variational inequalities and frictional contact problems

Download Book Variational Inequalities And Frictional Contact Problems in PDF format. You can Read Online Variational Inequalities And Frictional Contact Problems here in PDF, EPUB, Mobi or Docx formats.

Variational Inequalities And Frictional Contact Problems

Author : Anca Capatina
ISBN : 9783319101637
Genre : Mathematics
File Size : 61. 48 MB
Format : PDF, ePub
Download : 946
Read : 902

Download Now

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.

Variational Inequalities With Applications

Author : Mircea Sofonea
ISBN : 9780387874609
Genre : Mathematics
File Size : 72. 26 MB
Format : PDF, Kindle
Download : 449
Read : 571

Download Now

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.

Contact Problems In Elasticity

Author : N. Kikuchi
ISBN : 9780898714685
Genre : Science
File Size : 69. 14 MB
Format : PDF, ePub
Download : 843
Read : 942

Download Now

The contact of one deformable body with another lies at the heart of almost every mechanical structure. Here, in a comprehensive treatment, two of the field's leading researchers present a systematic approach to contact problems. Using variational formulations, Kikuchi and Oden derive a multitude of new results, both for classical problems and for nonlinear problems involving large deflections and buckling of thin plates with unilateral supports, dry friction with nonclassical laws, large elastic and elastoplastic deformations with frictional contact, dynamic contacts with dynamic frictional effects, and rolling contacts. This method exposes properties of solutions obscured by classical methods, and it provides a basis for the development of powerful numerical schemes.

Finite Dimensional Variational Inequalities And Complementarity Problems

Author : Francisco Facchinei
ISBN : 9780387218144
Genre : Mathematics
File Size : 88. 97 MB
Format : PDF, ePub
Download : 475
Read : 1056

Download Now

This is part one of a two-volume work presenting a comprehensive treatment of the finite-dimensional variational inequality and complementarity problem. It covers the basic theory of finite dimensional variational inequalities and complementarity problems. Coverage includes abundant exercises as well as an extensive bibliography. The book will be an enduring reference on the subject and provide the foundation for its sustained growth.

Nonlinear Inclusions And Hemivariational Inequalities

Author : Stanisław Migórski
ISBN : 9781461442318
Genre : Mathematics
File Size : 66. 52 MB
Format : PDF, ePub
Download : 121
Read : 607

Download Now

This book introduces the reader the theory of nonlinear inclusions and hemivariational inequalities with emphasis on the study of contact mechanics. The work covers both abstract results in the area of nonlinear inclusions, hemivariational inequalities as well as the study of specific contact problems, including their modelling and their variational analysis. Provided results are based on original research on the existence, uniqueness, regularity and behavior of the solution for various classes of nonlinear stationary and evolutionary inclusions. In carrying out the variational analysis of various contact models, one systematically uses results of hemivariational inequalities and, in this way, illustrates the applications of nonlinear analysis in contact mechanics. New mathematical methods are introduced and applied in the study of nonlinear problems, which describe the contact between a deformable body and a foundation. Contact problems arise in industry, engineering and geophysics. Their variational analysis presented in this book lies the background for their numerical analysis. This volume will interest mathematicians, applied mathematicians, engineers, and scientists as well as advanced graduate students.

Variational Hemivariational Inequalities With Applications

Author : Mircea Sofonea
ISBN : 9781351649292
Genre : Mathematics
File Size : 25. 66 MB
Format : PDF, Mobi
Download : 397
Read : 308

Download Now

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 Quasi Variational Inequalities In Mechanics

Author : Alexander S. Kravchuk
ISBN : 9781402063770
Genre : Technology & Engineering
File Size : 60. 83 MB
Format : PDF, Kindle
Download : 110
Read : 848

Download Now

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.

Models And Analysis Of Quasistatic Contact

Author : Meir Shillor
ISBN : 3540229159
Genre : Science
File Size : 60. 84 MB
Format : PDF, ePub, Docs
Download : 693
Read : 425

Download Now

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.

Analysis And Simulation Of Contact Problems

Author : Peter Wriggers
ISBN : 9783540317616
Genre : Technology & Engineering
File Size : 86. 31 MB
Format : PDF, Kindle
Download : 826
Read : 1159

Download Now

This carefully edited book offers a state-of-the-art overview on formulation, mathematical analysis and numerical solution procedures of contact problems. The contributions collected in this volume summarize the lectures presented by leading scientists in the area of contact mechanics, during the 4th Contact Mechanics International Symposium (CMIS) held in Hannover, Germany, 2005.

Advances In Applied Mathematics And Global Optimization

Author : David Y. Gao
ISBN : 9780387757148
Genre : Mathematics
File Size : 60. 38 MB
Format : PDF, ePub, Docs
Download : 125
Read : 1028

Download Now

The articles that comprise this distinguished annual volume for the Advances in Mechanics and Mathematics series have been written in honor of Gilbert Strang, a world renowned mathematician and exceptional person. Written by leading experts in complementarity, duality, global optimization, and quantum computations, this collection reveals the beauty of these mathematical disciplines and investigates recent developments in global optimization, nonconvex and nonsmooth analysis, nonlinear programming, theoretical and engineering mechanics, large scale computation, quantum algorithms and computation, and information theory.

Top Download:

Best Books