Complementary Variational Principles

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Complementary Variational Principles

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Author : A. M. Arthurs
language : en
Publisher: Oxford University Press, USA
Release Date : 1980

Complementary Variational Principles written by A. M. Arthurs and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Mathematics categories.

Complementary Variational Principles

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Author : G. P. Srivastava
language : en
Publisher:
Release Date : 1978

Complementary Variational Principles written by G. P. Srivastava and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with categories.

Variational Principles Of Theory Of Elasticity With Applications

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Author : Haichang Hu
language : en
Publisher: CRC Press
Release Date : 1984

Variational Principles Of Theory Of Elasticity With Applications written by Haichang Hu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Science categories.

Variational Principles Of Continuum Mechanics

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Author : Victor Berdichevsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-09-18

Variational Principles Of Continuum Mechanics written by Victor Berdichevsky and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-18 with Science categories.

Thereareabout500booksonvariationalprinciples. Theyareconcernedmostlywith the mathematical aspects of the topic. The major goal of this book is to discuss the physical origin of the variational principles and the intrinsic interrelations between them. For example, the Gibbs principles appear not as the rst principles of the theory of thermodynamic equilibrium but as a consequence of the Einstein formula for thermodynamic uctuations. The mathematical issues are considered as long as they shed light on the physical outcomes and/or provide a useful technique for direct study of variational problems. Thebookisacompletelyrewrittenversionoftheauthor’smonographVariational Principles of Continuum Mechanics which appeared in Russian in 1983. I have been postponing the English translation because I wished to include the variational pr- ciples of irreversible processes in the new edition. Reaching an understanding of this subject took longer than I expected. In its nal form, this book covers all aspects of the story. The part concerned with irreversible processes is tiny, but it determines the accents put on all the results presented. The other new issues included in the book are: entropy of microstructure, variational principles of vortex line dynamics, va- ational principles and integration in functional spaces, some stochastic variational problems, variational principle for probability densities of local elds in composites with random structure, variational theory of turbulence; these topics have not been covered previously in monographic literature.

Complementary Variational Principles In Elasticity And Plasticity

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Author : K. Washizu
language : en
Publisher:
Release Date : 1977

Complementary Variational Principles In Elasticity And Plasticity written by K. Washizu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with categories.

Duality Principles In Nonconvex Systems

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Author : David Yang Gao
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Duality Principles In Nonconvex Systems written by David Yang Gao and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.

Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can alsobe recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.

Variational Principles In Heat Transfer

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Author : Maurice Anthony Biot
language : en
Publisher:
Release Date : 1970

Variational Principles In Heat Transfer written by Maurice Anthony Biot and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Mathematics categories.

The book develops a variational treatment of heat transfer which includes heat conduction and convection. It is intended to provide the foundation of a unified analysis of irreversible processes by methods analogous to those of classical mechanics. This opens the way to a formulation of heat transfer and dissipative phenomena in complex systems by means of Lagrangian-type equations and generalized coordinates. At the same time this approach suggests many approximate procedures and drastic simplifications applicable to the practical solution of a large category of problems in physics and technology. (Author).

Variational Methods In Theoretical Mechanics

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Author : J.T. Oden
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Variational Methods In Theoretical Mechanics written by J.T. Oden and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

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. We also gratefully acknowedge that much of our own research work on va ri at i ona 1 theory was supported by the U. S. Ai r Force Offi ce of Scientific Research. We 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 painstaking job of typing the manuscript. This revised edition contains only minor revisions of the first. Some misprints and errors have been corrected, and some sections were deleted, which were felt to be out of date.

Variational Principles In Classical Mechanics

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Author : Douglas Cline
language : en
Publisher:
Release Date : 2018-08

Variational Principles In Classical Mechanics written by Douglas Cline and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08 with categories.

Two dramatically different philosophical approaches to classical mechanics were proposed during the 17th - 18th centuries. Newton developed his vectorial formulation that uses time-dependent differential equations of motion to relate vector observables like force and rate of change of momentum. Euler, Lagrange, Hamilton, and Jacobi, developed powerful alternative variational formulations based on the assumption that nature follows the principle of least action. These variational formulations now play a pivotal role in science and engineering.This book introduces variational principles and their application to classical mechanics. The relative merits of the intuitive Newtonian vectorial formulation, and the more powerful variational formulations are compared. Applications to a wide variety of topics illustrate the intellectual beauty, remarkable power, and broad scope provided by use of variational principles in physics.The second edition adds discussion of the use of variational principles applied to the following topics:(1) Systems subject to initial boundary conditions(2) The hierarchy of related formulations based on action, Lagrangian, Hamiltonian, and equations of motion, to systems that involve symmetries.(3) Non-conservative systems.(4) Variable-mass systems.(5) The General Theory of Relativity.Douglas Cline is a Professor of Physics in the Department of Physics and Astronomy, University of Rochester, Rochester, New York.

Special Topics In Structural Dynamics Volume 6

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Author : Gary Foss
language : en
Publisher: Springer Science & Business
Release Date : 2014-04-22

Special Topics In Structural Dynamics Volume 6 written by Gary Foss and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-22 with Technology & Engineering categories.

This sixth volume of eight from the IMAC - XXXII Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Linear Systems Substructure Modelling Adaptive Structures Experimental Techniques Analytical Methods Damage Detection Damping of Materials & Members Modal Parameter Identification Modal Testing Methods System Identification Active Control Modal Parameter Estimation Processing Modal Data