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: 9781483187198

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Introduction to the Theory of Shells provide a brief introduction to the foundations of shell theory, and to some of the important problems that can be tackled within the framework of shell theory. The book discusses topics on the Lamé problem and derivation of beam theory; the basic postulates, or assumptions of shell theory; membrane shells and the bending of circular cylinders; and axisymmetric vibrations of circular cylinders. Mathematicians and students of mathematics will find the book invaluable.

Table of Contents

  • Preface

    I. Preludes

    The Lame 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)

    0 IIIB. Strain-Displacement Relations in Curvilinear Coordinates

    0 IIIC. Verification of 'Equation (67)

    0 IIID. Alternate Derivation of the Equilibrium Equations

    0 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

    0 IVB. Stresses in an Ogival Dome

    V. The Bending of Circular Cylinders

    Basic Relations and Simplifications

    The Donnelly Sanders and Flugge 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

    0 VB. Influence Coefficients for the Axisymmetric Cylinder

    0 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: 9781483187198

About the Author

Clive L Dym

About the Editor

B. G. Neal

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