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008 120606s2012 enk b 001 0 eng
010 _a2012023155
020 _a9781107606654 (pbk.)
020 _a1107606659 (pbk.)
040 _aDLC
_cDLC
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_dUKMGB
_dBDX
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050 0 0 _aTA353
_b.S55 2012
082 0 0 _a620.105
_223
_bS.M.M
100 1 _aSofonea, Mircea.
245 1 0 _aMathematical models in contact mechanics /
_cM. Sofonea, A. Matei.
260 _aCambridge, UK ;
_aNew York :
_bCambridge University Press,
_c2012.
264 _aCambridge, UK ;
_aNew York :
_bCambridge University Press,
_c2012.
300 _axiv, 280 p. ;
_c23 cm.
336 _2rdacontent
_atext
337 _2rdamedia
_aunmediated
338 _2rdacarrier
_avolume
490 1 _aLondon mathematical society lecture note series ;
_v398.
504 _aIncludes bibliographical references and index.
505 8 _aMachine generated contents note: Preface; List of symbols; Part I. Introduction to Variational Inequalities: 1. Preliminaries on functional analysis; 2. Elliptic variational inequalities; 3. History-dependent variational inequalities; Part II. Modelling and Analysis of Contact Problems: 4. Modelling of contact problems; 5. Analysis of elastic contact problems; 6. Analysis of elastic-visco-plastic contact problems; 7. Analysis of piezoelectric contact problems; Bibliographical notes; References; Index.
520 _a"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"--
520 _a"Contact processes between deformable bodies abound in industry and everyday life and, for this reason, considerable efforts have been made in their modelling and analysis. Owing to their inherent complexity, contact phenomena lead to new and interesting mathematical models. Here and everywhere in this book by a mathematical model we mean a system of partial differential equations, associated with boundary conditions and initial conditions, eventually, which describes a specific contact process. The purpose of this book is to introduce the reader to some representative mathematical models which arise in Contact Mechanics. Our aim is twofold: first, to present a sound and rigorous description of the way in which the mathematical models are constructed; second, to present the mathematical analysis of such models which includes the variational formulation, existence, uniqueness and convergence results. To this end, we use results on various classes of variational inequalities in Hilbert spaces, that we present in an abstract functional framework. Also, we use various functional methods, including monotonicity, compactness, penalization, regularization and duality methods. Moreover, we pay particular attention to the mechanical interpretation of our results and, in this way, we illustrate the cross fertilization between modelling and applications on the one hand, and nonlinear analysis on the other hand"--
650 0 _aContact mechanics
_xMathematical models.
700 1 _aMatei, Andaluzia.
830 0 _aLondon Mathematical Society lecture note series ;
_v398.
856 4 2 _3Cover image
_uhttp://assets.cambridge.org/97811076/06654/cover/9781107606654.jpg
856 4 2 _3Abstract
_uhttp://repository.fue.edu.eg/xmlui/handle/123456789/1684
942 _cBK
_2ddc