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On A Pointwise Variational Principle Of Elasticity And Mathematical Physics
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Book Synopsis On a Pointwise Variational Principle of Elasticity and Mathematical Physics by : M. P. Stallybrass
Download or read book On a Pointwise Variational Principle of Elasticity and Mathematical Physics written by M. P. Stallybrass and published by . This book was released on 1963 with total page 41 pages. Available in PDF, EPUB and Kindle. Book excerpt: A method is discussed for constructing stationary functionals for the value of the solution of a linear boundary value problem, or of the derivatives of such a solution, at a specified, but arbitrary, point. The procedure is applicable to any boundary value problem governed by a linearly elliptic partial differential equation, or a system of such equations, for which global fundamental solutions exist. The technique is particularly suited to obtain approximate results in a class of mixed boundary value problems, involving a rigid body oscillating about various axes on the surface of an elastic half-space. The procedure is illustrated by constructing stationary expressions for the solution of a mixed boundary value problem associated with the Helmholtz equation and the class of elasto-dynamic problems referred to above. Method is applied to compute the displacement on the free surface of an elastic half-space due to the torsional oscillation of a finite disk situated on the surface. (Author).
Book Synopsis Variational Principles of Theory of Elasticity with Applications by : Haichang Hu
Download or read book Variational Principles of Theory of Elasticity with Applications written by Haichang Hu and published by CRC Press. This book was released on 1984 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Variational Principles of Continuum Mechanics by : Victor Berdichevsky
Download or read book Variational Principles of Continuum Mechanics written by Victor Berdichevsky and published by Springer Science & Business Media. This book was released on 2009-09-18 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reviews the two features of the variational approach: its use as a universal tool to describe physical phenomena and as a source for qualitative and quantitative methods of studying particular problems. Berdichevsky’s work differs from other books on the subject in focusing mostly on the physical origin of variational principles as well as establishing their interrelations. For example, the Gibbs principles appear as a consequence of the Einstein formula for thermodynamic fluctuations rather than as the first principles of the theory of thermodynamic equilibrium. Mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for the direct study of variational problems. In addition, a thorough account of variational principles discovered in various branches of continuum mechanics is given. This book, the second volume, describes how the variational approach can be applied to constructing models of continuum media, such as the theory of elastic plates; shells and beams; shallow water theory; heterogeneous mixtures; granular materials; and turbulence. It goes on to apply the variational approach to asymptotical analysis of problems with small parameters, such as the derivation of the theory of elastic plates, shells and beams from three-dimensional elasticity theory; and the basics of homogenization theory. A theory of stochastic variational problems is considered in detail too, along with applications to the homogenization of continua with random microstructures.
Book Synopsis The Mathematical Theory of Elasticity by : Richard B. Hetnarski
Download or read book The Mathematical Theory of Elasticity written by Richard B. Hetnarski and published by CRC Press. This book was released on 2016-04-19 with total page 837 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 add
Book Synopsis Symplectic Elasticity by : Weian Yao
Download or read book Symplectic Elasticity written by Weian Yao and published by World Scientific. This book was released on 2009 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solid mechanics problems have long been regarded as bottlenecks in the development of elasticity. In contrast to traditional solution methodologies, such as Timoshenko's theory of elasticity for which the main technique is the semi-inverse method, this book presents a new approach based on the Hamiltonian principle and the symplectic duality system where solutions are derived in a rational manner in the symplectic space. Departing from the conventional Euclidean space with one kind of variable, the symplectic space with dual variables thus provides a fundamental breakthrough. This book explains the new solution methodology by discussing plane isotropic elasticity, multiple layered plate, anisotropic elasticity, sectorial plate and thin plate bending problems in some detail. A number of existing problems without analytical solutions within the framework of classical approaches are solved analytically using this symplectic approach. Symplectic methodologies can be applied not only to problems in elasticity, but also to other solid mechanics problems. In addition, it can also be extended to various engineering mechanics and mathematical physics fields, such as vibration, wave propagation, control theory, electromagnetism and quantum mechanics.
Book Synopsis Variational Methods in Nonlinear Elasticity by : Pablo Pedregal
Download or read book Variational Methods in Nonlinear Elasticity written by Pablo Pedregal and published by SIAM. This book was released on 2000-01-01 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers the main vector variational methods developed to solve nonlinear elasticity problems. Presenting a general framework with a tight focus, the author provides a comprehensive exposition of a technically difficult, yet rapidly developing area of modern applied mathematics. The book includes the classical existence theory as well as a brief incursion into problems where nonexistence is fundamental. It also provides self-contained, concise accounts of quasi convexity, polyconvexity, and rank-one convexity, which are used in nonlinear elasticity.
Book Synopsis A Treatise on the Mathematical Theory of Elasticity by : A. E. H. Love
Download or read book A Treatise on the Mathematical Theory of Elasticity written by A. E. H. Love and published by Cambridge University Press. This book was released on 2013-01-03 with total page 663 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1927, this is a classic account of the mathematical theory of elasticity by English mathematician A. E. H. Love. The text provides a detailed explanation of the topic in its various aspects, revealing important relationships with general physics and applications to engineering.
Book Synopsis A Treatise on the Mathematical Theory of Elasticity by : Augustus Edward Hough Love
Download or read book A Treatise on the Mathematical Theory of Elasticity written by Augustus Edward Hough Love and published by . This book was released on 1892 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Variational Principles by : B. L. Moiseiwitsch
Download or read book Variational Principles written by B. L. Moiseiwitsch and published by Courier Corporation. This book was released on 2013-02-20 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text's primary objective is to demonstrate the expression of the equations of the various branches of mathematical physics in the succinct and elegant form of variational principles (and thereby illuminate their interrelationship). Its related intentions are to show how variational principles may be employed to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities (such as the phase shifts) that arise in the theory of scattering. Chapter-by-chapter treatment consists of analytical dynamics; optics, wave mechanics, and quantum mechanics; field equations; eigenvalue problems; and scattering theory. 1966 edition. Bibliography. Index.
Book Synopsis A Treatise on the Mathematical Theory of Elasticity by :
Download or read book A Treatise on the Mathematical Theory of Elasticity written by and published by CUP Archive. This book was released on with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Variational Methods in Elasticity and Plasticity by : Kyūichirō Washizu
Download or read book Variational Methods in Elasticity and Plasticity written by Kyūichirō Washizu and published by Pergamon. This book was released on 1968 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to Modern Variational Techniques in Mechanics and Engineering by : Bozidar D. Vujanovic
Download or read book An Introduction to Modern Variational Techniques in Mechanics and Engineering written by Bozidar D. Vujanovic and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Atanackovic has good track record with Birkhauser: his "Theory of Elasticity" book (4072-X) has been well reviewed. * Current text has received two excellent pre-pub reviews. * May be used as textbook in advanced undergrad/beginning grad advanced dynamics courses in engineering, physics, applied math departments. *Also useful as self-study reference for researchers and practitioners. * Many examples and novel applications throughout. Competitive literature---Meirovich, Goldstein---is outdated and does not include the synthesis of topics presented here.
Book Synopsis Elasticity and Plasticity by : J. N. Goodier
Download or read book Elasticity and Plasticity written by J. N. Goodier and published by Courier Dover Publications. This book was released on 2016-04-21 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprising two classic essays by experts on the mathematical theories of elasticity and plasticity, this volume is noteworthy for its contributions by Russian authors and others previously unrecognized in Western literature. 1958 edition.
Book Synopsis Variational Methods in Theoretical Mechanics by : J.T. Oden
Download or read book Variational Methods in Theoretical Mechanics written by J.T. Oden and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook written for use in a graduate-level course for students of mechanics and engineering science. It is designed to cover the essential features of modern variational methods and to demonstrate how a number of basic mathematical concepts can be used to produce a unified theory of variational mechanics. As prerequisite to using this text, we assume that the student is equipped with an introductory course in functional analysis at a level roughly equal to that covered, for example, in Kolmogorov and Fomin (Functional Analysis, Vol. I, Graylock, Rochester, 1957) and possibly a graduate-level course in continuum mechanics. Numerous references to supplementary material are listed throughout the book. We are indebted to Professor Jim Douglas of the University of Chicago, who read an earlier version of the manuscript and whose detailed suggestions were extremely helpful in preparing the final draft. He also gratefully acknowledge that much of our own research work on variational theory was supported by the U.S. Air Force Office of Scientific Research. He are indebted to Mr. Ming-Goei Sheu for help in proofreading. Finally, we wish to express thanks to Mrs. Marilyn Gude for her excellent and pains taking job of typing the manuscript. J. T. ODEN J. N. REDDY Table of Contents PREFACE 1. INTRODUCTION 1.1 The Role of Variational Theory in Mechanics. 1 1.2 Some Historical Comments ......... . 2 1.3 Plan of Study ............... . 5 7 2. MATHEMATICAL FOUNDATIONS OF CLASSICAL VARIATIONAL THEORY 7 2.1 Introduction . . . . . . . .
Book Synopsis Mathematical Elasticity by : Philippe G. Ciarlet
Download or read book Mathematical Elasticity written by Philippe G. Ciarlet and published by SIAM. This book was released on 2022-01-22 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second book of a three-volume set, asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear plate and shallow shell theories. Theory of Plates also illustrates how asymptotic methods allow for justification of the Kirchhoff–Love theory of nonlinear elastic plates and presents a detailed mathematical analysis of the von Kármán equations. An extended preface and extensive bibliography have been added to highlight the progress that has been made since the volume’s original publication. While each one of the three volumes is self-contained, together the Mathematical Elasticity set provides the only modern treatise on elasticity; introduces contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells; and contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.
Book Synopsis U.S. Government Research Reports by :
Download or read book U.S. Government Research Reports written by and published by . This book was released on 1964 with total page 1416 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Solution of Variational Inequalities in Mechanics by : Ivan Hlaváček
Download or read book Solution of Variational Inequalities in Mechanics written by Ivan Hlaváček and published by . This book was released on 1988-01-01 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt:
