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" The Linearized Theory of Elasticity "
by William S. Slaughter.
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BL
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| Record Number
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573412
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b402631
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| Main Entry
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Slaughter, William S.
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| Title & Author
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The Linearized Theory of Elasticity\ by William S. Slaughter.
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| Publication Statement
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Boston, MA :: Birkhäuser Boston :: Imprint: Birkhäuser,, 2002.
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| ISBN
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9781461200932
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: 9781461266082
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| Contents
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1 Review of Mechanics of Materials -- 1.1 Forces and Stress -- 1.2 Stress and Strain -- 1.3 Torsion of Circular Cylinders -- 1.4 Bending of Prismatic Beams -- Problems -- 2 Mathematical Preliminaries -- 2.1 Scalars and Vectors -- 2.2 Indicial Notation -- 2.3 Tensors -- 2.4 Tensor Calculus -- 2.5 Cylindrical and Spherical Coordinates -- Problems -- 3 Kinematics -- 3.1 Configurations -- 3.2 Strain Tensors: Referential Formulation -- 3.3 Strain Tensors: Spatial Formulation -- 3.4 Kinematic Linearization -- 3.5 Cylindrical and Spherical Coordinates -- Problems -- 4 Forces and Stress -- 4.1 Stress Tensors: Referential Formulation -- 4.2 Stress Tensors: Spatial Formulation -- 4.3 Kinematic Linearization -- 4.4 Cylindrical and Spherical Coordinates -- Problems -- 5 Constitutive Equations -- 5.1 Elasticity -- 5.2 Constitutive Linearization -- 5.3 Material Symmetry -- 5.4 Isotropic Materials -- 5.5 Cylindrical and Spherical Coordinates -- Problems -- 6 Linearized Elasticity Problems -- 6.1 Field Equations -- 6.2 Boundary Conditions -- 6.3 Useful Consequences of Linearity -- 6.4 Solution Methods -- Problems -- 7 Two-Dimensional Problems -- 7.1 Antiplane Strain -- 7.2 Plane Strain -- 7.3 Plane Stress -- 7.4 Airy Stress Function -- Problems -- 8 Torsion of Noncircular Cylinders -- 8.1 Warping Function -- 8.2 Prandtl Stress Function -- Problems -- 9 Three-Dimensional Problems -- 9.1 Field Theory Results -- 9.2 Potentials in Elasticity -- 9.3 Dislocation Surface -- 9.4 Eshelby's Inclusion Problems -- Problems -- 10 Variational Methods -- 10.1 Calculus of Variations -- 10.2 Energy Theorems in Elasticity -- 10.3 Approximate Solutions -- Problems -- 11 Complex Variable Methods -- 11.1 Functions of a Complex Variable -- 11.2 Antiplane Strain -- 11.3 Plane Strain/Stress -- Problems -- Appendix: General Curvilinear Coordinates -- A.l General Vector Bases -- A.1.1 Covariant and Contravariant Components -- A.1.2 Reciprocal Bases -- A.l.3 Higher-Order Tensors -- A.2 Curvilinear Coordinates -- A.2.1 Cartesian Coordinates -- A.2.2 Cylindrical Coordinates -- A.2.3 Spherical Coordinates -- A.2.4 Metric Tensor in a Natural Vector Basis -- A.2.5 Transformation Rule for Change of Coordinates -- A.3 Tensor Calculus -- A.3.l Gradient -- References.
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| Abstract
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This book is derived from notes used in teaching a first-year graduate-level course in elasticity in the Department of Mechanical Engineering at the University of Pittsburgh. This is a modern treatment of the linearized theory of elasticity, which is presented as a specialization of the general theory of continuum mechanics. It includes a comprehensive introduction to tensor analysis, a rigorous development of the governing field equations with an emphasis on recognizing the assumptions and approximations in herent in the linearized theory, specification of boundary conditions, and a survey of solution methods for important classes of problems. Two- and three-dimensional problems, torsion of noncircular cylinders, variational methods, and complex variable methods are covered. This book is intended as the text for a first-year graduate course in me chanical or civil engineering. Sufficient depth is provided such that the text can be used without a prerequisite course in continuum mechanics, and the material is presented in such a way as to prepare students for subsequent courses in nonlinear elasticity, inelasticity, and fracture mechanics. Alter natively, for a course that is preceded by a course in continuum mechanics, there is enough additional content for a full semester of linearized elasticity.
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Mathematics.
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Mechanics, applied.
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Materials.
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SpringerLink (Online service)
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