Theory of Flexible Shells book cover

Theory of Flexible Shells

Engineers and researchers concerned with the problems of thin-walled structures have a choice of books on shell theory. However, the almost exclusive concern of these books are shells designed for maximum strength and stiffness. Shells which are designed for maximum elastic displacements (flexible shells) have been used in industry for decades, but are largely ignored in shell-theory books due to tradition and to the wide variety of shapes and problems involved.This book presents the general theory of elastic shells and the deformation inherent in flexibility. For the analysis of stability of the two-dimensionally variable large elastic deformations, a local approach is developed.The specialized theory is then applied to the basic problems of flexible shells - tubes, open-section beams and shells of revolution. The results of parametric studies are presented in numerous graphs.

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Published: July 1987

Imprint: North-holland

ISBN: 978-0-444-87954-7

Contents

  • 1. Foundations of Thin-Shell Theory. Shell Geometry. Deformation of the Reference Surface. Hypotheses of the Theory. Shell Deformation. Equilibrium Equations. Elastic Energy. Constitutive Equations. Boundary Conditions. Temperature Effects. Static-Geometric Analogy. Novozhilov's Equations. The Donnell Equations and the Membrane Model of a Shell. 2. Flexible Shell Theory. Basic Flexible-Shell Problems. Reissner Equations. Schwerin-Chernina Equations. Governing Equations and the Model of Flexible Shell. Semi-Momentless Equations. Linear and Nonlinear Approximations. Matrix Form of Operations with Trigonometric Series. Trigonometric-Series Solution. 3. Tubes. Basic Problems of Tube Analysis. Bending of Long Curved Tubes. Noncircular Long Tubes. Lateral and Out-of-Plane Bending. Torsion. Tubes with Given Conditions on the Edges. Tubes of Unrestricted Curvature. Nonlinear Bending of Tubes with Given Conditions on Edges. Collapse of Bent Cylinder Shells and Curved Tubes. Buckling of Tubes and Torus Shells under External Pressure. Bourdon Tubes. Layered Tubes. 4. Open-Section Beams. Open Circular Section. Shallow Profiles. Profiles Allowing a Closed-Form Solution. Bimetallic Strip. 5. Flexible Shells of Revolution. Basic Problems. Bellows under Axial Tension and Normal Pressure. Bellows with Edge Constraints. Lateral Bending and Stability of Bellows. Torus Shell. References.

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