This book introduces key ideas and principles in the theory of elasticity with the help of symbolic computation. Differential and integral operators on vector and tensor fields of displacements, strains, and stresses are considered on a consistent and rigorous basis with respect to curvilinear orthogonal coordinate systems. Methods are illustrated using a variety of plane and three-dimensional elastic problems, and general theorems, fundamental solutions, displacements, and stress potentials are presented and discussed.
The book contains over 60 exercises and solutions in the form of Mathematica
notebooks that accompany each chapter. The demonstrated techniques can be applied to a large range of practical and fundamental problems. Written with Mathematica 5.2; Mathematica 6.0 compatible notebooks are available for download from the publisher's website.
Kinematics: Displacements and Strains | Dynamics and Statics: Stresses and Equilibrium | Linear Elasticity | General Principles in Problems of Elasticity | Stress Functions | Displacement Potentials | Energy Principles and Variational Formulations | Appendix 1: Differential Operators | Appendix 2: Mathematica
Tricks | Appendix 3: Plotting Parametric Meshes
Alexander Korsunsky's Packages and Notebooks