Solution Of Variational Inequalities In Mechanics
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Author |
: Ivan Hlavacek |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 285 |
Release |
: 2012-12-06 |
ISBN-10 |
: 9781461210481 |
ISBN-13 |
: 1461210488 |
Rating |
: 4/5 (81 Downloads) |
Synopsis Solution of Variational Inequalities in Mechanics by : Ivan Hlavacek
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).
Author |
: Ivan Hlaváček |
Publisher |
: |
Total Pages |
: 275 |
Release |
: 1988-01-01 |
ISBN-10 |
: 3540965971 |
ISBN-13 |
: 9783540965978 |
Rating |
: 4/5 (71 Downloads) |
Synopsis Solution of Variational Inequalities in Mechanics by : Ivan Hlaváček
Author |
: I. Hlavávcek |
Publisher |
: |
Total Pages |
: 292 |
Release |
: 1988-07-08 |
ISBN-10 |
: 1461210496 |
ISBN-13 |
: 9781461210498 |
Rating |
: 4/5 (96 Downloads) |
Synopsis Solution of Variational Inequalities in Mechanics by : I. Hlavávcek
Author |
: Alexander S. Kravchuk |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 337 |
Release |
: 2007-09-04 |
ISBN-10 |
: 9781402063770 |
ISBN-13 |
: 1402063776 |
Rating |
: 4/5 (70 Downloads) |
Synopsis Variational and Quasi-Variational Inequalities in Mechanics by : Alexander S. Kravchuk
The essential aim of this book is to consider a wide set of problems arising in the mathematical modeling of mechanical systems under unilateral constraints. In these investigations elastic and non-elastic deformations, friction and adhesion phenomena are taken into account. All the necessary mathematical tools are given: local boundary value problem formulations, construction of variational equations and inequalities and their transition to minimization problems, existence and uniqueness theorems, and variational transformations (Friedrichs and Young-Fenchel-Moreau) to dual and saddle-point search problems.
Author |
: Anca Capatina |
Publisher |
: Springer |
Total Pages |
: 242 |
Release |
: 2014-09-16 |
ISBN-10 |
: 9783319101637 |
ISBN-13 |
: 3319101633 |
Rating |
: 4/5 (37 Downloads) |
Synopsis Variational Inequalities and Frictional Contact Problems by : Anca Capatina
Variational Inequalities and Frictional Contact Problems contains a carefully selected collection of results on elliptic and evolutionary quasi-variational inequalities including existence, uniqueness, regularity, dual formulations, numerical approximations and error estimates ones. By using a wide range of methods and arguments, the results are presented in a constructive way, with clarity and well justified proofs. This approach makes the subjects accessible to mathematicians and applied mathematicians. Moreover, this part of the book can be used as an excellent background for the investigation of more general classes of variational inequalities. The abstract variational inequalities considered in this book cover the variational formulations of many static and quasi-static contact problems. Based on these abstract results, in the last part of the book, certain static and quasi-static frictional contact problems in elasticity are studied in an almost exhaustive way. The readers will find a systematic and unified exposition on classical, variational and dual formulations, existence, uniqueness and regularity results, finite element approximations and related optimal control problems. This part of the book is an update of the Signorini problem with nonlocal Coulomb friction, a problem little studied and with few results in the literature. Also, in the quasi-static case, a control problem governed by a bilateral contact problem is studied. Despite the theoretical nature of the presented results, the book provides a background for the numerical analysis of contact problems. The materials presented are accessible to both graduate/under graduate students and to researchers in applied mathematics, mechanics, and engineering. The obtained results have numerous applications in mechanics, engineering and geophysics. The book contains a good amount of original results which, in this unified form, cannot be found anywhere else.
Author |
: Michel Chipot |
Publisher |
: |
Total Pages |
: 140 |
Release |
: 1984 |
ISBN-10 |
: UCAL:B4178518 |
ISBN-13 |
: |
Rating |
: 4/5 (18 Downloads) |
Synopsis Variational Inequalities and Flow in Porous Media by : Michel Chipot
Author |
: Mircea Sofonea |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 235 |
Release |
: 2009-04-05 |
ISBN-10 |
: 9780387874609 |
ISBN-13 |
: 0387874607 |
Rating |
: 4/5 (09 Downloads) |
Synopsis Variational Inequalities with Applications by : Mircea Sofonea
This book is motivated by stimulating problems in contact mechanics, emphasizing antiplane frictional contact with linearly elastic and viscoelastic materials. It focuses on the essentials with respect to the qualitative aspects of several classes of variational inequalities (VIs). Clearly presented, easy to follow, and well-referenced, this work treats almost entirely VIs of the second kind, with much of the material being state-of-the-art.
Author |
: D. Goeleven |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 361 |
Release |
: 2013-12-11 |
ISBN-10 |
: 9781441987587 |
ISBN-13 |
: 1441987584 |
Rating |
: 4/5 (87 Downloads) |
Synopsis Variational and Hemivariational Inequalities - Theory, Methods and Applications by : D. Goeleven
This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and concrete problems in mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems. The book is self-contained and it offers, for the first time, the possibility to learn about inequality models and to acquire the essence of the theory in a relatively short time. Audience: The book is suitable for researchers, and for doctoral and post-doctoral courses.
Author |
: Igor Konnov |
Publisher |
: Elsevier |
Total Pages |
: 251 |
Release |
: 2007-02-08 |
ISBN-10 |
: 9780080471389 |
ISBN-13 |
: 0080471382 |
Rating |
: 4/5 (89 Downloads) |
Synopsis Equilibrium Models and Variational Inequalities by : Igor Konnov
The concept of equilibrium plays a central role in various applied sciences, such as physics (especially, mechanics), economics, engineering, transportation, sociology, chemistry, biology and other fields. If one can formulate the equilibrium problem in the form of a mathematical model, solutions of the corresponding problem can be used for forecasting the future behavior of very complex systems and, also, for correcting the the current state of the system under control. This book presents a unifying look on different equilibrium concepts in economics, including several models from related sciences.- Presents a unifying look on different equilibrium concepts and also the present state of investigations in this field- Describes static and dynamic input-output models, Walras, Cassel-Wald, spatial price, auction market, oligopolistic equilibrium models, transportation and migration equilibrium models- Covers the basics of theory and solution methods both for the complementarity and variational inequality problems- The methods are illustrated by applications and exercises to economic equilibrium models
Author |
: Weimin Han |
Publisher |
: Springer |
Total Pages |
: 389 |
Release |
: 2015-03-02 |
ISBN-10 |
: 9783319144900 |
ISBN-13 |
: 3319144901 |
Rating |
: 4/5 (00 Downloads) |
Synopsis Advances in Variational and Hemivariational Inequalities by : Weimin Han
This volume is comprised of articles providing new results on variational and hemivariational inequalities with applications to Contact Mechanics unavailable from other sources. The book will be of particular interest to graduate students and young researchers in applied and pure mathematics, civil, aeronautical and mechanical engineering, and can be used as supplementary reading material for advanced specialized courses in mathematical modeling. New results on well posedness to stationary and evolutionary inequalities and their rigorous proofs are of particular interest to readers. In addition to results on modeling and abstract problems, the book contains new results on the numerical methods for variational and hemivariational inequalities.