Variational Inequalities And Frictional Contact Problems PDF Download
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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 | : N. Kikuchi |
Publisher | : SIAM |
Total Pages | : 498 |
Release | : 1988-01-01 |
Genre | : Science |
ISBN | : 0898714680 |
Download Contact Problems in Elasticity Book in PDF, ePub and Kindle
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.
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 | : Mamdouh H. (Mamdouh Hussien) Refaat |
Publisher | : National Library of Canada = Bibliothèque nationale du Canada |
Total Pages | : 318 |
Release | : 1996 |
Genre | : |
ISBN | : 9780612116429 |
Download Nonlinear Finite Element Analysis of Frictional Contact Problems Using Variational Inequalities [microform] Book in PDF, ePub and Kindle
Author | : N. Kikuchi |
Publisher | : |
Total Pages | : |
Release | : 1979 |
Genre | : |
ISBN | : |
Download Contact problems in elasticity Book in PDF, ePub and Kindle
Author | : Christof Eck |
Publisher | : CRC Press |
Total Pages | : 398 |
Release | : 2005-03-17 |
Genre | : Mathematics |
ISBN | : 1420027360 |
Download Unilateral Contact Problems Book in PDF, ePub and Kindle
The mathematical analysis of contact problems, with or without friction, is an area where progress depends heavily on the integration of pure and applied mathematics. This book presents the state of the art in the mathematical analysis of unilateral contact problems with friction, along with a major part of the analysis of dynamic contact problems
Author | : Mircea Sofonea |
Publisher | : Cambridge University Press |
Total Pages | : 295 |
Release | : 2012-09-13 |
Genre | : Science |
ISBN | : 1139577204 |
Download Mathematical Models in Contact Mechanics Book in PDF, ePub and Kindle
This text provides a complete introduction to the theory of variational inequalities with emphasis on contact mechanics. It covers existence, uniqueness and convergence results for variational inequalities, including the modelling and variational analysis of specific frictional contact problems with elastic, viscoelastic and viscoplastic materials. New models of contact are presented, including contact of piezoelectric materials. Particular attention is paid to the study of history-dependent quasivariational inequalities and to their applications in the study of contact problems with unilateral constraints. The book fully illustrates the cross-fertilisation between modelling and applications on the one hand and nonlinear mathematical analysis on the other. Indeed, the reader will gain an understanding of how new and nonstandard models in contact mechanics lead to new types of variational inequalities and, conversely, how abstract results concerning variational inequalities can be applied to prove the unique solvability of the corresponding contact problems.
Author | : Weimin Han |
Publisher | : American Mathematical Soc. |
Total Pages | : 464 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821831925 |
Download Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity Book in PDF, ePub and Kindle
Índice: Function spaces and their properties; Introduction to finite difference and finite element approximations; Variational inequalities; Constitutive relations in solid mechanics; Background on variational and numerical analysis in contact mechanics; Contact problems in elasticity; Bilateral contact with slip dependent friction; Frictional contact with normal compliance; Frictional contact with normal damped response; Other viscoelastic contact problems; Frictionless contact with dissipative potential; Frictionless contact between two viscoplastic bodies; Bilateral contact with Tresca's friction law; Other viscoelastic contact problems; Bibliography; Index.
Author | : Aleksander Czekanski |
Publisher | : |
Total Pages | : 0 |
Release | : 2001 |
Genre | : |
ISBN | : |
Download Novel Nonlinear Finite Element Analysis of Dynamic Contact Problems Using Variational Inequalities Book in PDF, ePub and Kindle
Dynamic contact problems play an important role in dictating the integrity, performance and safety of many engineering systems/components involved in vehicle design, armament and ballistics, metal forming/cutting, and surface treatments, just to name a few. Despite their importance to the mechanical integrity of the systems examined, dynamic contact effects are frequently treated using oversimplifying assumptions, which neglect the main feature of the problem. This is because of the complexity of the governing system of equations. In this work, dynamic frictional contact problems are formulated using the more reliable and consistent variational inequalities (VI) approach. Three aspects of the problem are accordingly examined. The first is concerned with the development of the appropriate variational inequality formulations and solution strategies for dynamic frictional contact problems involving material and geometrical nonlinearity. Two models of surfaces are taken into account: (i) perfectly smooth surfaces, and (ii) more realistic surfaces, which take into account the change in compliance due to surface roughness. A new technique for representing the kinematic contact conditions is developed. Two newly devised numerical procedures are devised to solve the general dynamic frictional contact problem for elastic and elasto-plastic media. The first solution strategy, which regularises friction, is based upon the iterative use of mathematical programming and Lagrange multipliers. The second approach is accomplished using a nondifferentiable optimisation algorithm, through a sequence of mathematical programming sub-problems. The second aspect of the work is concerned with the selection of a suitable time integration scheme for contact problems. The values of the time integration parameters are so chosen to ensure that the solution is second order accurate, unconditionally stable, preserves energy and momentum during rigid impact, thus minimising numerical oscillations and ensuring optimal numerical dissipation. Finally, the developed algorithms are validated and applied to the analysis of several interesting engineering problems. The numerical predictions are compared to existing experiments as well as a commercial finite element code. The results reveal that the new dynamic friction contact formulations are more accurate than the traditional variational methods. These newly developed algorithms should provide designers with a powerful tool for treating dynamic elasto-plastic problems involving frictional contact.
Author | : Peter Wriggers |
Publisher | : Springer Science & Business Media |
Total Pages | : 393 |
Release | : 2006-08-15 |
Genre | : Science |
ISBN | : 3540317619 |
Download Analysis and Simulation of Contact Problems Book in PDF, ePub and Kindle
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.