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Small elastic deformations of thin shells

Author: Paul Seide
Publisher: Leyden : Noordhoff International Pub., 1975.
Series: Monographs and textbooks on mechanics of solids and fluids.; Mechanics of surface structures, v. 1.
Edition/Format:   Print book : EnglishView all editions and formats
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Additional Physical Format: Online version:
Seide, Paul.
Small elastic deformations of thin shells.
Leyden : Noordhoff International Pub., 1975
(OCoLC)609624019
Document Type: Book
All Authors / Contributors: Paul Seide
ISBN: 9028600647 9789028600645
OCLC Number: 1601799
Description: xvi, 654 pages ; 24 cm.
Contents: I The Linear Theory of Shells.- 1 Geometry of Surfaces.- 1.1 Geometric Relations for Surfaces.- 1.2 Lines of Curvature.- 1.3 Surfaces of Revolution.- 1.4 Parallel Surfaces.- 1.5 Small Deformations of a Surface.- 2 The Linear Theory of Transversely Rigid Shells.- 2.1 Fundamental Definitions.- 2.2 Equations of Three-Dimensional Elasticity.- 2.3 Assumptions of Shell Theory.- 2.4 Displacements and Strains.- 2.5 Stress Resultants and Equilibrium Equations.- 2.6 Statically Equivalent Force Systems.- 2.7 Overall Force-Strain Relations.- 2.8 The Principle of Virtual Work and Boundary Conditions.- 2.9 Strain Energy and the Principle of Minimum Potential Energy.- 2.10 Stress Functions.- 2.11 Transverse Shear and Normal Stresses.- Appendix Boundary Conditions at Edges which are Not Lines of Curvature.- 3 Simplifications of Shell Theory.- 3.1 Modification of Overall Force-Strain Relationships.- 3.2 Internal Stress Distribution.- 3.3 Approximate Reduction of Shell Theory: Vlasov's Equations.- 3.4 Shallow Shells.- 3.5 Exact Reduction of Shell Theory for Zero Poisson's Ratio (I) Complex Stress Resultants.- 3.6 Exact Reduction of Shell Theory for Zero Poisson's Ratio (II) Complex Displacements.- 3.7 Approximate Reduction of Shell Theory for Nonzero Poisson's Ratio.- 3.8 The Membrane Theory of Shells.- 3.9 Transformation of the Equations of Membrane Theory.- II Axisymmetric Deformations of Shells of Revolution.- 4 The Cylindrical Shell.- 4.1 General Relations for Cylindrical Shells.- 4.2 Edge-Loaded Cylindrical Shells.- (A) Semi-Infinite Cylinder.- (B) Symmetrically Loaded Finite Cylinder.- (C) Antisymmetrically Loaded Finite Cylinder.- (D) Finite Cylinder Loaded at One Edge.- 4.3 Particular Integrals for Surface-Loaded Cylindrical Shells.- 4.4 Some Solutions of Cylindrical Shell Problems.- (A) Compressed Cylinder with Rigid End Rings.- (B) Pressurized Cylinder with Rigid Movable End Plates.- (C) Effect of Restraint of Longitudinal Movement.- (D) Effect of End Plate Flexibility.- 4.5 Pressurized Cylinder with an Abrupt Thickness Change.- 4.6 Cylinder in a Rigid Collar.- 5 The Conical Shell.- 5.1 General Relations for Conical Shells.- 5.2 Solution of the Homogeneous Deflection Equation.- 5.3 Edge-Loaded Conical Shells.- (A) Semi-Infinite Cones.- (B) Complete Cones.- (C) Finite Conical Frustums.- 5.4 Particular Solutions of the Conical Shell Equations.- 5.5 Complete Conical Shell Subjected to External Pressure.- 6 The Spherical Shell.- 6.1 General Relations for Spherical Shells.- 6.2 A Particular Solution of the Bending Equations.- 6.3 Some Relations for the Complementary Solution.- 6.4 Solutions by Means of Legendre Functions.- 6.5 Shallow Spherical Shells.- 6.6 Closed Spherical Cap under Edge Loading.- 6.7 Tangent Cone Approximation.- 6.8 Particular Solutions for Spherical Shells.- 6.9 Complete Sphere Subjected to Internal or External Pressure.- 6.10 Spherical Shell with Concentrated Loads at the Poles.- 6.11 Spherical Cap Loaded at the Apex.- 6.12 Effect of Method of Load Application.- 7 Shells of Arbitrary Meridian.- 7.1 General Equations for Arbitrary Shells of Revolution.- 7.2 An Approximate Complementary Solution of the Bending Equations.- 7.3 The Variable ?.- 7.4 Approximate Complementary Solutions Valid at Points with Horizontal Tangents.- 7.4.1 The Ellipsoidal Shell.- 7.4.2 The Circular Toroidal Shell.- 7.5 Membrane Theory as a Particular Solution of the Bending Equations.- 7.6 Some Particular Solutions for Circular Toroidal Shells.- 8 Torsion and Circumferential Bending of Shells of Revolution.- 8.1 Torsion of Shells of Revolution.- 8.2 Circumferential Bending of Shells of Revolution.- III Asymmetrically Loaded Shells.- 9 Asymmetric Deformations of Spherical Shells.- 9.1 General Relations for Asymmetrically Loaded Spherical Shells.- 9.2 'Wind' Loading of Spherical Shells.- 9.3 Edge-Loaded Spherical Shells: Inextensional Deformations and Membrane Stress States.- 9.4 Complex Variable Representation of Membrane Stress States.- 9.5 Edge-Loaded Spherical Shells: Mixed Bending-Stretching Solutions.- 9.6 Bending of a Spherical Shell by Moments at the Poles: Exact Solution.- 9.7 Bending of a Spherical Shell by Moments at the Poles: Shallow Shell Theory.- 9.8 Bending of a Spherical Shell by Tangential Loads.- 9.9 Some Other Problems of Edge-Loaded Spherical Shells.- 9.10 Surface-Loaded Spherical Shells.- 10 Asymmetric Deformations of Circular Cylindrical Shells.- 10.1 General Relations for Cylindrical Shells.- 10.2 Simplifications of the Equations for Radial and Edge Loading.- 10.3 Cylinders Loaded Along Circular Edges.- 10.4 End-Loaded Cantilevered Cylinder with a Rigid End Ring.- 10.5 Infinite Cylindrical Shell Loaded By Diametrically Opposed Concentrated Loads.- 10.6 Results for Some Other Concentrated Loads.- 10.7 Particular Solutions for Complete Cylindrical Shells.- 10.8 Edge-Loaded Cylindrical Strips.- 10.9 Infinite Cylindrical Strips.- 10.10 Stress Concentration Around Holes.- 10.10.1 Effect of a Hole on a Circular Cylinder under Uniform Tension.- 11 Results for Other Shells.- 11.1 'Wind' Loading of Arbitrary Shells of Revolution.- 11.2 Conical Frustums Subjected to End Loads.- 11.3 Numerical Solution of the Bending Equations for Shells Of Revolution.- 11.4 Shallow Translational Shells.- 11.5 Finite Element Analysis of Shells of Arbitrary Middle Surface.- 12 Nonuniform Anisotropic Shells.- 12.1 Necessity for Modifications of the Theory of Shells.- 12.2 Effect of Thermal Loading.- 12.3 Effect of Nonuniform Wall Thickness.- 12.3.1 Derivation of Equations for Shells of Nonuniform Wall Thickness.- 12.3.2 Axisymmetric Deformations of Nonuniformly Thick Shells of Revolution.- 12.3.3 Cylindrical Shell of Linearly Varying Thickness.- 12.3.4 Conical Shell of Linearly Varying Thickness.- 12.4 Effects of Anisotropy.- 12.5 Layered Shells.- 12.6 Stiffened Shells.- IV Dynamics of Shells.- 13 Free Vibrations of Shells.- 13.1 Equations of Motion.- 13.2 Free Harmonic Vibrations.- 13.3 Orthogonality Conditions for Vibration Mode Shapes.- 13.4 Free Vibrations of Cylindrical Shells.- 13.4.1 Simply Supported Cylindrical Shells.- 13.4.2 Minimum Frequency of Vibration.- 13.4.3 Effects of Other Edge Conditions.- 13.5 Free Vibrations of Spherical Shells.- 13.5.1 Vibrations of Spherical Shell Segments.- 13.5.2 Torsional Vibrations of Spherical Caps.- 13.5.3 Approximate Solutions for Shallow Spherical Caps.- 13.5.4 Vibrations of Complete Spherical Shells.- 13.6 Vibration Characteristics of Conical Shells.- 14 Response of Shells to Dynamic Loading.- 14.1 Solution of Initial Value Problems.- 14.2 Solution of Problems Involving Time-Dependent Surface or Edge Loading.- 14.3 Periodic Surface and Edge Forces.- 14.4 Solution of Problems Involving Time-Dependent Edge Displacements.- 14.5 Some Examples of Modal Analysis.- 14.6 Other Methods of Solution of Shell Response Problems.- Author Index.
Series Title: Monographs and textbooks on mechanics of solids and fluids.; Mechanics of surface structures, v. 1.
Responsibility: Paul Seide.
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