvilinear Coordinates

    Appendix IIIC. Verification of Equation (67)

    Appendix IIID. Alternate Derivation of the Equilibrium Equations

    Appendix IIIE. Strain Parameter Values for Rigid Body Motions

    IV. Membrane Shells

    General Formulation of Membrane Theory

    Shells of Revolution with Straight Generators

    Some Examples of Axisymmetric Shells of Revolution

    Appendix IVA. Stresses in a Pressurized Oval Cylinder

    Appendix IVB. Stresses in an Ogival Dome

    V. The Bending of Circular Cylinders

    Basic Relations and Simplifications

    The Donnell, Sanders and Flügge Equations

    The Axisymmetric, Semi-Infinite Cylinder

    Decay Lengths and Edge Effects

    The Donnell Equation and Some of Its Solutions for Asymmetric Deformation

    Appendix VA. Cylinders with Variable Wall Thickness

    Appendix VB. Influence Coefficients for the Axisymmetric Cylinder

    Appendix VC. The Maxwell-Betti Theorem

    VI. Shells of Revolution

    General Formulation and Uncoupling Procedures

    The Reissner-Meissner Theory of Axisymmetric Shells of Revolution

    The Geckeler Approximation for Steep Shells

    The Reissner Theory for Shallow Shells

    Appendix VIA. The Shell Mating Problem

    VII. Axisymmetric Vibrations of Circular Cylinders

    Free Vibrations—Frequencies, Mode Shapes, Orthogonality

    Forced Vibrations—Normal Modes Solution

    Forced Vibrations—Williams' Method for Time-Dependent Boundary Conditions



Product details

  • No. of pages: 172
  • Language: English
  • Copyright: © Pergamon 1974
  • Published: January 1, 1974
  • Imprint: Pergamon
  • eBook ISBN: 9781483136677

About the Author

Clive L Dym

About the Editor

B. G. Neal

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