Variational Views In Mechanics

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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.

Variational Views In Mechanics

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Author : Paolo Maria Mariano
language : en
Publisher: Springer Nature
Release Date : 2022-02-08

Variational Views In Mechanics written by Paolo Maria Mariano and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-02-08 with Mathematics categories.

This volume provides a timely survey of interactions between the calculus of variations and theoretical and applied mechanics. Chapters have been significantly expanded since preliminary versions appeared in a special issue of the Journal of Optimization Theory and Applications (184(1), 2020) on “Calculus of Variations in Mechanics and Related Fields”. The variety of topics covered offers researchers an overview of problems in mechanics that can be analyzed with variational techniques, making this a valuable reference for researchers in the field. It also presents ideas for possible future areas of research, showing how the mastery of these foundational mathematical techniques can be used for many exciting applications. Specific topics covered include: Topology optimization Identification of material properties Optimal control Plastic flows Gradient polyconvexity Obstacle problems Quasi-monotonicity Variational Views in Mechanics will appeal to researchers in mathematics, solid-states physics, and mechanical, civil, and materials engineering.

Variational Principles In Physics

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Author : Jean-Louis Basdevant
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-12-18

Variational Principles In Physics written by Jean-Louis Basdevant 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 2006-12-18 with Science categories.

Variational principles have proven to be surprisingly fertile. For example, Fermat used variational methods to demonstrate that light follows the fastest route from one point to another, an idea which came to be a cornerstone of geometrical optics. This book explains variational principles and charts their use throughout modern physics. It examines the analytical mechanics of Lagrange and Hamilton, the basic tools of any physicist. The book also offers simple but rich first impressions of Einstein’s General Relativity, Feynman’s Quantum Mechanics, and more that reveal amazing interconnections between various fields of physics.

Solution Of Variational Inequalities In Mechanics

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Author : Ivan Hlavacek
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Solution Of Variational Inequalities In Mechanics written by Ivan Hlavacek 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.

The idea for this book was developed in the seminar on problems of con tinuum mechanics, which has been active for more than twelve years at the Faculty of Mathematics and Physics, Charles University, Prague. This seminar has been pursuing recent directions in the development of mathe matical applications in physics; especially in continuum mechanics, and in technology. It has regularly been attended by upper division and graduate students, faculty, and scientists and researchers from various institutions from Prague and elsewhere. These seminar participants decided to publish in a self-contained monograph the results of their individual and collective efforts in developing applications for the theory of variational inequalities, which is currently a rapidly growing branch of modern analysis. The theory of variational inequalities is a relatively young mathematical discipline. Apparently, one of the main bases for its development was the paper by G. Fichera (1964) on the solution of the Signorini problem in the theory of elasticity. Later, J. L. Lions and G. Stampacchia (1967) laid the foundations of the theory itself. Time-dependent inequalities have primarily been treated in works of J. L. Lions and H. Bnlzis. The diverse applications of the variational in equalities theory are the topics of the well-known monograph by G. Du vaut and J. L. Lions, Les iniquations en micanique et en physique (1972).

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.

Solid Mechanics

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Author : Clive L. Dym
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-05

Solid Mechanics written by Clive L. Dym 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 2013-04-05 with Science categories.

Solid Mechanics: A Variational Approach, Augmented Edition presents a lucid and thoroughly developed approach to solid mechanics for students engaged in the study of elastic structures not seen in other texts currently on the market. This work offers a clear and carefully prepared exposition of variational techniques as they are applied to solid mechanics. Unlike other books in this field, Dym and Shames treat all the necessary theory needed for the study of solid mechanics and include extensive applications. Of particular note is the variational approach used in developing consistent structural theories and in obtaining exact and approximate solutions for many problems. Based on both semester and year-long courses taught to undergraduate seniors and graduate students, this text is geared for programs in aeronautical, civil, and mechanical engineering, and in engineering science. The authors’ objective is two-fold: first, to introduce the student to the theory of structures (one- and two-dimensional) as developed from the three-dimensional theory of elasticity; and second, to introduce the student to the strength and utility of variational principles and methods, including briefly making the connection to finite element methods. A complete set of homework problems is included.

Stochastic Variational Approach To Quantum Mechanical Few Body Problems

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Author : Yasuyuki Suzuki
language : en
Publisher: Springer
Release Date : 2014-03-12

Stochastic Variational Approach To Quantum Mechanical Few Body Problems written by Yasuyuki Suzuki and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 with Science categories.

Geometry Of The Time Dependent Variational Principle In Quantum Mechanics

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Author : P. Kramer
language : en
Publisher:
Release Date : 2014-01-15

Geometry Of The Time Dependent Variational Principle In Quantum Mechanics written by P. Kramer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Models And Analysis Of Quasistatic Contact

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Author : Meir Shillor
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-09-16

Models And Analysis Of Quasistatic Contact written by Meir Shillor 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 2004-09-16 with Science categories.

The mathematical theory of contact mechanics is a growing field in engineering and scientific computing. This book is intended as a unified and readily accessible source for mathematicians, applied mathematicians, mechanicians, engineers and scientists, as well as advanced students. The first part describes models of the processes involved like friction, heat generation and thermal effects, wear, adhesion and damage. The second part presents many mathematical models of practical interest and demonstrates the close interaction and cross-fertilization between contact mechanics and the theory of variational inequalities. The last part reviews further results, gives many references to current research and discusses open problems and future developments. The book can be read by mechanical engineers interested in applications. In addition, some theorems and their proofs are given as examples for the mathematical tools used in the models.

Shape And Shape Changes In Mechanics

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Author : Michel Frémond
language : en
Publisher: Springer Nature
Release Date : 2025-05-09

Shape And Shape Changes In Mechanics written by Michel Frémond and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-09 with Technology & Engineering categories.

This book provides an innovative description of motion with large deformations and the possibility of defects and dislocations. The theory is based on the stretch and angular matrices of the polar decomposition allowing convex potentials. Third-order gradient theories are required to account for mechanical everyday experiments, for instance assemblies of solid structures with different spatial dimensions. Second-order gradient theories are required for thermal experiments. Using the principle of virtual power and new convex potentials, the position of either solid or fluid structures together with the matrix accounting for the defects and dislocations is computed. Defects and dislocations are present in case an internal stress is large enough. Engineers and scientists active in solid and fluid engineering, mathematics, and numerics should be aware of this predictive theory. Damage, shape memory alloys, Cosserat materials, and surface tension are investigated in this framework.