The Linearized Theory of Elasticity

The Linearized Theory of Elasticity by William S. Slaughter.

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 theo...

Full description

Saved in:
Bibliographic Details
Main Author: Slaughter, William S. (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2002.
Edition:1st ed. 2002.
Series:Springer eBook Collection.
Subjects:
Mechanics.
Mechanics, Applied.
Mechanical engineering.
Applied mathematics.
Engineering mathematics.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 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.

Similar Items