Mathematical Models In Contact Mechanics
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Mathematical Models In Contact Mechanics
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Author : Mircea Sofonea
language : en
Publisher: Cambridge University Press
Release Date : 2012-09-13
Mathematical Models In Contact Mechanics written by Mircea Sofonea and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-13 with Science categories.
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.
Well Posed Nonlinear Problems
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Author : Mircea Sofonea
language : en
Publisher: Springer Nature
Release Date : 2023-11-28
Well Posed Nonlinear Problems written by Mircea Sofonea and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-28 with Mathematics categories.
This monograph presents an original method to unify the mathematical theories of well-posed problems and contact mechanics. The author uses a new concept called the Tykhonov triple to develop a well-posedness theory in which every convergence result can be interpreted as a well-posedness result. This will be useful for studying a wide class of nonlinear problems, including fixed-point problems, inequality problems, and optimal control problems. Another unique feature of the manuscript is the unitary treatment of mathematical models of contact, for which new variational formulations and convergence results are presented. Well-Posed Nonlinear Problems will be a valuable resource for PhD students and researchers studying contact problems. It will also be accessible to interested researchers in related fields, such as physics, mechanics, engineering, and operations research.
Modelling And Control In Solid Mechanics
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Author : A.M. Khludnev
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-01-21
Modelling And Control In Solid Mechanics written by A.M. Khludnev 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 1997-01-21 with Computers categories.
This book covers the boundary value problems for a wide range of mathematical models of the mechanics of deformable bodies, in particular, the boundary value problems concerning plates and shells, crack theory, and elastoplastic bodies. An essential feature of the discussed boundary value problems is the availability of the inequality type constraints imposed on solutions such as the impenetration condition for contact problems, the yield plasticity condition, etc. As a consequence, the presence of free boundaries is typical of the boundary value problems concerned. The objective of the book is to display some new methods of analyzing such problems, as well as to perform research on new models evolved from engineering practice. Readers will find a variety of new mathematical models describing some contact problems for plates and shells, an equilibrium of plates involving cracks, etc. Furthermore, some new mathematical methods are presented which were specially developed by the authors to study the problems concerned. These help to convey a comprehensive picture of the present state of mathematical problems on the free-boundary elasticity and plasticity theory. The book is intended for postgraduates, scientists and engineers.and for Students interested in problems of modelling and optimal control in the mechanics of deformable bodies.
Analysis And Simulation Of Contact Problems
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Author : Peter Wriggers
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-15
Analysis And Simulation Of Contact Problems written by Peter Wriggers 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 2006-08-15 with Science categories.
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.
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.
Contact Mechanics Ii
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Author : M. H. Aliabadi
language : en
Publisher: Computational Mechanics
Release Date : 1995
Contact Mechanics Ii written by M. H. Aliabadi and has been published by Computational Mechanics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Contact mechanics categories.
Conference proceedings including papers on mechanical models such as rolling, impact and shock, unilateral contact; numerical models such as finite element method, boundary element method, and the integral equations; engineering applications such as fracture mechanics and composite materials and mathematical models.
Contact Modeling For Solids And Particles
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Author : Alexander Popp
language : en
Publisher: Springer
Release Date : 2018-05-19
Contact Modeling For Solids And Particles written by Alexander Popp and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-19 with Science categories.
The book conveys modern techniques and the latest state-of-the-art with regard to the most fundamental aspects of computational contact mechanics. However, since contact can readily be interpreted as a special type of interface problem, it seems advisable not to isolate contact mechanics, but rather to address it in the context of a broader class of problems denoted as computational interface mechanics. The book gives a clear understanding of the underlying physics of interfaces, and a comprehensive insight into the current state-of-the-art and selected cutting-edge research directions in the computational treatment of interface effects. It focuses on the modeling of friction, wear, lubrication, cohesive interfaces, grain boundaries, phase boundaries, fracture, thermo-mechanics and particulate contact (e.g. granular media). Also the most important computational aspects are addressed, including discretization techniques for finite deformations, solution algorithms for single- and multi-processor computing environments, multi-scale approaches, discrete element models and multi-physics problems including contact and interface constraints. Among the computational techniques covered in this book are finite element (FEM) and boundary element (BEM) methods, atomistic models, molecular dynamics (MD), discrete element methods (DEM), coupling approaches for multi-scale simulations, and tools for an efficient automated FEM code generation.
Mathematical Modelling In Solid Mechanics
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Author : Francesco dell'Isola
language : en
Publisher: Springer
Release Date : 2017-03-10
Mathematical Modelling In Solid Mechanics written by Francesco dell'Isola and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-10 with Science categories.
This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling analysis of elasto-plastic structures engineering optimization and design, global optimization and related algorithms The book presents selected papers presented at ETAMM 2016. It includes new and original results written by internationally recognized specialists.
Computational Contact Mechanics
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Author : Peter Wriggers
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-01
Computational Contact Mechanics written by Peter Wriggers 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 2008-04-01 with Science categories.
Topics of this book span the range from spatial and temporal discretization techniques for contact and impact problems with small and finite deformations over investigations on the reliability of micromechanical contact models over emerging techniques for rolling contact mechanics to homogenization methods and multi-scale approaches in contact problems.
Analysis And Approximation Of Contact Problems With Adhesion Or Damage
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Author : Mircea Sofonea
language : en
Publisher: CRC Press
Release Date : 2005-09-26
Analysis And Approximation Of Contact Problems With Adhesion Or Damage written by Mircea Sofonea and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-26 with Mathematics categories.
Research into contact problems continues to produce a rapidly growing body of knowledge. Recognizing the need for a single, concise source of information on models and analysis of contact problems, accomplished experts Sofonea, Han, and Shillor carefully selected several models and thoroughly study them in Analysis and Approximation of Contact P