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Author : R. Trémolières
Publisher : Elsevier
Page : 807 pages
File Size : 24,71 MB
Release : 2011-08-18
Category : Mathematics
ISBN : 0080875297
Numerical Analysis of Variational Inequalities
Author : Anca Capatina
Publisher : Springer
Page : 242 pages
File Size : 17,27 MB
Release : 2014-09-16
Category : Mathematics
ISBN : 3319101633
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 : Weimin Han
Publisher : Springer
Page : 389 pages
File Size : 30,89 MB
Release : 2015-03-02
Category : Mathematics
ISBN : 3319144901
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.
Author : Roland Glowinski
Publisher : Springer Science & Business Media
Page : 506 pages
File Size : 22,67 MB
Release : 2013-06-29
Category : Science
ISBN : 3662126133
This book describes the mathematical background and reviews the techniques for solving problems, including those that require large computations such as transonic flows for compressible fluids and the Navier-Stokes equations for incompressible viscous fluids. Finite element approximations and non-linear relaxation, and nonlinear least square methods are all covered in detail, as are many applications. This volume is a classic in a long-awaited softcover re-edition.
Author : David Kinderlehrer
Publisher : SIAM
Page : 328 pages
File Size : 16,73 MB
Release : 2000-01-01
Category : Mathematics
ISBN : 0898714664
Unabridged republication is a resource for topics in elliptic equations and systems and free boundary problems.
Author : Ioannis K. Argyros
Publisher : Polimetrica s.a.s.
Page : 605 pages
File Size : 14,34 MB
Release : 2009
Category : Mathematics
ISBN : 8876991492
Author : N. Kikuchi
Publisher : SIAM
Page : 508 pages
File Size : 24,47 MB
Release : 1988-01-01
Category : Science
ISBN : 9781611970845
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. Among the novel results presented here are algorithms for contact problems with nonlinear and nonlocal friction, and very effective algorithms for solving problems involving the large elastic deformation of hyperelastic bodies with general contact conditions. Includes detailed discussion of numerical methods for nonlinear materials with unilateral contact and friction, with examples of metalforming simulations. Also presents algorithms for the finite deformation rolling contact problem, along with a discussion of numerical examples.
Author : Joachim Gwinner
Publisher : CRC Press
Page : 405 pages
File Size : 42,63 MB
Release : 2021-12-24
Category : Mathematics
ISBN : 1351857673
Uncertainty Quantification (UQ) is an emerging and extremely active research discipline which aims to quantitatively treat any uncertainty in applied models. The primary objective of Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications is to present a comprehensive treatment of UQ in variational inequalities and some of its generalizations emerging from various network, economic, and engineering models. Some of the developed techniques also apply to machine learning, neural networks, and related fields. Features First book on UQ in variational inequalities emerging from various network, economic, and engineering models Completely self-contained and lucid in style Aimed for a diverse audience including applied mathematicians, engineers, economists, and professionals from academia Includes the most recent developments on the subject which so far have only been available in the research literature
Author : Mircea Sofonea
Publisher : Springer Science & Business Media
Page : 235 pages
File Size : 33,32 MB
Release : 2009-04-05
Category : Mathematics
ISBN : 0387874607
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 : R. Glowinski
Publisher : Springer
Page : 264 pages
File Size : 32,58 MB
Release : 1980
Category : Computers
ISBN :
Originally published in the "Springer Series in Computational Physics," this classic in applied mathematics, computational physics and engineering is still a valuable resource for practitioners in industry and physics as well as for advanced students.