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Theory of Elastic Thin Shells Solid and Structural Mechanics 1st Edition - January 1, 1961
Author: A. L. Gol'Denveizer
Editors: Th. Von Kármán, H. L. Dryden
eBook ISBN: 9781483164625 9 7 8 - 1 - 4 8 3 1 - 6 4 6 2 - 5
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… Read more
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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.
Translation Editor's Preface to English Edition Author's Preface to English Edition Preface Part 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. Application of the Methods of the Theory of Functions of a Complex Variable to the Analysis of Spherical Membrane Shells 17. Integral Equations of Equilibrium 18. Static Meaning of Poles of the Complex Stress Function Chapter 8. Analysis of Closed Spherical Membrane Shells 19. Analysis of Closed Spherical Membrane Shells under the Action of Concentrated. Forces and Moments 20. Example 21. Displacements of a Closed Spherical Shell Subjected to Concentrated forces and Moments 22. Analysis of Closed Spherical Membrane Shells Subjected to Distributed Loads 23. Generalizations Chapter 9. Analysis of Membrane Shells Taking Boundary Conditions into Account 24. The Simplest Problems in Which Account Must be Taken of Boundary Conditions 25. Examples 26. Number of Solutions of Static and Geometric Problems for Membrane Shells of Positive Curvature 27. Examples of Statically Determinate and Geometrically Variable Membrane Shells Part III Circular Cylindrical Shells Chapter 10. Method of Expansion in Trigonometric Series 1. Basic Equations of the Theory of Cylindrical Shells 2. The Solving Equation of Circular Cylindrical Shells 3. Application of Trigonometric Series to the Analysis of Circular Cylindrical Shells Chapter 11. Analysis of Closed Cylindrical Shells 4. Basic Formulas for Analysis 5. Properties of Roots of the Characteristic Equation. Simplification of the Characteristic Equation 6. Physical Meaning of Zero Roots of the Characteristic Equation 7. Analysis of the State of Stress of Closed Cylindrical Shells 8. Approximate Methods of Analysis of the Basic State of Stress of Circular Cylindrical Shells 9. Approximate Methods of Analysis of Edge Effects 10. States of Stress Corresponding to Large Values of m 11. Imposition of Boundary Conditions Chapter 12. Analysis of Open Cylindrical Shells 12. Basic Formulas for Analysis 13. Properties of Roots of Characteristic Equation 14. Analysis of the State of Stress in Open Cylindrical Shells 15. Approximate Methods of Analysis of Open Cylindrical Shells 16. Imposition of Boundary Conditions Part IV Analysis of the State of Stress in an Arbitrary Shell Chapter 15. Asymptotic Integrations of Partial Differential Equations 1. Classification of Linear Differential Operators with Partial Derivatives 2. Nomenclature and Notations 3. Asymptotic Expansion of Integrals of a Homogeneous Differential Equation 4. Three Fundamental Cases 5. Construction of Functions of Variation 6. Integrals with Given Non-Characteristic Supporting Contour 7. Case of Multiple Characteristics 8. Integrals with Given Characteristic Supporting Contour 9. Asymptotic Expansion of Particular Solution of a Nonhomogeneous Partial Differential Equation 10. Example Chapter 14. Asymptotic Integration of Equations of the Theory of Shells 11. Asymptotic Integration of a System of Equations 12. Non-Contradictory values of Indices of Intensity 13. Construction of Functions of Variation 14. Determination of Coefficients of Asymptotic Expansion of Functions of Intensity for Fundamental Integrals 15. Construction of Approximate Equations of the Theory of Shells 16. Asymptotic Error of Equations of Membrane Theory 17· Elementary States of Stress in an Arbitrary Shell 18. The Complete State of Stress in an Arbitrary Shell Chapter 15. Elementary States of Stress 19. Fundamental State of Stress. Membrane and Pure Bending States of Stress 20. Approximate Equations for States of Stress with Large Indices of Variation 21. Region of Applicability of Equation (20.ll) 22. Simple Edge Effect 23. Integration of the Solving Equation of Simple Edge Effect 24. Solving Equations of Non-degenerate Generalized Edge Effects 25. Solving Equations of Generalized Edge Effect in a Shell of Zero Curvature 26. Range of Applicability of Solving Equations (25.5) 27. Further Simplification of Solving Equations (25.5) 28. Range of Applicability of Membrane Theory in the Analysis of Shells of Zero Curvature 29. Estimating the Accuracy of Construction of a Complete State of Stress Part V Approximate Methods of Analysis of Shells Chapter 16. Application of Expansions in Orthogonal Functions to the Analysis of Shells 1. Expansion of Functions in Fourier Series 2. Methods of Construction of Closed Orthogonal Systems of Functions 3. Continuation 4. Index of Variation of the State of Stress and of External Loading Chapter 17. General Approximate Methods 5. Membrane Theory 6. Region of Applicability of Membrane Theory 7. Properties of the Simple Edge Effect 8. Approximate Theory of the Simple Edge Effect 9. Analysis of Shells by the Membrane Theory with Consideration of Edge Effects 10. Particular Cases 11. Example 12. Approximate Methods of Analysis of Shells with Large Indices of Variation 13. Example 14. Shells with Non-rigidly Supported Edges Chapter 18. Cylindrical and Conical Shells 15. The Generalized Edge Effect in a Shell of Zero Curvature 16. The Solving Equations of the Generalized Edge Effect in Shells of Zero Curvature 17. Integration of the Solving Equations of the Generalized Edge Effect for Cylindrical Shells 18. Imposition of Boundary Conditions . 19. Integration of Equations of the Generalized Edge Effect for Conical Shells 20. Analysis of the State of Stress of Shells of Zero Curvature 21. Approximate Theory of the Non-degenerate Edge Effect 22. Integration of Equations of the Non-degenerate Edge Effect for Cylindrical and Conical Shells 23. Integration of System (22.9) 24. Continuation 25. Tables of Elastic Reactions and of Elastic Displacements of Cylindrical Shells of Medium Reduced Length 26. Example 27. Analysis of Cylindrical Shells of Medium Reduced Length Subjected to Loads Distributed along a Generator 28. Example 29. Analysis of Conical Shells Author's Addendum to English Edition (Some Mathematical Problems of the Linear Theory of Elastic Thin Shells) Author's Amendments Author Index Subject Index
Published: January 1, 1961
eBook ISBN: 9781483164625
Th. Von Kármán Affiliations and expertise
Case Institute of Technology, Cleveland, Ohio H. L. Dryden Affiliations and expertise
Case Institute of Technology, Cleveland, Ohio