# Linear Elastic Theory of Thin Shells

## 1st Edition

### The Commonwealth and International Library: Structures and Solid Body Mechanics Division

**Authors:**J. E. Gibson

**Editors:**B. G. Neal

**eBook ISBN:**9781483180731

**Imprint:**Pergamon

**Published Date:**1st January 1965

**Page Count:**192

## Description

Linear Elastic Theory of Thin Shells presents membrane and bending theories for open and closed cylindrical shells and shells of arbitrary shape. This book aims to develop the analysis through membrane theory to bending theory for shells and to limit the type of mathematics used.

Organized into eight chapters, this book begins with an overview of the solid material enclosed between two closely spaced doubly curved surfaces. This text then examines the five stress resultants for closed cylindrical shell. Other chapters consider the theoretical stresses that are closely related to the actual stresses determined experimentally in practice. This book discusses as well the numerical analysis of more complicated shell structures. The final chapter deals with the correlation between experimental and theoretical stresses in shells.

This book is intended to be suitable for final year engineering and post-graduate students. Design and consulting engineers will also find this book extremely useful.

## Table of Contents

Preface

1 General Introduction to Shell Theory

1.1 Introduction

1.2 Reference Axes for Shell Surfaces

1.3 Membrane Stress Resultants

1.4 Bending Stress Resultants

1.5 Membrane Theory for Circular Cylindrical Shell

1.6 Horizontal Cylindrical Tank Supported at Ends

1.7 Vertical Cylindrical Tank Filled with Liquid

1.8 Cantilever Cylindrical Shell Subjected to Gravitational Load

2 Bending Theory of Closed Circular Cylindrical Shells Under Axisymmetric Loads

2.1 Introduction

2.2 Equations of Equilibrium

2.3 Membrane Strains

2.4 Bending Strains

2.5 Combined Strain of "z-Surface"

2.6 Strain-Stress Resultant Equations

2.7 Strain Displacement Equations

2.8 Curvature Displacement Equations

2.9 Stress Resultant Displacement Equations

2.10 Reduction to Compatibility Equation

2.11 Solution of Compatibility Equation

2.12 Cylindrical Tank Filled with Liquid

2.13 Cylindrical Pressure Vessel with Thick End Plates

2.14 Numerical Examples

3 Bending Theory of Open Circular Cylindrical Shells

3.1 Introduction

3.2 Equations of Equilibrium

3.3 Strain Displacement Equations of Middle Surface

3.4 Curvature Displacement Equations of Middle Surface

3.5 Strain-Stress Resultant Equations

3.6 Equation of Compatibility

3.7 Solution of Equation for Simply Supported Open Cylindrical Shell

3.8 Solution for Symmetrical Loading (Complementary Function)

3.9 Complementary Functions in Tabular Form

3.10 Particular Integral for Uniform Load

3.11 Boundary Conditions at a Free Edge

3.12 Numerical Examples

4 Membrane Theory for Shells of Revolution

4.1 Introduction

4.2 Equations of Equilibrium

4.3 Membrane Theory for Shells of Revolution Under Axisymmetric Load

4.4 Simply Supported Spherical Dome Under Axisymmetric Load

4.5 Spherical Storage Tank

4.6 Conical Shell

4.7 Numerical Example

5 Bending Theory for Shells of Revolution Under Axisymmetric Load

5.1 Introduction

5.2 Equations of Equilibrium

5.3 Strain Displacement Equations of Middle Surface

5.4 Curvature Displacement Equations of Middle Surface

5.5 Stress Resultant-Displacement Equations

5.6 Spherical Shells Under Axisymmetric Load

5.7 Simplified Theory for Spherical Shells Under Axisymmetric Load

5.8 Spherical Dome with Rigidly Fixed Edge

5.9 Spherical Dome with Simply Supported Edge

5.10 Comparison of Exact and Approximate Theories

5.11 Numerical Example

6 Membrane Theory for Shells of General Shape

6.1 Introduction

6.2 Geometry of Surface of General Shape

6.3 Membrane Equations of Equilibrium

6.4 Transformation of Equations of Equilibrium

6.5 Solution of Transformed Equations of Equilibrium

6.6 Hyperbolic Paraboloid

6.6.1 Uniform Vertical Load

6.6.2 Uniform Gravitational Load on hyperbolic Paraboloid

6.7 Parabolic Conoid

6.7.1 Membrane Analysis of Parabolic Conoid Under Uniform Gravitational Load

6.7.2 Boundary Conditions

6.7.3 Method of Solution

7 Analysis of Thin Shells for Bending and Membrane Stresses by Computer Programs

7.1 Introduction

7.2 Boundary Conditions for Open Multicylindrical Shells without Edge Beams

7.3 Solution of Boundary Conditions

7.4 Computer Program

7.5 General Multi-Open-Shell Program

7.6 Examples for General "Feather Edge" Multi-Shell Program

7.6.1 Partially Loaded Cylindrical Shell

7.6.2 Degenerate Theory for Plate Structures

7.6.3 Folded Plate Roof Under Wind Loading

7.6.4 Convergency of "Degenerate Theory" Solutions for Folded Plate Structures

7.7 Multi-Cylindrical Shell with Edge Beams

7.7.1 Stringer Bridge of Three Lanes

7.8 Further Programs for the General Analysis of Shell Structures

8 Experimental Investigation of Shells

8.1 Introduction

8.2 Investigation of Single Open Cylindrical Shell

8.3 Experimental Investigation of Large Scale Cylindrical Shell with Small Edge Beams

8.4 Investigation of Small Scale Multi-Cylindrical Shell

8.5 Investigation of Folded Plate Structure

8.6 Investigation of Closed Cylindrical Tank

8.7 Conclusions

References

Index

## Details

- No. of pages:
- 192

- Language:
- English

- Copyright:
- © Pergamon 1965

- Published:
- 1st January 1965

- Imprint:
- Pergamon

- eBook ISBN:
- 9781483180731