Mathematical Elasticity

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Author: Philippe G. Ciarlet
Publisher: Elsevier
ISBN: 9780444817761
Size: 78.75 MB
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Mathematical Elasticity by Philippe G. Ciarlet

Original Title: Mathematical Elasticity

This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible.

Mathematical Elasticity

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Publisher: Elsevier
ISBN: 9780080535913
Size: 46.34 MB
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Mathematical Elasticity by

Original Title: Mathematical Elasticity

The objective of Volume II is to show how asymptotic methods, with the thickness as the small parameter, indeed provide a powerful means of justifying two-dimensional plate theories. More specifically, without any recourse to any a priori assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in H1 towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established. In the nonlinear case, again after ad hoc scalings have been performed, it is shown that the leading term of a formal asymptotic expansion of the three-dimensional solution satisfies well-known two-dimensional equations, such as those of the nonlinear Kirchhoff-Love theory, or the von Kármán equations. Special attention is also given to the first convergence result obtained in this case, which leads to two-dimensional large deformation, frame-indifferent, nonlinear membrane theories. It is also demonstrated that asymptotic methods can likewise be used for justifying other lower-dimensional equations of elastic shallow shells, and the coupled pluri-dimensional equations of elastic multi-structures, i.e., structures with junctions. In each case, the existence, uniqueness or multiplicity, and regularity of solutions to the limit equations obtained in this fashion are also studied.

Mathematical Problems In Elasticity

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Author: Remigio Russo
Publisher: World Scientific
ISBN: 9789810225766
Size: 77.11 MB
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Mathematical Problems In Elasticity by Remigio Russo

Original Title: Mathematical Problems In Elasticity

In this volume, five papers are collected that give a good sample of the problems and the results characterizing some recent trends and advances in this theory. Some of them are devoted to the improvement of a general abstract knowledge of the behavior of elastic bodies, while the others mainly deal with more applicative topics.

Mathematical Foundations Of Elasticity

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Author: Jerrold E. Marsden
Publisher: Courier Corporation
ISBN: 0486142272
Size: 25.89 MB
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Mathematical Foundations Of Elasticity by Jerrold E. Marsden

Original Title: Mathematical Foundations Of Elasticity

Graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It presents a classical subject in a modern setting, with examples of newer mathematical contributions. 1983 edition.

The Mathematical Theory Of Elasticity Second Edition

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Author: Richard B. Hetnarski
Publisher: CRC Press
ISBN: 143982889X
Size: 62.12 MB
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The Mathematical Theory Of Elasticity Second Edition by Richard B. Hetnarski

Original Title: The Mathematical Theory Of Elasticity Second Edition

Through its inclusion of specific applications, The Mathematical Theory of Elasticity, Second Edition continues to provide a bridge between the theory and applications of elasticity. It presents classical as well as more recent results, including those obtained by the authors and their colleagues. Revised and improved, this edition incorporates additional examples and the latest research results. New to the Second Edition Exposition of the application of Laplace transforms, the Dirac delta function, and the Heaviside function Presentation of the Cherkaev, Lurie, and Milton (CLM) stress invariance theorem that is widely used to determine the effective moduli of elastic composites The Cauchy relations in elasticity A body force analogy for the transient thermal stresses A three-part table of Laplace transforms An appendix that explores recent developments in thermoelasticity Although emphasis is placed on the problems of elastodynamics and thermoelastodynamics, the text also covers elastostatics and thermoelastostatics. It discusses the fundamentals of linear elasticity and applications, including kinematics, motion and equilibrium, constitutive relations, formulation of problems, and variational principles. It also explains how to solve various boundary value problems of one, two, and three dimensions. This professional reference includes access to a solutions manual for those wishing to adopt the book for instructional purposes.

A Treatise On The Mathematical Theory Of Elasticity

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Author: Augustus Edward Hough Love
Size: 56.23 MB
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A Treatise On The Mathematical Theory Of Elasticity by Augustus Edward Hough Love

Original Title: A Treatise On The Mathematical Theory Of Elasticity

An indispensable reference work for engineers, mathematicians, and physicists, this book is the most complete and authoritative treatment of classical elasticity in a single volume. Beginning with elementary notions of extension, simple shear and homogeneous strain, the analysis rapidly undertakes a development of types of strain, displacements corresponding to a given strain, cubical dilatation, composition of strains and a general theory of strains. A detailed analysis of stress including the stress quadric and uniformly varying stress leads into an exposition of the elasticity of solid bodies. Based upon the work-energy concept, experimental results are examined and the significance of elastic constants in general theory considered. Hooke's Law, elastic constants, methods of determining stress, thermo-elastic equations, and other topics are carefully discussed. --Back cover.

Introduction To Mathematical Elasticity

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Author: L. P. Lebedev
Publisher: World Scientific
ISBN: 9814273724
Size: 43.50 MB
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Introduction To Mathematical Elasticity by L. P. Lebedev

Original Title: Introduction To Mathematical Elasticity

This book provides the general reader with an introduction to mathematical elasticity, by means of general concepts in classic mechanics, and models for elastic springs, strings, rods, beams and membranes. Functional analysis is also used to explore more general boundary value problems for three-dimensional elastic bodies, where the reader is provided, for each problem considered, a description of the deformation; the equilibrium in terms of stresses; the constitutive equation; the equilibrium equation in terms of displacements; formulation of boundary value problems; and variational principles, generalized solutions and conditions for solvability.Introduction to Mathematical Elasticity will also be of essential reference to engineers specializing in elasticity, and to mathematicians working on abstract formulations of the related boundary value problems.

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