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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.
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
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
- No. of pages:
- © Pergamon 1974
- 1st January 1974
- eBook ISBN:
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