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Mathematical Models In Contact Mechanics
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Book Synopsis Mathematical Models in Contact Mechanics by : Mircea Sofonea
Download or read book Mathematical Models in Contact Mechanics written by Mircea Sofonea and published by Cambridge University Press. This book was released on 2012-09-13 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Modelling in Solid Mechanics by : Francesco dell'Isola
Download or read book Mathematical Modelling in Solid Mechanics written by Francesco dell'Isola and published by Springer. This book was released on 2017-03-10 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Modelling and Control in Solid Mechanics by : A.M. Khludnev
Download or read book Modelling and Control in Solid Mechanics written by A.M. Khludnev and published by Springer Science & Business Media. This book was released on 1997-01-21 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Well-Posed Nonlinear Problems by : Mircea Sofonea
Download or read book Well-Posed Nonlinear Problems written by Mircea Sofonea and published by Springer Nature. This book was released on 2023-11-28 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Models and Analysis of Quasistatic Contact by : Meir Shillor
Download or read book Models and Analysis of Quasistatic Contact written by Meir Shillor and published by Springer Science & Business Media. This book was released on 2004-09-16 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Contact Modeling for Solids and Particles by : Alexander Popp
Download or read book Contact Modeling for Solids and Particles written by Alexander Popp and published by Springer. This book was released on 2018-05-19 with total page 235 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Analysis and Simulation of Contact Problems by : Peter Wriggers
Download or read book Analysis and Simulation of Contact Problems written by Peter Wriggers and published by Springer Science & Business Media. This book was released on 2006-08-15 with total page 393 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Numerical Methods in Contact Mechanics by : Vladislav A. Yastrebov
Download or read book Numerical Methods in Contact Mechanics written by Vladislav A. Yastrebov and published by John Wiley & Sons. This book was released on 2013-02-13 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational contact mechanics is a broad topic which brings together algorithmic, geometrical, optimization and numerical aspects for a robust, fast and accurate treatment of contact problems. This book covers all the basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact kinematics and resolution schemes for both sequential and parallel computer architectures. The book is self-contained and intended for people working on the implementation and improvement of contact algorithms in a finite element software. Using a new tensor algebra, the authors introduce some original notions in contact kinematics and extend the classical formulation of contact elements. Some classical and new resolution methods for contact problems and associated ready-to-implement expressions are provided. Contents: 1. Introduction to Computational Contact. 2. Geometry in Contact Mechanics. 3. Contact Detection. 4. Formulation of Contact Problems. 5. Numerical Procedures. 6. Numerical Examples. About the Authors Vladislav A. Yastrebov is a postdoctoral-fellow in Computational Solid Mechanics at MINES ParisTech in France. His work in computational contact mechanics was recognized by the CSMA award and by the Prix Paul Caseau of the French Academy of Technology and Electricité de France.
Book Synopsis Modeling and Control in Solid Mechanics by : A M Khludnev
Download or read book Modeling and Control in Solid Mechanics written by A M Khludnev and published by . This book was released on 1997-01-21 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Computational Contact Mechanics by : Peter Wriggers
Download or read book Computational Contact Mechanics written by Peter Wriggers and published by Springer Science & Business Media. This book was released on 2006-10-06 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of the valuable reference source for numerical simulations of contact mechanics suitable for many fields. These include civil engineering, car design, aeronautics, metal forming, or biomechanics. For this second edition, illustrative simplified examples and new discretisation schemes and adaptive procedures for coupled problems are added. This book is at the cutting edge of an area of significant and growing interest in computational mechanics.
Book Synopsis Numerics of Unilateral Contacts and Friction by : Christian Studer
Download or read book Numerics of Unilateral Contacts and Friction written by Christian Studer and published by Springer Science & Business Media. This book was released on 2009-05-06 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mechanics provides the link between mathematics and practical engineering app- cations. It is one of the oldest sciences, and many famous scientists have left and will leave their mark in this fascinating ?eld of research. Perhaps one of the most prominentscientists in mechanics was Sir Isaac Newton, who with his “laws of - tion” initiated the description of mechanical systems by differential equations. And still today, more than 300 years after Newton, this mathematical concept is more actual than ever. The rising computer power and the development of numerical solvers for diff- ential equations allowed engineersall over the world to predict the behavior of their physical systems fast and easy in an numerical way. And the trend to computational simulation methods is still further increasing, not only in mechanics, but practically in all branches of science. Numerical simulation will probablynot solve the world’s engineering problems, but it will help for a better understanding of the mechanisms of our models.
Download or read book Contact Mechanics written by J.R. Barber and published by Springer. This book was released on 2018-02-09 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the solution of contact problems with an emphasis on idealized (mainly linear) elastic problems that can be treated with elementary analytical methods. General physical and mathematical features of these solutions are highlighted. Topics covered include the contact of rough surfaces and problems involving adhesive (e.g. van der Waals) forces. The author is a well-known researcher in the subject with hands-on experience of the topics covered and a reputation for lucid explanations. The target readership for the book includes researchers who encounter contact problems but whose primary focus is not contact mechanics. Coverage is also suitable for a graduate course in contact mechanics and end-of-chapter problems are included.
Book Synopsis Contact Mechanics II by : M. H. Aliabadi
Download or read book Contact Mechanics II written by M. H. Aliabadi and published by Computational Mechanics. This book was released on 1995 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Analysis and Approximation of Contact Problems with Adhesion or Damage by : Mircea Sofonea
Download or read book Analysis and Approximation of Contact Problems with Adhesion or Damage written by Mircea Sofonea and published by CRC Press. This book was released on 2005-09-26 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Contact Problems in Elasticity by : N. Kikuchi
Download or read book Contact Problems in Elasticity written by N. Kikuchi and published by SIAM. This book was released on 1988-01-01 with total page 508 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Mathematical Modeling in Continuum Mechanics by : Roger Temam
Download or read book Mathematical Modeling in Continuum Mechanics written by Roger Temam and published by Cambridge University Press. This book was released on 2005-05-19 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.
Book Synopsis Computational Contact Mechanics by : Peter Wriggers
Download or read book Computational Contact Mechanics written by Peter Wriggers and published by Springer Science & Business Media. This book was released on 2008-04-01 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
