Shells of revolution
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Bibliographic Information
Shells of revolution
（Developments in civil engineering, v. 30）
Elsevier , Polish Scientific Publishers, 1991
- Other Title
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Powłoki obrotowe sprężyste
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Translation of: Powłoki obrotowe sprężyste
Includes bibliographical references
Description and Table of Contents
Description
The very early diverse application of shells of revolution, first in architecture and later in structures serving other purposes, led to the publication of many extensive studies concerned with the theory and methods of solving various problems relating to the mechanics of these structures. The work presented here gives a comprehensive treatise on the development of the linear theory of elastic shells of revolution, based upon analytical methods of investigating their mechanical properties. The volume reviews the fundamentals of the theory of perforated shells, presents the derivation of the Meissner-type equations in a generalized form valid for a large class of shells and extends the application of the method of undetermined coefficients for static and dynamic problems. Each part of the book begins with derivations of the basic equations of shells of arbitrary shape. This enables the reader to familiarize himself to a large extent with the fundamentals of the general linear theory of shells. Each of the three parts of the book and even the chapters can be studied separately.
Table of Contents
- 1. Introduction.Selected formulae of differential geometry. Selected equations from elasticity theory. Parts: I. Thin Continuous Shells. 2. Foundations of the general theory of shells.The Kirchoff-Love Theory. Vlasov's simplified theory and the theory of shallow shells. 3. Shells of Revolution of Arbitrary Meridian. Arbitrary state of loading. Rotationally symmetric and antisymmetric states of loading. 4. Statics and dynamics of spherical shells.Basic equations. Solution algorithm for displacements. Solution of the equations of Vlasov's theory. Solution for a shallow shell. A solution of Reissner's equations. 5. Statics and dynamics of conical shells. Basic equations. Solution algorithm for equations of motion expressed in terms of displacements. Solution of the governing equations of Vlasov's theory. Solution of Meissner's equations. 6. Statics and dynamics of cylindrical shells.Basic equations. Solution algorithm of equations of motion in terms of displacements. Solution of the equations of Vlasov's theory. Rotationally-symmetric bending. 7. Shells of atypical shape. Basic equations for certain shells. Rotationally-symmetric bending of shallow shells of atypical shape. 8. Membrane theory of shells.Assumptions and basic equations in curvature coordinates. Shells of revolution of arbitrary meridian. Spherical shell. Conical shell. Cylindrical shell. Hyperboloidal and toroidal shells under rotationally-symmetric loading. 9. Approximate calculations by the edge effect method.Assumptions and basic equations. Edge effects. Examples. 10. Foundations of theory of thin layered shells.Assumptions and equations of theory in curvature coordinates. Equations for shells of revolution. II. Shells of Moderate Thickness. 11. Foundations of theory of moderately-thick shells.Equations of the theory in curvature coordinates. Shells of revolution: Meissner-type equations for rotationally symmetric bending. 12. Spherical shell.Refined equations. Rotationally-symmetric bending state
- Reissner-type equations. A solving algorithm of the problem. Application of power series. 13. Cylindrical shell. Refined equations. Rotationally-symmetric bending state
- Meissner-type equations. Solution algorithm for the problem
- Example. III. Perforated Shells. 14. Foundations of the theory of perforated shells.Equations of the theory in curvature coordinates. Shells of revolution under rotationally-symmetric loading. 15. Spherical shells. Equations. Application of real power series. Application of complex power series. Determination of quantities independent of boundary conditions
- Examples. 16. Cylindrical shells. Equations. Solution algorithm. Various cases of loading
- example. References. Index.
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