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Author: N. Kikuchi
Publisher: SIAM
ISBN: 9781611970845
Category : Science
Languages : en
Pages : 508
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Book Description
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: N. Kikuchi
Publisher: SIAM
ISBN: 9781611970845
Category : Science
Languages : en
Pages : 508
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Book Description
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: L. A. Galin
Publisher: Springer Science & Business Media
ISBN: 1402090439
Category : Science
Languages : en
Pages : 325
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Book Description
L.A. Galin’s book on contact problems is a remarkable work. Actually there are two books: the first, published in 1953 deals with contact problems in the classical theory of elasticity; this is the one that was translated into English in 1961. The second book, published in 1980, included the first, and then had new sections on contact problems for viscoelastic materials, and rough contact problems; this section has not previously been translated into English. In this new translation, the original text and the mathematical analysis have been completely revised, new material has been added, and the material appearing in the 1980 Russian translation has been completely rewritten. In addition there are three essays by students of Galin, bringing the analysis up to date.
Author: Zdeněk Dostál
Publisher: Springer
ISBN: 1493968343
Category : Mathematics
Languages : en
Pages : 341
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Book Description
This book presents a comprehensive and self-contained treatment of the authors’ newly developed scalable algorithms for the solutions of multibody contact problems of linear elasticity. The brand new feature of these algorithms is theoretically supported numerical scalability and parallel scalability demonstrated on problems discretized by billions of degrees of freedom. The theory supports solving multibody frictionless contact problems, contact problems with possibly orthotropic Tresca’s friction, and transient contact problems. It covers BEM discretization, jumping coefficients, floating bodies, mortar non-penetration conditions, etc. The exposition is divided into four parts, the first of which reviews appropriate facets of linear algebra, optimization, and analysis. The most important algorithms and optimality results are presented in the third part of the volume. The presentation is complete, including continuous formulation, discretization, decomposition, optimality results, and numerical experiments. The final part includes extensions to contact shape optimization, plasticity, and HPC implementation. Graduate students and researchers in mechanical engineering, computational engineering, and applied mathematics, will find this book of great value and interest.
Author: Abigail Judge
Publisher: Oxford University Press
ISBN: 0190235209
Category : Family & Relationships
Languages : en
Pages : 353
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Book Description
Overcoming Parent-Child Contact Problems describes interventions for families experiencing a high conflict divorce impasse where a child is resisting contact with a parent.
Author: Mircea Sofonea
Publisher: CRC Press
ISBN: 1420034839
Category : Mathematics
Languages : en
Pages : 239
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Book Description
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
Author: Christof Eck
Publisher: CRC Press
ISBN: 1420027360
Category : Mathematics
Languages : en
Pages : 418
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Book Description
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: Peter Wriggers
Publisher: Springer
ISBN: 3709124964
Category : Science
Languages : en
Pages : 255
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Book Description
The book gives an overview on formulation, mathematical analysis and numerical solution procedures of contact problems. In this respect the book should be of value to applied mathematicians and engineers who are concerned with contact mechanics.
Author: Anca Capatina
Publisher: Springer
ISBN: 3319101633
Category : Mathematics
Languages : en
Pages : 242
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Book Description
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: Walter Sextro
Publisher: Springer Science & Business Media
ISBN: 3540468714
Category : Science
Languages : en
Pages : 163
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Book Description
The aim of this book is to describe an efficient procedure to model dynamical contact problems with friction. This procedure is applied to different practical problems and validated by experiments. Friction contacts are used to transmit forces or to dissipate energy. Examples for dynamical engineering systems with friction are brakes, machine tools, motors, turbines, bearings or wheel-rail systems. A better understanding of friction phenomena can result in improvements like the reduction of noise and maintenance costs, increased life time of machines and improved energy efficiency. Dependent on the features of the friction contact, different contact models and solution methods are applied.
Author: G.M.L. Gladwell
Publisher: Springer Science & Business Media
ISBN: 9789028607606
Category : Science
Languages : en
Pages : 740
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Book Description
