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.
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
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- © Pergamon 1974
- 1st January 1974
- eBook ISBN: