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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Sprache: Englisch
Contact in Structural Mechanics treats the problem of contact in the context of large deformations and the Coulomb friction law. The proposed formulation is based on a weak form that generalizes the classical principle of virtual powers in the sense that the weak form also encompasses all the contact laws. This formulation is thus a weighted residue method and has the advantage of being amenable to a standard finite element discretization.
This book provides the reader with a detailed description of contact kinematics and the variation calculus of kinematic quantities, two essential subjects for any contact study. The numerical resolution is carried out in statics and dynamics. In both cases, the derivation of the contact tangent matrix – an essential ingredient for iterative calculation – is explained in detail. Several numerical examples are presented to illustrate the efficiency of the method.
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Seitenzahl: 419
Veröffentlichungsjahr: 2024
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To my parents
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Series EditorNoël Challamel
Contact in Structural Mechanics
A Weighted Residual Approach
Anh Le van
First published 2024 in Great Britain and the United States by ISTE Ltd and John Wiley & Sons, Inc.
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced, stored or transmitted, in any form or by any means, with the prior permission in writing of the publishers, or in the case of reprographic reproduction in accordance with the terms and licenses issued by the CLA. Enquiries concerning reproduction outside these terms should be sent to the publishers at the undermentioned address:
ISTE Ltd27-37 St George’s RoadLondon SW19 4EUUKwww.iste.co.uk
John Wiley & Sons, Inc.111 River StreetHoboken, NJ 07030USA
www.wiley.com
© ISTE Ltd 2024The rights of Anh Le van to be identified as the author of this work have been asserted by him in accordance with the Copyright, Designs and Patents Act 1988.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s), contributor(s) or editor(s) and do not necessarily reflect the views of ISTE Group.
Library of Congress Control Number: 2023949724
British Library Cataloguing-in-Publication DataA CIP record for this book is available from the British LibraryISBN 978-1-78630-906-8
Preface
Contact is a phenomenon that must be taken into account in structure mechanics when dealing with several bodies that are connected, or that are likely to come into contact with one another. When compared to contactless mechanical problems, the novelty concerns the appearance of nonclassical boundary conditions, which are not expressed simply in terms of prescribed displacements or stresses. These contact boundary conditions, which include both equations and also inequalities, impose the non-interpenetration of the bodies and other more or less complex relations between the relative slipping and stresses at the boundary. Contact thus brings two difficulties:
The first comes from the fact that the contact laws are written along portions of the boundary of each body. It is therefore necessary to master how to calculate the geometry of these surfaces (in the 3D case). Moreover, in general, contact surfaces evolve throughout the deformations of the bodies and are the unknowns of the problem themselves.
The second difficulty is due to the inequalities contained within the contact laws. The mechanical problem is therefore necessarily nonlinear, even when assuming only small perturbations. From a numerical point of view, inequalities are known to be more difficult to deal with than equalities.
There are many works in the literature which deal with both theoretical and numerical questions of the contact problem and which are carried out in different contexts, small or large deformations, static or dynamic, with or without friction, with Coulomb friction or with other more complex interface laws.
Theoretical studies on the existence and uniqueness of the solution or analytical solutions are difficult, even in the absence of friction and with only small deformations. A numerical solution is also difficult to obtain when friction is taken into account, especially when using a more sophisticated friction law than Coulomb’s friction law, or when working within the framework of large deformations with large relative slips. For several decades, many numerical formulations, along with many variations, have been proposed to solve the various complicated contact problems in structural mechanics, and in efficient and robust ways.
This work presents a method to solve the contact problem numerically, with large deformations and with Coulomb friction. The proposed formulation differs from the others, insofar as it is based upon a weak form generalizing the principle of virtual power, which is well known in noncontact problems. The weak form is a relation of weighted residuals, just like the principle of virtual power. Consequently, it can be discretized using the finite element method by following the same typical approach as in a contactless problem. The difference with a contactless problem is that here we obtain a system of coupled equations with unknown displacements and unknown contact stresses.
Apart from the weak form of the weighted residuals, which is specific to this work, the other parts are essentially shared with the other contact formulations in the literature. Thus, for example, contact kinematics has the same formulation here as is in the other ones. Regardless of the approach chosen, the numerical solution of the nonlinear matrix system of equations calls upon an iterative Newton-type scheme, and the contact tangent matrix is obtained using the linearization or the variation techniques, which will be described in this work.
The author hopes that this book can serve as a preliminary reading that allows the reader to acquire the necessary basic notions, before delving into the beautiful and immense existing literature on contact problems.
December 2023
