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Elasticity with Mathematica: An Introduction to Continuum Mechanics and Linear Elasticity
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| Organization: | CNRS and Ecole Polytechnique |
| Organization: | University of Oxford |
| Department: | Engineering Science |
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| Publisher: | Cambridge University Press (New York, NY) |
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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
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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.
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elasticity, linear elasticity, continuum mechanics, kinematics, dynamics, statics, particle motion, deformation, strain, stress, stress tensor, strain tensor, tensor, stress functions, strain energy, plane stress, plane strain, virtual power, energy potentials, elastic coefficients, material symmetry, isotropic elasticity, superposition principle, virtual work theorem, hole geometries, elastic wedge, quasistatic deformation, displacement potentials, Hooke, Saint Venant, Airy stress function, Beltrami, Galerkin, Lamé, Papkovich-Neuber potentials, Cauchy, Rayleigh-Ritz, elastostatic, spectral analysis, extremum theorems, incompatibility operator, differential operators, parametric meshes, Mathematica 5.2, Mathematica 6.0
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http://www.eng.ox.ac.uk/elasticity/
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