Finite Element Approximation Of Contact And Friction In Elasticity

Author : Franz Chouly,Patrick Hild,Yves Renard
Publisher : Springer Nature
Page : 306 pages
File Size : 43,7 Mb
Release : 2023-06-23
Category : Mathematics
ISBN : 9783031314230

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Finite Element Approximation of Contact and Friction in Elasticity by Franz Chouly,Patrick Hild,Yves Renard Pdf

This book presents the mathematics behind the formulation, approximation, and numerical analysis of contact and friction problems. It also provides a survey of recent developments in the numerical approximation of such problems as well as several remaining unsolved issues. Particular focus is placed on the Signorini problem and on frictionless unilateral contact in small strain. The final chapters cover more complex, applications-oriented problems, such as frictional contact, multi-body contact, and large strain. Finite Element Approximation of Contact and Friction in Elasticity will be a valuable resource for researchers in the area. It may also be of interest to those studying scientific computing and computational mechanics.

Author : N. Kikuchi,J. T. Oden
Publisher : SIAM
Page : 498 pages
File Size : 43,9 Mb
Release : 1988-01-01
Category : Science
ISBN : 9780898714685

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Contact Problems in Elasticity by N. Kikuchi,J. T. Oden Pdf

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,Weimin Han,Meir Shillor
Publisher : CRC Press
Page : 220 pages
File Size : 53,7 Mb
Release : 2005-09-26
Category : Mathematics
ISBN : 9781420034837

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Analysis and Approximation of Contact Problems with Adhesion or Damage by Mircea Sofonea,Weimin Han,Meir Shillor Pdf

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 : Juilung Julian Hsu
Publisher : Unknown
Page : 374 pages
File Size : 52,5 Mb
Release : 1990
Category : Electronic
ISBN : WISC:89032821498

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Constitutive Modeling and Finite Element Analysis of Frictional Contact Problems by Juilung Julian Hsu Pdf

Author : Susumu Takahashi
Publisher : Springer Science & Business Media
Page : 227 pages
File Size : 46,5 Mb
Release : 2013-03-08
Category : Science
ISBN : 9783642845024

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Elastic Contact Analysis by Boundary Elements by Susumu Takahashi Pdf

This book presents a new formulation of the boundary element method for two-dimensional and axisymmetric contact problems. The solution procedure includes the effects of non-frictional as well as frictional contact between elastic bodies. Following a literature survey of various experimental and analytical approaches for solving elastic contact problems, a comprehensive review of numerical techniques used for analyses of contact problems is presented. The boundary element formulations for two-, three-dimensional and axisymmetric problems in elasticity are derived and numerical implementation using constant and linear elements is described. For analysis of contact problems, boundary elements are employed to compute flexibility matrices representing the relationship between tractions and displacements only at nodes coming into contact. The contact analysis is performed using the flexibility matrices in conjunction with contact boundary conditions. In this approach, only equations corresponding to the node coming into contact are required and consequently very efficient computation is achieved. Furthermore, the boundary element analysis and the contact analysis are performed separately, which makes it easy to implement the contact analysis procedure into boundary element codes. A new contact criterion for nodes coming into contact is proposed. Load incremental and iterative schemes are used to obtain accurate solutions. Some classical Hertz and non-Hertz contact problems are studied and results are found to be in good agreement with analytical and other numerical solutions.

Author : K. J. Bathe
Publisher : Elsevier
Page : 314 pages
File Size : 44,8 Mb
Release : 2014-05-23
Category : Technology & Engineering
ISBN : 9781483161747

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Nonlinear Finite Element Analysis and Adina by K. J. Bathe Pdf

Nonlinear Finite Element Analysis and ADINA contains the proceedings of the Fourth ADINA Conference held at Massachusetts Institute of Technology on June 15-17, 1983. Separating the papers presented in the conference as chapters, this book first elucidates the use of ADINA for analysis of mines with explosive fills. Subsequent chapters explore the use of ADINA in soil mechanics; nonlinear shell analysis; analysis of bond between prestressed steel and concrete; determination and simulation of stable crack growth; offshore structures analysis; modeling of traveling-loads and time-dependent masses; and comparison of two slideline methods. Other notable applications of ADINA are also shown.

Author : Tod A. Laursen
Publisher : Springer Science & Business Media
Page : 466 pages
File Size : 41,9 Mb
Release : 2013-03-14
Category : Science
ISBN : 9783662048641

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Computational Contact and Impact Mechanics by Tod A. Laursen Pdf

Many physical systems require the description of mechanical interaction across interfaces if they are to be successfully analyzed. Examples in the engineered world range from the design of prosthetics in biomedical engi neering (e. g. , hip replacements); to characterization of the response and durability of head/disk interfaces in computer magnetic storage devices; to development of pneumatic tires with better handling characteristics and increased longevity in automotive engineering; to description of the adhe sion and/or relative slip between concrete and reinforcing steel in structural engineering. Such mechanical interactions, often called contact/impact in teractions, usually necessitate at minimum the determination of areas over which compressive pressures must act to prevent interpenetration of the mechanical entities involved. Depending on the application, frictional be havior, transient interaction of interfaces with their surroundings (e. g. , in termittent stick/slip), thermo-mechanical coupling, interaction with an in tervening lubricant and/or fluid layer, and damage of the interface (i. e. , wear) may also be featured. When taken together (or even separately!), these features have the effect of making the equations of mechanical evolu tion not only highly nonlinear, but highly nonsmooth as well. While many modern engineering simulation packages possess impressive capabilities in the general area of nonlinear mechanics, it can be contended that methodologies typically utilized for contact interactions are relatively immature in comparison to other components of a nonlinear finite element package, such as large deformation kinematics, inelastic material modeling, nonlinear equation solving, or linear solver technology.

Author : Shen R. Wu,Lei Gu
Publisher : John Wiley & Sons
Page : 352 pages
File Size : 48,5 Mb
Release : 2012-07-30
Category : Mathematics
ISBN : 9781118382073

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Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics by Shen R. Wu,Lei Gu Pdf

A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in mastering the explicit finite element method and programming code without requiring extensive background knowledge of the general finite element. The authors present topics relating to the variational principle, numerical procedure, mechanical formulation, and fundamental achievements of the convergence theory. In addition, key topics and techniques are provided in four clearly organized sections: • Fundamentals explores a framework of the explicit finite element method for nonlinear transient dynamics and highlights achievements related to the convergence theory • Element Technology discusses four-node, three-node, eight-node, and two-node element theories • Material Models outlines models of plasticity and other nonlinear materials as well as the mechanics model of ductile damage • Contact and Constraint Conditions covers subjects related to three-dimensional surface contact, with examples solved analytically, as well as discussions on kinematic constraint conditions Throughout the book, vivid figures illustrate the ideas and key features of the explicit finite element method. Examples clearly present results, featuring both theoretical assessments and industrial applications. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics is an ideal book for both engineers who require more theoretical discussions and for theoreticians searching for interesting and challenging research topics. The book also serves as an excellent resource for courses on applied mathematics, applied mechanics, and numerical methods at the graduate level.

Author : Jiri Nedoma,Jiri Stehlik,Ivan Hlavacek,Josef Danek,Tatjana Dostalova,Petra Preckova
Publisher : John Wiley & Sons
Page : 458 pages
File Size : 54,5 Mb
Release : 2011-06-09
Category : Science
ISBN : 9781118006467

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Mathematical and Computational Methods in Biomechanics of Human Skeletal Systems by Jiri Nedoma,Jiri Stehlik,Ivan Hlavacek,Josef Danek,Tatjana Dostalova,Petra Preckova Pdf

Cutting-edge solutions to current problems in orthopedics, supported by modeling and numerical analysis Despite the current successful methods and achievements of good joint implantations, it is essential to further optimize the shape of implants so they may better resist extreme long-term mechanical demands. This book provides the orthopedic, biomechanical, and mathematical basis for the simulation of surgical techniques in orthopedics. It focuses on the numerical modeling of total human joint replacements and simulation of their functions, along with the rigorous biomechanics of human joints and other skeletal parts. The book includes: An introduction to the anatomy and biomechanics of the human skeleton, biomaterials, and problems of alloarthroplasty The definition of selected simulated orthopedic problems Constructions of mathematical model problems of the biomechanics of the human skeleton and its parts Replacement parts of the human skeleton and corresponding mathematical model problems Detailed mathematical analyses of mathematical models based on functional analysis and finite element methods Biomechanical analyses of particular parts of the human skeleton, joints, and corresponding replacements A discussion of the problems of data processing from nuclear magnetic resonance imaging and computer tomography This timely book offers a wealth of information on the current research in this field. The theories presented are applied to specific problems of orthopedics. Numerical results are presented and discussed from both biomechanical and orthopedic points of view and treatment methods are also briefly addressed. Emphasis is placed on the variational approach to the investigated model problems while preserving the orthopedic nature of the investigated problems. The book also presents a study of algorithmic procedures based on these simulation models. This is a highly useful tool for designers, researchers, and manufacturers of joint implants who require the results of suggested experiments to improve existing shapes or to design new shapes. It also benefits graduate students in orthopedics, biomechanics, and applied mathematics.

Author : Weimin Han,Mircea Sofonea
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 50,7 Mb
Release : 2002
Category : Contact mechanics
ISBN : 9780821831922

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Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity by Weimin Han,Mircea Sofonea Pdf

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 : Stéphane P. A. Bordas,Erik Burman,Mats G. Larson,Maxim A. Olshanskii
Publisher : Springer
Page : 361 pages
File Size : 55,8 Mb
Release : 2018-03-13
Category : Mathematics
ISBN : 9783319714318

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Geometrically Unfitted Finite Element Methods and Applications by Stéphane P. A. Bordas,Erik Burman,Mats G. Larson,Maxim A. Olshanskii Pdf

This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and augmented Lagrangian techniques. It is aimed at researchers in applied mathematics, scientific computing or computational engineering.

Author : Michael E. Plesha
Publisher : Unknown
Page : 24 pages
File Size : 49,7 Mb
Release : 1986
Category : Electronic
ISBN : NASA:31769000575368

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A Constitutive Law for Finite Element Contact Problems with Unclassical Friction by Michael E. Plesha Pdf

Author : O. C. Zienkiewicz,K. Morgan
Publisher : Courier Corporation
Page : 356 pages
File Size : 48,5 Mb
Release : 2013-04-22
Category : Technology & Engineering
ISBN : 9780486318011

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Finite Elements and Approximation by O. C. Zienkiewicz,K. Morgan Pdf

A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises. Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher order finite element approximation, mapping and numerical integration, variational methods, and partial discretization and time-dependent problems. A survey of generalized finite elements and error estimates concludes the text.

Author : Anca Capatina
Publisher : Springer
Page : 242 pages
File Size : 51,5 Mb
Release : 2014-09-16
Category : Mathematics
ISBN : 9783319101637

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Variational Inequalities and Frictional Contact Problems by Anca Capatina Pdf

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 : Anonim
Publisher : Unknown
Page : 400 pages
File Size : 47,6 Mb
Release : 1948
Category : Mechanics, Applied
ISBN : OSU:32435026160655

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Applied mechanics reviews by Anonim Pdf