variational inequalities with applications a study of antiplane frictional contact problems 18 advances in mechanics and mathematics

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Variational Inequalities With Applications

Author : Mircea Sofonea
ISBN : 9780387874609
Genre : Mathematics
File Size : 77. 80 MB
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This book is motivated by stimulating problems in contact mechanics, emphasizing antiplane frictional contact with linearly elastic and viscoelastic materials. It focuses on the essentials with respect to the qualitative aspects of several classes of variational inequalities (VIs). Clearly presented, easy to follow, and well-referenced, this work treats almost entirely VIs of the second kind, with much of the material being state-of-the-art.

Variational Hemivariational Inequalities With Applications

Author : Mircea Sofonea
ISBN : 9781351649292
Genre : Mathematics
File Size : 53. 79 MB
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This research monograph represents an outcome of the cross-fertilization between nonlinear functional analysis and mathematical modelling, and demonstrates its application to solid and contact mechanics. Based on authors’ original results, it introduces a general fixed point principle and its application to various nonlinear problems in analysis and mechanics. The classes of history-dependent operators and almost history-dependent operators are exposed in a large generality. A systematic and unified presentation contains a carefully-selected collection of new results on variational-hemivariational inequalities with or without unilateral constraints. A wide spectrum of static, quasistatic, dynamic contact problems for elastic, viscoelastic and viscoplastic materials illustrates the applicability of these theoretical results. Written for mathematicians, applied mathematicians, engineers and scientists, it is also a valuable tool for graduate students and researchers in nonlinear analysis, mathematical modelling, mechanics of solids, and contact mechanics.

Variational Inequalities And Frictional Contact Problems

Author : Anca Capatina
ISBN : 9783319101637
Genre : Mathematics
File Size : 29. 53 MB
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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.

Mathematical Models In Contact Mechanics

Author : Mircea Sofonea
ISBN : 9781107606654
Genre : Science
File Size : 78. 40 MB
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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.

Nonlinear Inclusions And Hemivariational Inequalities

Author : Stanisław Migórski
ISBN : 9781461442325
Genre : Mathematics
File Size : 59. 65 MB
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This book introduces the reader the theory of nonlinear inclusions and hemivariational inequalities with emphasis on the study of contact mechanics. The work covers both abstract results in the area of nonlinear inclusions, hemivariational inequalities as well as the study of specific contact problems, including their modelling and their variational analysis. Provided results are based on original research on the existence, uniqueness, regularity and behavior of the solution for various classes of nonlinear stationary and evolutionary inclusions. In carrying out the variational analysis of various contact models, one systematically uses results of hemivariational inequalities and, in this way, illustrates the applications of nonlinear analysis in contact mechanics. New mathematical methods are introduced and applied in the study of nonlinear problems, which describe the contact between a deformable body and a foundation. Contact problems arise in industry, engineering and geophysics. Their variational analysis presented in this book lies the background for their numerical analysis. This volume will interest mathematicians, applied mathematicians, engineers, and scientists as well as advanced graduate students.

Canonical Duality Theory

Author : David Yang Gao
ISBN : 9783319580173
Genre : Mathematics
File Size : 77. 59 MB
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This book on canonical duality theory provides a comprehensive review of its philosophical origin, physics foundation, and mathematical statements in both finite- and infinite-dimensional spaces. A ground-breaking methodological theory, canonical duality theory can be used for modeling complex systems within a unified framework and for solving a large class of challenging problems in multidisciplinary fields in engineering, mathematics, and the sciences. This volume places a particular emphasis on canonical duality theory’s role in bridging the gap between non-convex analysis/mechanics and global optimization. With 18 total chapters written by experts in their fields, this volume provides a nonconventional theory for unified understanding of the fundamental difficulties in large deformation mechanics, bifurcation/chaos in nonlinear science, and the NP-hard problems in global optimization. Additionally, readers will find a unified methodology and powerful algorithms for solving challenging problems in complex systems with real-world applications in non-convex analysis, non-monotone variational inequalities, integer programming, topology optimization, post-buckling of large deformed structures, etc. Researchers and graduate students will find explanation and potential applications in multidisciplinary fields.

Applications And Algorithms

Author :
ISBN : UOM:39015053971654
Genre : Control theory
File Size : 78. 45 MB
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International Aerospace Abstracts

Author :
ISBN : STANFORD:36105007165058
Genre : Aeronautics
File Size : 65. 91 MB
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Thermodynamik Der Irreversiblen Prozesse

Author : R. Haase
ISBN : 9783642884856
Genre : Science
File Size : 34. 72 MB
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Theoretische Physik 1

Author : Reiner M. Dreizler
ISBN : 9783540705581
Genre : Science
File Size : 23. 92 MB
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Der Grundkurs „Theoretische Physik" in vier in sich geschlossenen Bänden basiert auf langjährig, in der Praxis erprobten Vorlesungen. Die Aufbereitung der theoretisch-physikalischen Grundlagen ist hier aufs engste mit dem entsprechenden Stoff aus der Mathematik verknüpft. Der erste Band erarbeitet schrittweise die Grundlagen der Physik anhand der klassischen Mechanik. Die CD-ROM enthält einen auf die Bedürfnisse von Physik-Studierenden zugeschnittenen Mathematik-Teil sowie eine interaktive Aufgabensammlung mit ‚Experimentiermöglichkeiten’.

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