Nonsmooth Nonconvex Mechanics

Author : David Yang Gao,Raymond W. Ogden,Georgios E. Stavroulakis
Publisher : Springer Science & Business Media
Page : 505 pages
File Size : 49,8 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302759

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Nonsmooth/Nonconvex Mechanics by David Yang Gao,Raymond W. Ogden,Georgios E. Stavroulakis Pdf

Nonsmooth and nonconvex models arise in several important applications of mechanics and engineering. The interest in this field is growing from both mathematicians and engineers. The study of numerous industrial applications, including contact phenomena in statics and dynamics or delamination effects in composites, require the consideration of nonsmoothness and nonconvexity. The mathematical topics discussed in this book include variational and hemivariational inequalities, duality, complementarity, variational principles, sensitivity analysis, eigenvalue and resonance problems, and minimax problems. Applications are considered in the following areas among others: nonsmooth statics and dynamics, stability of quasi- static evolution processes, friction problems, adhesive contact and debonding, inverse problems, pseudoelastic modeling of phase transitions, chaotic behavior in nonlinear beams, and nonholonomic mechanical systems. This volume contains 22 chapters written by various leading researchers and presents a cohesive and authoritative overview of recent results and applications in the area of nonsmooth and nonconvex mechanics. Audience: Faculty, graduate students, and researchers in applied mathematics, optimization, control and engineering.

Author : J.J. Moreau,P.D. Panagiotopoulos
Publisher : Springer
Page : 466 pages
File Size : 49,7 Mb
Release : 2014-05-04
Category : Science
ISBN : 9783709126240

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Nonsmooth Mechanics and Applications by J.J. Moreau,P.D. Panagiotopoulos Pdf

Author : Jean Jacques Moreau,P. D. Panagiotopoulos,Gilbert Strang
Publisher : Birkhauser
Page : 358 pages
File Size : 46,8 Mb
Release : 1988
Category : Mathematics
ISBN : UOM:39015020863174

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Topics in Nonsmooth Mechanics by Jean Jacques Moreau,P. D. Panagiotopoulos,Gilbert Strang Pdf

Author : Vladimir F. Demyanov,Georgios E. Stavroulakis,L.N. Polyakova,P. D. Panagiotopoulos
Publisher : Springer
Page : 349 pages
File Size : 41,7 Mb
Release : 2013-11-15
Category : Computers
ISBN : 1461368448

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Quasidifferentiability and Nonsmooth Modelling in Mechanics, Engineering and Economics by Vladimir F. Demyanov,Georgios E. Stavroulakis,L.N. Polyakova,P. D. Panagiotopoulos Pdf

Nonsmooth energy functions govern phenomena which occur frequently in nature and in all areas of life. They constitute a fascinating subject in mathematics and permit the rational understanding of yet unsolved or partially solved questions in mechanics, engineering and economics. This is the first book to provide a complete and rigorous presentation of the quasidifferentiability approach to nonconvex, possibly nonsmooth, energy functions, of the derivation and study of the corresponding variational expressions in mechanics, engineering and economics, and of their numerical treatment. The new variational formulations derived are illustrated by many interesting numerical problems. The techniques presented will permit the reader to check any solution obtained by other heuristic techniques for nonconvex, nonsmooth energy problems. A civil, mechanical or aeronautical engineer can find in the book the only existing mathematically sound technique for the formulation and study of nonconvex, nonsmooth energy problems. Audience: The book will be of interest to pure and applied mathematicians, physicists, researchers in mechanics, civil, mechanical and aeronautical engineers, structural analysts and software developers. It is also suitable for graduate courses in nonlinear mechanics, nonsmooth analysis, applied optimization, control, calculus of variations and computational mechanics.

Author : Pierre Alart,Olivier Maisonneuve,R. Tyrrell Rockafellar
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 45,9 Mb
Release : 2006-06-26
Category : Technology & Engineering
ISBN : 9780387291956

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Nonsmooth Mechanics and Analysis by Pierre Alart,Olivier Maisonneuve,R. Tyrrell Rockafellar Pdf

This book’s title, Nonsmooth Mechanics and Analysis, refers to a major domain of mechanics, particularly those initiated by the works of Jean Jacques Moreau. Nonsmooth mechanics concerns mechanical situations with possible nondifferentiable relationships, eventually discontinuous, as unilateral contact, dry friction, collisions, plasticity, damage, and phase transition. The basis of the approach consists in dealing with such problems without resorting to any regularization process. Indeed, the nonsmoothness is due to simplified mechanical modeling; a more sophisticated model would require too large a number of variables, and sometimes the mechanical information is not available via experimental investigations. Therefore, the mathematical formulation becomes nonsmooth; regularizing would only be a trick of arithmetic without any physical justification. Nonsmooth analysis was developed, especially in Montpellier, to provide specific theoretical and numerical tools to deal with nonsmoothness. It is important not only in mechanics but also in physics, robotics, and economics. Audience This book is intended for researchers in mathematics and mechanics.

Author : E.S. Mistakidis,Georgios E. Stavroulakis
Publisher : Springer Science & Business Media
Page : 295 pages
File Size : 51,7 Mb
Release : 2013-11-21
Category : Technology & Engineering
ISBN : 9781461558293

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Nonconvex Optimization in Mechanics by E.S. Mistakidis,Georgios E. Stavroulakis Pdf

Nonconvexity and nonsmoothness arise in a large class of engineering applica tions. In many cases of practical importance the possibilities offered by opti mization with its algorithms and heuristics can substantially improve the per formance and the range of applicability of classical computational mechanics algorithms. For a class of problems this approach is the only one that really works. The present book presents in a comprehensive way the application of opti mization algorithms and heuristics in smooth and nonsmooth mechanics. The necessity of this approach is presented to the reader through simple, represen tative examples. As things become more complex, the necessary material from convex and nonconvex optimization and from mechanics are introduced in a self-contained way. Unilateral contact and friction problems, adhesive contact and delamination problems, nonconvex elastoplasticity, fractal friction laws, frames with semi rigid connections, are among the applications which are treated in details here. Working algorithms are given for each application and are demonstrated by means of representative examples. The interested reader will find helpful references to up-to-date scientific and technical literature so that to be able to work on research or engineering topics which are not directly covered here.

Author : P. D. Panagiotopoulos
Publisher : Unknown
Page : 482 pages
File Size : 51,8 Mb
Release : 2002
Category : Mechanics, Analytic
ISBN : 9604317865

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Nonsmooth/nonconvex mechanics with applications in engineering : ; a volume dedicated to the memory of Prof. P. D. Panagiotopoulos ; [proceedings of the international conference, 5-6 July 2002, Thessaloniki, Greece] by P. D. Panagiotopoulos Pdf

Author : Yoshihiro Kanno
Publisher : CRC Press
Page : 447 pages
File Size : 54,9 Mb
Release : 2011-04-05
Category : Science
ISBN : 9781420094237

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Nonsmooth Mechanics and Convex Optimization by Yoshihiro Kanno Pdf

"This book concerns matter that is intrinsically difficult: convex optimization, complementarity and duality, nonsmooth analysis, linear and nonlinear programming, etc. The author has skillfully introduced these and many more concepts, and woven them into a seamless whole by retaining an easy and consistent style throughout. The book is not all theory: There are many real-life applications in structural engineering, cable networks, frictional contact problems, and plasticity... I recommend it to any reader who desires a modern, authoritative account of nonsmooth mechanics and convex optimization." — Prof. Graham M.L. Gladwell, Distinguished Professor Emeritus, University of Waterloo, Fellow of the Royal Society of Canada "... reads very well—the structure is good, the language and style are clear and fluent, and the material is rendered accessible by a careful presentation that contains many concrete examples. The range of applications, particularly to problems in mechanics, is admirable and a valuable complement to theoretical and computational investigations that are at the forefront of the areas concerned." — Prof. B. Daya Reddy, Department of Mathematics and Applied Mathematics, Director of Centre for Research in Computational and Applied Mechanics, University of Cape Town, South Africa "Many materials and structures (e.g., cable networks, membrane) involved in practical engineering applications have complex responses that cannot be described by smooth constitutive relations. ... The author shows how these difficult problems can be tackled in the framework of convex analysis by arranging the carefully chosen materials in an elegant way. Most of the contents of the book are from the original contributions of the author. They are both mathematically rigorous and readable. This book is a must-read for anyone who intends to get an authoritative and state-of-art description for the analysis of nonsmooth mechanics problems with theory and tools from convex analysis." — Prof. Xu Guo, State Key Laboratory of Structural Analysis for Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology

Author : Jaroslav Haslinger,Georgios E. Stavroulakis
Publisher : Springer Science & Business Media
Page : 320 pages
File Size : 48,5 Mb
Release : 2007-08-03
Category : Technology & Engineering
ISBN : 9783211482438

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Nonsmooth Mechanics of Solids by Jaroslav Haslinger,Georgios E. Stavroulakis Pdf

Nonsmooth mechanics is a relatively complex field and requires a good knowledge of mechanics as well as a good background in some parts of modern mathematics. The present volume of lecture notes follows a very successful advanced school, with the aim to cover as much as possible all these aspects. It includes contributions that cover mechanical aspects as well as the mathematical and numerical treatment.

Author : David Yang Gao
Publisher : Springer Science & Business Media
Page : 429 pages
File Size : 43,7 Mb
Release : 2012-11-08
Category : Technology & Engineering
ISBN : 9789048195770

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Complementarity, Duality and Symmetry in Nonlinear Mechanics by David Yang Gao Pdf

Complementarity, duality, and symmetry are closely related concepts, and have always been a rich source of inspiration in human understanding through the centuries, particularly in mathematics and science. The Proceedings of IUTAM Symposium on Complementarity, Duality, and Symmetry in Nonlinear Mechanics brings together some of world's leading researchers in both mathematics and mechanics to provide an interdisciplinary but engineering flavoured exploration of the field's foundation and state of the art developments. Topics addressed in this book deal with fundamental theory, methods, and applications of complementarity, duality and symmetry in multidisciplinary fields of nonlinear mechanics, including nonconvex and nonsmooth elasticity, dynamics, phase transitions, plastic limit and shakedown analysis of hardening materials and structures, bifurcation analysis, entropy optimization, free boundary value problems, minimax theory, fluid mechanics, periodic soliton resonance, constrained mechanical systems, finite element methods and computational mechanics. A special invited paper presented important research opportunities and challenges of the theoretical and applied mechanics as well as engineering materials in the exciting information age. Audience: This book is addressed to all scientists, physicists, engineers and mathematicians, as well as advanced students (doctoral and post-doctoral level) at universities and in industry.

Author : Dimitri Beskos,Giulio Maier
Publisher : Springer
Page : 311 pages
File Size : 46,5 Mb
Release : 2014-05-04
Category : Technology & Engineering
ISBN : 9783709127902

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Boundary Element Advances in Solid Mechanics by Dimitri Beskos,Giulio Maier Pdf

This volume presents and discusses recent advances in boundary element methods and their solid mechanics applications. It illustrates these methods in their latest forms, developed during the last five to ten years, and demonstrates their advantages in solving a wide range of solid mechanics problems.

Author : Anonim
Publisher : Unknown
Page : 410 pages
File Size : 42,8 Mb
Release : 2001
Category : Mechanics, Applied
ISBN : UIUC:30112043751830

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Applied Mechanics Reviews by Anonim Pdf

Author : Georgios E. Stavroulakis
Publisher : Springer Science & Business Media
Page : 419 pages
File Size : 40,5 Mb
Release : 2012-10-19
Category : Technology & Engineering
ISBN : 9783642339677

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Recent Advances in Contact Mechanics by Georgios E. Stavroulakis Pdf

Contact mechanics is an active research area with deep theoretical and numerical roots. The links between nonsmooth analysis and optimization with mechanics have been investigated intensively during the last decades, especially in Europe. The study of complementarity problems, variational -, quasivariational- and hemivariational inequalities arising in contact mechanics and beyond is a hot topic for interdisciplinary research and cooperation. The needs of industry for robust solution algorithms suitable for large scale applications and the regular updates of the respective elements in major commercial computational mechanics codes, demonstrate that this interaction is not restricted to the academic environment. The contributions of this book have been selected from the participants of the CMIS 2009 international conference which took place in Crete and continued a successful series of specialized contact mechanics conferences.

Author : David Yang Gao
Publisher : Springer Science & Business Media
Page : 463 pages
File Size : 47,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475731767

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Duality Principles in Nonconvex Systems by David Yang Gao Pdf

Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics. Topics covered include the classical (minimax) mono-duality of convex static equilibria, the beautiful bi-duality in dynamical systems, the interesting tri-duality in non-convex problems and the complicated multi-duality in general canonical systems. A potentially powerful sequential canonical dual transformation method for solving fully nonlinear problems is developed heuristically and illustrated by use of many interesting examples as well as extensive applications in a wide variety of nonlinear systems, including differential equations, variational problems and inequalities, constrained global optimization, multi-well phase transitions, non-smooth post-bifurcation, large deformation mechanics, structural limit analysis, differential geometry and non-convex dynamical systems. With exceptionally coherent and lucid exposition, the work fills a big gap between the mathematical and engineering sciences. It shows how to use formal language and duality methods to model natural phenomena, to construct intrinsic frameworks in different fields and to provide ideas, concepts and powerful methods for solving non-convex, non-smooth problems arising naturally in engineering and science. Much of the book contains material that is new, both in its manner of presentation and in its research development. A self-contained appendix provides some necessary background from elementary functional analysis. Audience: The book will be a valuable resource for students and researchers in applied mathematics, physics, mechanics and engineering. The whole volume or selected chapters can also be recommended as a text for both senior undergraduate and graduate courses in applied mathematics, mechanics, general engineering science and other areas in which the notions of optimization and variational methods are employed.

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 4646 pages
File Size : 42,9 Mb
Release : 2008-09-04
Category : Mathematics
ISBN : 9780387747583

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Encyclopedia of Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf

The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".