Variational And Quasi Variational Inequalities In Mechanics PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Variational And Quasi Variational Inequalities In Mechanics PDF full book. Access full book title Variational And Quasi Variational Inequalities In Mechanics.
| Author | : Alexander S. Kravchuk |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 337 |
| Release | : 2007-09-04 |
| Genre | : Technology & Engineering |
| ISBN | : 1402063776 |
Download Variational and Quasi-Variational Inequalities in Mechanics Book in PDF, ePub and Kindle
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 |
| Genre | : Mathematics |
| ISBN | : 3319101633 |
Download Variational Inequalities and Frictional Contact Problems Book in PDF, ePub and Kindle
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 | : Michael Hintermüller |
| Publisher | : Springer Nature |
| Total Pages | : 396 |
| Release | : 2019-11-27 |
| Genre | : Mathematics |
| ISBN | : 3030331164 |
Download Topics in Applied Analysis and Optimisation Book in PDF, ePub and Kindle
This volume comprises selected, revised papers from the Joint CIM-WIAS Workshop, TAAO 2017, held in Lisbon, Portugal, in December 2017. The workshop brought together experts from research groups at the Weierstrass Institute in Berlin and mathematics centres in Portugal to present and discuss current scientific topics and to promote existing and future collaborations. The papers include the following topics: PDEs with applications to material sciences, thermodynamics and laser dynamics, scientific computing, nonlinear optimization and stochastic analysis.
| Author | : M. Chipot |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 127 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461211204 |
Download Variational Inequalities and Flow in Porous Media Book in PDF, ePub and Kindle
These notes are the contents of a one semester graduate course which taught at Brown University during the academic year 1981-1982. They are mainly concerned with regularity theory for obstacle problems, and with the dam problem, which, in the rectangular case, is one of the most in teresting applications of Variational Inequalities with an obstacle. Very little background is needed to read these notes. The main re sults of functional analysis which are used here are recalled in the text. The goal of the two first chapters is to introduce the notion of Varia tional Inequality and give some applications from physical mathematics. The third chapter is concerned with a regularity theory for the obstacle problems. These problems have now invaded a large domain of applied mathematics including optimal control theory and mechanics, and a collec tion of regularity results available seems to be timely. Roughly speaking, for elliptic variational inequalities of second order we prove that the solution has as much regularity as the obstacle(s). We combine here the theory for one or two obstacles in a unified way, and one of our hopes is that the reader will enjoy the wide diversity of techniques used in this approach. The fourth chapter is concerned with the dam problem. This problem has been intensively studied during the past decade (see the books of Baiocchi-Capelo and Kinderlehrer-Stampacchia in the references). The relationship with Variational Inequalities has already been quoted above.
| Author | : Mircea Sofonea |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 235 |
| Release | : 2009-04-05 |
| Genre | : Mathematics |
| ISBN | : 0387874607 |
Download Variational Inequalities with Applications Book in PDF, ePub and Kindle
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 | : Ivan Hlavacek |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 285 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 1461210488 |
Download Solution of Variational Inequalities in Mechanics Book in PDF, ePub and Kindle
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 |
| Genre | : Continuum mechanics |
| ISBN | : 9783540965978 |
Download Solution of Variational Inequalities in Mechanics Book in PDF, ePub and Kindle
| Author | : F. Giannessi |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 304 |
| Release | : 2013-06-29 |
| Genre | : Social Science |
| ISBN | : 1489913580 |
Download Variational Inequalities and Network Equilibrium Problems Book in PDF, ePub and Kindle
This volume brings forth a set of papers presented at the conference on "Varia tional Inequalities and network equilibrium problems", held in Erice at the "G. Stam pacchia" School of the "E. Majorana" Centre for Scientific Culture in the period 19~25 June 1994. The meeting was conceived to contribute to the exchange between Variational Analysis and equilibrium problems, especially those related to network design. Most of the approaches and viewpoints of these fields are present in the volume, both as concerns the theory and the applications of equilibrium problems to transportation, computer and electric networks, to market behavior, and to bi~level programming. Being convinced of the great importance of equilibrium problems as well as of their complexity, the organizers hope that the merging of points of view coming from differ ent fields will stimulate theoretical research and applications. In this context Variational and Quasi~Variational Inequalities have shown them selves to be very important models for equilibrium problems. As a consequence in the last two decades they have received a lot of attention both as to mathematical inves tigation and applications. The proof that the above mentioned equilibrium problems can be expressed, in terms of Variational or Quasi~Variational Inequalities also in the non~standard and non~symmetric cases, has been a crucial improvement.
| Author | : Meir Shillor |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 288 |
| Release | : 2004-09-16 |
| Genre | : Science |
| ISBN | : 9783540229155 |
Download Models and Analysis of Quasistatic Contact Book in PDF, ePub and Kindle
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.
| Author | : Mircea Sofonea |
| Publisher | : CRC Press |
| Total Pages | : 334 |
| Release | : 2017-10-23 |
| Genre | : Mathematics |
| ISBN | : 1351649299 |
Download Variational-Hemivariational Inequalities with Applications Book in PDF, ePub and Kindle
This research monograph represents an outcome of the cross-fertilization between nonlinear functional analysis and mathematical modelling, and demonstrates its application to solid and contact mechanics. Based on authors’ original results, it introduces a general fixed point principle and its application to various nonlinear problems in analysis and mechanics. The classes of history-dependent operators and almost history-dependent operators are exposed in a large generality. A systematic and unified presentation contains a carefully-selected collection of new results on variational-hemivariational inequalities with or without unilateral constraints. A wide spectrum of static, quasistatic, dynamic contact problems for elastic, viscoelastic and viscoplastic materials illustrates the applicability of these theoretical results. Written for mathematicians, applied mathematicians, engineers and scientists, it is also a valuable tool for graduate students and researchers in nonlinear analysis, mathematical modelling, mechanics of solids, and contact mechanics.
