The Linearized Theory of Elasticity [Paperback]

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.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 LinearilÃr