Variational-Hemivariational Inequalities with Applications
Variational-Hemivariational Inequalities with Applications

Author: Mircea Sofonea

Publisher: CRC Press

Published: 2017-10-23

Total Pages: 412

ISBN-13: 1351649299

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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.

Hemivariational Inequalities
Hemivariational Inequalities

Author: Panagiotis D. Panagiotopoulos

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 453

ISBN-13: 3642516777

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The aim of the present book is the formulation, mathematical study and numerical treatment of static and dynamic problems in mechanics and engineering sciences involving nonconvex and nonsmooth energy functions, or nonmonotone and multivalued stress-strain laws. Such problems lead to a new type of variational forms, the hemivariational inequalities, which also lead to multivalued differential or integral equations. Innovative numerical methods are presented for the treament of realistic engineering problems. This book is the first to deal with variational theory of engineering problems involving nonmonotone multivalue realations, their mechanical foundation, their mathematical study (existence and certain approximation results) and the corresponding eigenvalue and optimal control problems. All the numerical applications give innovative answers to as yet unsolved or partially solved engineering problems, e.g. the adhesive contact in cracks, the delamination problem, the sawtooth stress-strain laws in composites, the shear connectors in composite beams, the semirigid connections in steel structures, the adhesive grasping in robotics, etc. The book closes with the consideration of hemivariational inequalities for fractal type geometries and with the neural network approach to the numerical treatment of hemivariational inequalities.

Mathematical Theory of Hemivariational Inequalities and Applications
Mathematical Theory of Hemivariational Inequalities and Applications

Author: Zdzistaw Naniewicz

Publisher: CRC Press

Published: 2021-07-28

Total Pages: 291

ISBN-13: 1000445054

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Gives a complete and rigorous presentation of the mathematical study of the expressions - hemivariational inequalities - arising in problems that involve nonconvex, nonsmooth energy functions. A theory of the existence of solutions for inequality problems involving monconvexity and nonsmoothness is established.

Nonlinear Inclusions and Hemivariational Inequalities
Nonlinear Inclusions and Hemivariational Inequalities

Author: Stanisław Migórski

Publisher: Springer Science & Business Media

Published: 2012-09-18

Total Pages: 293

ISBN-13: 146144232X

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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.

Nonsmooth Variational Problems and Their Inequalities
Nonsmooth Variational Problems and Their Inequalities

Author: Siegfried Carl

Publisher: Springer Science & Business Media

Published: 2007-06-07

Total Pages: 404

ISBN-13: 038746252X

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This monograph focuses primarily on nonsmooth variational problems that arise from boundary value problems with nonsmooth data and/or nonsmooth constraints, such as multivalued elliptic problems, variational inequalities, hemivariational inequalities, and their corresponding evolution problems. It provides a systematic and unified exposition of comparison principles based on a suitably extended sub-supersolution method.

Finite Element Method for Hemivariational Inequalities
Finite Element Method for Hemivariational Inequalities

Author: J. Haslinger

Publisher: Springer Science & Business Media

Published: 1999-08-31

Total Pages: 298

ISBN-13: 9780792359517

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Hemivariational inequalities represent an important class of problems in nonsmooth and nonconvex mechanics. By means of them, problems with nonmonotone, possibly multivalued, constitutive laws can be formulated, mathematically analyzed and finally numerically solved. The present book gives a rigorous analysis of finite element approximation for a class of hemivariational inequalities of elliptic and parabolic type. Finite element models are described and their convergence properties are established. Discretized models are numerically treated as nonconvex and nonsmooth optimization problems. The book includes a comprehensive description of typical representants of nonsmooth optimization methods. Basic knowledge of finite element mathematics, functional and nonsmooth analysis is needed. The book is self-contained, and all necessary results from these disciplines are summarized in the introductory chapter. Audience: Engineers and applied mathematicians at universities and working in industry. Also graduate-level students in advanced nonlinear computational mechanics, mathematics of finite elements and approximation theory. Chapter 1 includes the necessary prerequisite materials.

Analysis and Approximation of Contact Problems with Adhesion or Damage
Analysis and Approximation of Contact Problems with Adhesion or Damage

Author: Mircea Sofonea

Publisher: CRC Press

Published: 2005-09-26

Total Pages: 220

ISBN-13: 1420034839

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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

Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities
Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities

Author: Dumitru Motreanu

Publisher: Springer Science & Business Media

Published: 1999

Total Pages: 332

ISBN-13: 9780792354567

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The present book is the first ever published in which a new type of eigenvalue problem is studied, one that is very useful for applications: eigenvalue problems related to hemivariational inequalities, i.e. involving nonsmooth, nonconvex, energy functions. New existence, multiplicity and perturbation results are proved using three different approaches: minimization, minimax methods and (sub)critical point theory. Nonresonant and resonant cases are studied both for static and dynamic problems and several new qualitative properties of the hemivariational inequalities are obtained. Both simple and double eigenvalue problems are studied, as well as those constrained on the sphere and those which are unconstrained. The book is self-contained, is written with the utmost possible clarity and contains highly original results. Applications concerning new stability results for beams, plates and shells with adhesive supports, etc. illustrate the theory. Audience: applied and pure mathematicians, civil, aeronautical and mechanical engineers.

Noncoercive Variational Problems and Related Results
Noncoercive Variational Problems and Related Results

Author: Daniel Goeleven

Publisher: CRC Press

Published: 1996-10-10

Total Pages: 186

ISBN-13: 9780582304024

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In establishing a general theory of the existence of solutions for noncoercive variational problems and constrained problems formulated as variational inequalities or hemivariational inequalities, this Research Note illustrates recent mathematical approaches and results with various examples from mathematics and mechanics. The book unifies ideas for the treatment of various noncoercive problems and provides previously unpublished results for variational inequalities and hemivariational inequalities. The author points out important applications in mechanics and their mathfematical tratment using recession tools. This book will be of particular interest to researchers in pure and aplied mathematics and mechanics.

Variational Methods
Variational Methods

Author: Michael Struwe

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 292

ISBN-13: 3662041944

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Hilberts talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateaus problem by Douglas and Rad. This third edition gives a concise introduction to variational methods and presents an overview of areas of current research in the field, plus a survey on new developments.