Gibson / Neal Linear Elastic Theory of Thin Shells

The Commonwealth and International Library: Structures and Solid Body Mechanics Division
1. Auflage 2014
ISBN: 978-1-4831-8073-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 192 Seiten, Web PDF

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.

Autoren/Hrsg.

Gibson, J. E.

Neal, B. G.

Inhaltsverzeichnis

1;Front Cover;1
2;Linear Elastic Theory of Thin Shells;4
3;Copyright Page;5
4;Table of Contents;6
5;PREFACE;10
6;CHAPTER
1. GENERAL INTRODUCTION TO SHELL THEORY;12
6.1;1.1. Introduction;12
6.2;1.2. Reference Axes for Shell Surfaces;13
6.3;1.3. Membrane Stress Resultants;13
6.4;1.4. Bending Stress Resultants;14
6.5;1.5. Membrane Theory for Circular Cylindrical Shell;16
6.6;1.6. Horizontal Cylindrical Tank Supported at Ends;20
6.7;1.7. Vertical Cylindrical Tank filled with Liquid;22
6.8;1.8. Cantilever Cylindrical Shell Subjected to Gravitational Load;23
7;CHAPTER
2. BENDING THEORY OF CLOSED CIRCULAR CYLINDRICAL SHELLS UNDER AXISYMMETRIC LOADS;27
7.1;2.1. Introduction;27
7.2;2.2. Equations of Equilibrium;29
7.3;2.3. Membrane Strains;31
7.4;2.4. Bending Strains;32
7.5;2.5. Combined Strain of "z surface";34
7.6;2.6.
Strain–Stress Resultant Equations;34
7.7;2.7. Strain Displacement Equations;37
7.8;2.8. Curvature Displacement Equations;39
7.9;2.9. Stress Resultant Displacement Equations;40
7.10;2.10. Reduction to Compatibility Equation;41
7.11;2.11. Solution of Compatibility Equation;42
7.12;2.12. Cylindrical Tank filled with Liquid;44
7.13;2.13. Cylindrical Pressure Vessel with Thick End Plates;47
7.14;2.14. Numerical Examples;50
8;CHAPTER
3. BENDING THEORY OF OPEN CIRCULAR CYLINDRICAL SHELLS;54
8.1;3.1. Introduction;54
8.2;3.2. Equations of Equilibrium;56
8.3;3.3. Strain Displacement Equations of the Middle Surface;58
8.4;3.4. Curvature Displacement Equations of the Middle Surface;61
8.5;3.5.
Strain–Stress Resultant Equations;62
8.6;3.6. Equation of Compatibility;63
8.7;3.7. Solution of Equation for Simply Supported Open Cylindrical
Shell;64
8.8;3.8. Solution for Symmetrical
Loading (Complementary Function);66
8.9;3.9. Complementary Functions in Tabular Form;69
8.10;3.10. Particular Integral for Uniform Load;71
8.11;3.11. Boundary Conditions at a Free Edge;75
8.12;3.12. Numerical Examples;76
9;CHAPTER 4. MEMBRANE THEORY
FOR SHELLS OF REVOLUTION;81
9.1;4.1. Introduction;81
9.2;4.2. Equations of Equilibrium;83
9.3;4.3. Membrane Theory for Shells of Revolution under Axisymmetric Load;87
9.4;4.4. Simply Supported Spherical Dome under Axisymmetrical Load;89
9.5;4.5. Spherical Storage Tank;91
9.6;4.6. Conical Shell;93
9.7;4.7. Numerical Example;95
10;CHAPTER 5. BENDING THEORY FOR
SHELLS OF REVOLUTION UNDER AXISYMMETRIC;96
10.1;5.1. Introduction;96
10.2;5.2. Equations of Equilibrium;98
10.3;5.3. Strain Displacement Equations of Middle Surface;102
10.4;5.4. Curvature Displacement Equations of the Middle Surface;104
10.5;5.5.
Stress Resultant–Displacement Equations;108
10.6;5.6. Spherical Shells under Axisymmetric Load;110
10.7;5.7. Simplified Theory for Spherical Shells under Axisymmetric Load;113
10.8;5.8. Spherical Dome with Rigidly Fixed Edge;116
10.9;5.9. Spherical Dome with Simply Supported Edge;118
10.10;5.10. Comparison of Exact and Approximate Theories;119
10.11;5.11. Numerical Example;121
11;CHAPTER
6. MEMBRANE THEORY FOR SHELLS OF GENERAL SHAPE;122
11.1;6.1. Introduction;122
11.2;6.2. Geometry of Surface of General Shape;122
11.3;6.3. Membrane Equations of Equilibrium;124
11.4;6.4. Transformation of Equations of Equilibrium;127
11.5;6.5. Solution of Transformed Equations of Equilibrium;128
11.6;6.6. Hyperbolic Paraboloid;129
11.7;6.7. Parabolic Conoid;137
12;CHAPTER 7. ANALYSIS OF THIN SHELLS FOR BENDING AND MEMBRANE
STRESSES BY COMPUTER PROGRAMMES;143
12.1;7.1. Introduction;143
12.2;7.2. Boundary Conditions for Open Multi-Cylindrical Shells
without Edge Beams;144
12.3;7.3. Solution of Boundary Conditions;148
12.4;7.4. Computer Programme;150
12.5;7.5. General Multi-Open-Shell Programme;151
12.6;7.6. Examples for General "Feather Edge"
Multi-Shell Programme;153
12.7;7.7. Multi-Cylindrical Shell with Edge Beams;165
12.8;7.8. Further Programmes for the General Analysis of Shell Structures;170
13;CHAPTER
8. EXPERIMENTAL INVESTIGATION OF SHELLS;172
13.1;8.1. Introduction;172
13.2;8.2. Investigation of Single Open Cylindrical Shell;173
13.3;8.3. Experimental Investigation of Large Scale Cylindrical Shell with Small Edge Beams;177
13.4;8.4. Investigation of Small Scale Multi-Cylindrical Shell;179
13.5;8.5. Investigation of Folded Plate Structure;183
13.6;8.6. Investigation of Closed Cylindrical Tank hinged at the Base and subjected to Hydrostatic Pressure;187
13.7;8.7. Conclusions;190
14;REFERENCES;191
15;INDEX;192