Synopsis
This book is a first monographic treatise comprising one hundred years of development of the linear theory of elastic shells of revolution. The investigation of their mechanical properties is based upon analytical methods. The content of the book is carefully arranged. The original authors' contribution to the theory as well as new results are put forward, the hitherto existing theories and results being exhaustively encompassed. In particular, the book provides 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 in the static and dynamic problems. The monograph provides a variety of algorithms for solving static or dynamic problems of shells of various shapes and boundary conditions, subjected to various types of loading. Efficiency of these algorithms follows from the given examples. All algorithms are based on analytical methods, both known and new ones, in particular those based on the special functions and the functions defined by power series whose coefficients are determined by appropriate recurrence formulae. Not only is the efficiency of the applied analytical methods competitive in comparison with contemporarily popular numerical methods, but they will also provide the reader with benchmark examples for testing new computational algorithms and programmes. Each of the three parts of the book can be studied separately. The bibliography consists of 152 items and it also includes the references which have been directly used in the course of writing this monograph.
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Shells of Revolution
Seller: killarneybooks, Inagh, CLARE, Ireland
Seller rating 5 out of 5 stars
Hardcover. Condition: Good. Cloth hardcover, ix+ 618 pages, NOT ex-library. Weight: 1335g. Very good interior: clean and bright with unmarked text, free of inscriptions and stamps. External age-spotting on upper page edges. Dust jacket shows short edge-nicks, gently frayed spine ends, faint shelfworn marks. -- Contents: 1. Introduction [Scope and Object; Selected Formulas of Differential Geometry; Selected Equations from Elasticity Theory]; Part I Thin Continuous Shells 2. Foundations of the General Theory of Shells [Basic Equations of the Kirchhoff-Love Linear Theory of Shells; Vlasov's Simplified Theory and the Theory of Shallow Shells] 3. Shells of Revolution of Arbitrary Meridian [Arbitrary State of Loading; Rotationally-Symmetric State 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; 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 Displacement 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; Analysis of the Edge Effects; Examples of Applications of the Edge Effect Method] 10. Foundations of the Theory of Thin Layered Shells [Assumptions and Equations of the Theory in Curvature Coordinates; Equations for Shells of Revolution]; Part II Shells of Moderate Thickness 11. Foundations of the 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; Solving Algorithm. Application of Power Series; Example] 13. Cylindrical Shell ["Refined" Equations; Rotationally-Symmetric Bending State. Meissner-Type Equations; Solution Algorithm for the Problem; Example] Part 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 Shell [Equations; Application of Real Power Series; Application of Complex Power Series (Hypergeometric Functions); Determination of Quantities Independent of Boundary Conditions. Examples] 16. Cylindrical Shell [Equations; Solution Algorithm; Various Cases of Loading. Example]; References; Subject Index -- First monographic treatise comprising 100 years of development of the linear theory of elastic shells of revolution. The investigation of their mechanical properties is based on analytical methods. The book provides 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 in the static and dynamic problems. It offers a variety of algorithms for solving static or dynamic problems of shells of various shapes and boundary conditions, subjected to various types of loading. Each of the book's three parts can be studied separately. Seller Inventory # 009407