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Author | : Mircea Sofonea |
Publisher | : CRC Press |
Total Pages | : 412 |
Release | : 2017-10-23 |
Genre | : Mathematics |
ISBN | : 1351649299 |
Download Variational-Hemivariational Inequalities with Applications Book in PDF, ePub and Kindle
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.
Author | : Panagiotis D. Panagiotopoulos |
Publisher | : Springer Science & Business Media |
Total Pages | : 453 |
Release | : 2012-12-06 |
Genre | : Technology & Engineering |
ISBN | : 3642516777 |
Download Hemivariational Inequalities Book in PDF, ePub and Kindle
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.
Author | : Mircea Sofonea |
Publisher | : |
Total Pages | : 0 |
Release | : 2024-12-23 |
Genre | : |
ISBN | : 9781032587165 |
Download Variational-Hemivariational Inequalities with Applications Book in PDF, ePub and Kindle
Author | : Mircea Sofonea |
Publisher | : CRC Press |
Total Pages | : 329 |
Release | : 2017-10-23 |
Genre | : Mathematics |
ISBN | : 1498761593 |
Download Variational-Hemivariational Inequalities with Applications Book in PDF, ePub and Kindle
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.
Author | : D. Goeleven |
Publisher | : Springer |
Total Pages | : 410 |
Release | : 2013-11-22 |
Genre | : Mathematics |
ISBN | : 9781461346463 |
Download Variational and Hemivariational Inequalities Theory, Methods and Applications Book in PDF, ePub and Kindle
This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and concrete problems in mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems. The book is self-contained and it offers, for the first time, the possibility to learn about inequality models and to acquire the essence of the theory in a relatively short time.
Author | : Zdzistaw Naniewicz |
Publisher | : CRC Press |
Total Pages | : 291 |
Release | : 2021-07-28 |
Genre | : Mathematics |
ISBN | : 1000445054 |
Download Mathematical Theory of Hemivariational Inequalities and Applications Book in PDF, ePub and Kindle
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.
Author | : Weimin Han |
Publisher | : Springer |
Total Pages | : 389 |
Release | : 2015-03-02 |
Genre | : Mathematics |
ISBN | : 3319144901 |
Download Advances in Variational and Hemivariational Inequalities Book in PDF, ePub and Kindle
This volume is comprised of articles providing new results on variational and hemivariational inequalities with applications to Contact Mechanics unavailable from other sources. The book will be of particular interest to graduate students and young researchers in applied and pure mathematics, civil, aeronautical and mechanical engineering, and can be used as supplementary reading material for advanced specialized courses in mathematical modeling. New results on well posedness to stationary and evolutionary inequalities and their rigorous proofs are of particular interest to readers. In addition to results on modeling and abstract problems, the book contains new results on the numerical methods for variational and hemivariational inequalities.
Author | : Stanisław Migórski |
Publisher | : Springer Science & Business Media |
Total Pages | : 293 |
Release | : 2012-09-18 |
Genre | : Mathematics |
ISBN | : 146144232X |
Download Nonlinear Inclusions and Hemivariational Inequalities Book in PDF, ePub and Kindle
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.
Author | : D. Goeleven |
Publisher | : Springer Science & Business Media |
Total Pages | : 361 |
Release | : 2013-12-11 |
Genre | : Mathematics |
ISBN | : 1441987584 |
Download Variational and Hemivariational Inequalities - Theory, Methods and Applications Book in PDF, ePub and Kindle
This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on various examples and applications in mechanics. The work can be seen as a book of applied nonlinear analysis entirely devoted to the study of inequality problems, i.e. variational inequalities and hemivariational inequalities in mathematical models and their corresponding applications to unilateral mechanics. It contains a systematic investigation of the interplay between theoretical results and concrete problems in mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems. The book is self-contained and it offers, for the first time, the possibility to learn about inequality models and to acquire the essence of the theory in a relatively short time. Audience: The book is suitable for researchers, and for doctoral and post-doctoral courses.
Author | : Siegfried Carl |
Publisher | : Springer Science & Business Media |
Total Pages | : 404 |
Release | : 2007-06-07 |
Genre | : Mathematics |
ISBN | : 038746252X |
Download Nonsmooth Variational Problems and Their Inequalities Book in PDF, ePub and Kindle
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.