Theory of Elastic Thin Shells
Solid and Structural Mechanics
Published on 15. May 2014
680 pages
978-1-4831-6462-5 (ISBN)
Description
Theory of Elastic Thin Shells discusses the mathematical foundations of shell theory and the approximate methods of solution. The present volume was originally published in Russian in 1953, and remains the only text which formulates as completely as possible the different sets of basic equations and various approximate methods of shell analysis emphasizing asymptotic integration. The book is organized into five parts. Part I presents the general formulation and equations of the theory of shells, which are based on the well-known hypothesis of the preservation of the normal element. Part II is devoted to the membrane theory--the most widely used approximate method of analysis of shells that was formulated at approximately the same time as the more general bending theory. In Part III methods of analysis of circular cylindrical shells with the aid of trigonometric series are considered. Part IV is essentially mathematical in character and its purpose is to justify the approximate methods of shell analysis. In Part V approximate methods of analysis of shells are formulated.
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Content
Translation Editor's Preface to English Edition Author's Preface to English Edition PrefacePart I Basic Relations in the Theory of Shells Chapter 1. Brief Outline of the Theory of Surfaces 1. Curvilinear Coordinates on a Surface and the First Quadratic Form 2. Basic and Auxiliary Trihedra of a Surface. Decomposition of an Arbitrary Vector Along Axes of Basic and Auxiliary Trihedra 3. Gauss-Weingarten Derivative Formulas. Codazzi-Gauss Equations 4. Resolution of Derivatives of an Arbitrary Vector along the Axes of the Basic and Auxiliary Trihedra 5. Second Quadratic Form of a Surface and Dupin's Indicatrix 6. Conjugate Lines, Lines of Curvature, Asymptotic Lines 7. Gaussian Curvature and Bending of Surfaces 8. Fundamental Formulas of the Theory of Surfaces in Orthogonal Coordinates Chapter 2. Static and Geometric Relations of the Theory of Shells 9. Forces and Moments 10. Forces and Moments along Oblique Sections 11. External Loads 12. Equilibrium Equations of the Shell 13. Stress Functions 14. Vectors of Elastic Displacement and of Elastic Rotation of the Middle Surface 15· Components of Tangential Deformation (Strain) of the Middle Surface of the Shell 16. Expansions for the Derivatives of the Vector of Elastic Displacement 17· Components of Bending Deformation (Strain) of the Middle Surface 18. Expressions for Derivatives of the Vector of Elastic Rotation 19· Expressions for Components of Deformation and Angles of Rotation in Terms of Displacements 20· Determination of Displacements on the Basis of Given Components of Deformation. Equations of Compatibility of Strain 21. Transformation of Components of Strain Chapter 5. Relations of Elasticity. General Theorems of the Theory of Shells 22. Fundamental Hypothesis of the Theory of Shells 23. Relations of Elasticity 24. Supplementary Equations of the Theory of Shells 25. Work of Forces and Moments, of Thin Shells 26. Strain Energy 27· Analysis of Some Variants of Elasticity Relations Chapter 4. Fundamental Equations of the Theory of Shells 28. Summary of Fundamental Relations of the Theory of Shells 29· Complete System of Equations of the Theory of Shells 30. Static-Geometric Analogy 31. Equations of Compatibility in Terms of Forces and Moments 32. Equations of Equilibrium in Terms of Displacements 33· Boundary Conditions Part II Membrane Theory Chapter 5· Membrane Theory of Shells of Arbitrary Shape 1. General Assumptions of Membrane Theory 2. Static, Geometric and Mixed Problems of Membrane Theory 3. Boundary Conditions in Membrane Theory 4· Three Classes of Membrane Shells 5· Relations between Membrane Theory and the Theory of Infinitesimal Flexures of Surfaces 6. Conjugate Geometric and Static Problems of Membrane Theory 7· Membrane Shell of Positive Curvature with One Geometric Condition Chapter 6. Membrane Theory of Shells of Zero Curvature 8. Curvilinear Coordinates on Cylindrical and Conical Surfaces 9. General Integral of Equations of Membrane Theory of Shells of Zero Curvature 10. Boundary Conditions 11. Examination of the State of Stress of a Cylindrical Membrane Shell 12. Examples of Analysis of Cylindrical Membrane Shells 13. Examples of Analysis of Cylindrical Membrane Shells, Continued Chapter 7. Membrane Theory of Spherical Shells 14. Transformation of Membrane Equations of a Spherical Shell 15. Integration Methods for the Equations of Membrane Theory of Spherical Shells 16.
