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