Elasticity With Mathematica ®: An Introduction To Continuum Mechanics And Linear Elasticity

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This book gives an introduction to the 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. As a consequence, vector and tensor objects can be manipulated readily, and fundamental concepts can be illustrated and problems solved with ease. The method is illustrated using a variety of plane and three-dimensional elastic problems. General theorems, fundamental solutions, displacements, and stress potentials are presented and discussed. The Rayleigh-Ritz method for obtaining approximate solutions is introduced for elastostatic and spectral analysis problems. The book contains more than 60 exercises and solutions in the form of Mathematica notebooks that accompany every chapter. Once the reader learns and masters the techniques, they can be applied to a large range of practical and fundamental problems. Andrei Constantinescu is currently Directeur de Recherche at CNRS: the French National Center for Scientific Research in the Laboratoire de Mecanique des ´ Solides, and Associated Professor at Ecole Polytechnique, Palaiseau, near Paris. He teaches courses on continuum mechanics, elasticity, fatigue, and inverse problems at engineering schools from the ParisTech Consortium. His research is in applied mechanics and covers areas ranging from inverse problems and the identification of defects and constitutive laws to fatigue and lifetime prediction of structures. The results have applied through collaboration and consulting for companies such as ´ the car manufacturer Peugeot-Citroen, energy providers Electricit e´ de France and Gaz de France, and the aeroengine manufacturer MTU. Alexander Korsunsky is currently Professor in the Department of Engineering Science, University of Oxford. He is also a Fellow and Dean at Trinity College, Oxford. He teaches courses in England and France on engineering alloys, fracture mechanics, applied elasticity, advanced stress analysis, and residual stresses. His research interests are in the field of experimental characterization and theoretical analysis of deformation and fracture of metals, polymers, and concrete, with emphasis on thermo-mechanical fatigue and damage. He is particularly interested in residual stress effects and their measurement by advanced diffraction techniques using neutrons and high-energy X-rays at synchrotron sources and in the laboratory. He is a member of the Science Advisory Committee of the European Synchrotron Radiation Facility in Grenoble, and he leads the development of the new engineering instrument (JEEP) at Diamond Light Source near Oxford. i PAB CUFX161-Constantinescu August 13, 2007 17:14 ii PAB CUFX161-Constantinescu August 13, 2007 17:14 Elasticity with MATHEMATICA
R AN INTRODUCTION TO CONTINUUM MECHANICS AND LINEAR ELASTICITY Andrei Constantinescu CNRS and Ecole Polytechniqu