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Variational And Quasi Variational Inequalities In Mechanics

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Variational And Quasi Variational Inequalities In Mechanics

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Author : Alexander S. Kravchuk
language : en
Publisher: Springer
Release Date : 2009-09-03

Variational And Quasi Variational Inequalities In Mechanics written by Alexander S. Kravchuk and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-03 with Technology & Engineering categories.

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.

Variational And Quasi Variational Inequalities In Mechanics

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Author : Alexander S. Kravchuk
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-09-04

Variational And Quasi Variational Inequalities In Mechanics written by Alexander S. Kravchuk 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 2007-09-04 with Technology & Engineering categories.

Variational Inequalities And Frictional Contact Problems

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Author : Anca Capatina
language : en
Publisher: Springer
Release Date : 2014-09-16

Variational Inequalities And Frictional Contact Problems written by Anca Capatina and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-16 with Mathematics categories.

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.

Nonsmooth Variational Problems And Their Inequalities

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Author : Siegfried Carl
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-07

Nonsmooth Variational Problems And Their Inequalities written by Siegfried Carl 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 2007-06-07 with Mathematics categories.

This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. It provides a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method.

Hemivariational Inequalities

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Author : Panagiotis D. Panagiotopoulos
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Hemivariational Inequalities written by Panagiotis D. Panagiotopoulos 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 Technology & Engineering categories.

The aim of the present book is the formulation, mathematical study and numerical treatment of static and dynamic problems in mechanics and engineering sciences involving nonconvex and nonsmooth energy functions, or nonmonotone and multivalued stress-strain laws. Such problems lead to a new type of variational forms, the hemivariational inequalities, which also lead to multivalued differential or integral equations. Innovative numerical methods are presented for the treament of realistic engineering problems. This book is the first to deal with variational theory of engineering problems involving nonmonotone multivalue realations, their mechanical foundation, their mathematical study (existence and certain approximation results) and the corresponding eigenvalue and optimal control problems. All the numerical applications give innovative answers to as yet unsolved or partially solved engineering problems, e.g. the adhesive contact in cracks, the delamination problem, the sawtooth stress-strain laws in composites, the shear connectors in composite beams, the semirigid connections in steel structures, the adhesive grasping in robotics, etc. The book closes with the consideration of hemivariational inequalities for fractal type geometries and with the neural network approach to the numerical treatment of hemivariational inequalities.

Global Bifurcation In Variational Inequalities

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Author : Vy Khoi Le
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-01-24

Global Bifurcation In Variational Inequalities written by Vy Khoi Le 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 1997-01-24 with Mathematics categories.

An up-to-date and unified treatment of bifurcation theory for variational inequalities in reflexive spaces and the use of the theory in a variety of applications, such as: obstacle problems from elasticity theory, unilateral problems; torsion problems; equations from fluid mechanics and quasilinear elliptic partial differential equations. The tools employed are those of modern nonlinear analysis. Accessible to graduate students and researchers who work in nonlinear analysis, nonlinear partial differential equations, and additional research disciplines that use nonlinear mathematics.

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.

Variational Hemivariational Inequalities With Applications

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Author : Mircea Sofonea
language : en
Publisher: Chapman & Hall/CRC
Release Date : 2018

Variational Hemivariational Inequalities With Applications written by Mircea Sofonea and has been published by Chapman & Hall/CRC this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.

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.

Variational And Quasivariational Inequalities

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Author : C. Baiocchi
language : en
Publisher: John Wiley & Sons
Release Date : 1984

Variational And Quasivariational Inequalities written by C. Baiocchi and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.

Variational And Quasi Variational Inequalities In Mechanics

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