Nonsmooth Mechanics Of Solids

Author : Jaroslav Haslinger
Publisher : Springer Science & Business Media
ISBN 13 : 3211482431
Total Pages : 320 pages
Book Rating : 4.38/5 ( download)

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Download or read book Nonsmooth Mechanics of Solids written by Jaroslav Haslinger and published by Springer Science & Business Media. This book was released on 2007-08-03 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : J.J. Moreau
Publisher : Springer
ISBN 13 : 370912624X
Total Pages : 466 pages
Book Rating : 4.40/5 ( download)

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Download or read book Nonsmooth Mechanics and Applications written by J.J. Moreau and published by Springer. This book was released on 2014-05-04 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Bernard Brogliato
Publisher : Springer Science & Business Media
ISBN 13 : 1447105575
Total Pages : 565 pages
Book Rating : 4.72/5 ( download)

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Download or read book Nonsmooth Mechanics written by Bernard Brogliato and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 565 pages. Available in PDF, EPUB and Kindle. Book excerpt: Thank you for opening the second edition of this monograph, which is devoted to the study of a class of nonsmooth dynamical systems of the general form: ::i; = g(x,u) (0. 1) f(x, t) 2: 0 where x E JRn is the system's state vector, u E JRm is the vector of inputs, and the function f (-, . ) represents a unilateral constraint that is imposed on the state. More precisely, we shall restrict ourselves to a subclass of such systems, namely mechanical systems subject to unilateral constraints on the position, whose dynamical equations may be in a first instance written as: ii= g(q,q,u) (0. 2) f(q, t) 2: 0 where q E JRn is the vector of generalized coordinates of the system and u is an in put (or controller) that generally involves a state feedback loop, i. e. u= u(q, q, t, z), with z= Z(z, q, q, t) when the controller is a dynamic state feedback. Mechanical systems composed of rigid bodies interacting fall into this subclass. A general prop erty of systems as in (0. 1) and (0. 2) is that their solutions are nonsmooth (with respect to time): Nonsmoothness arises primarily from the occurence of impacts (or collisions, or percussions) in the dynamical behaviour, when the trajectories attain the surface f(x, t) = O. They are necessary to keep the trajectories within the subspace = {x : f(x, t) 2: O} of the system's state space.

Author : Bernard Brogliato
Publisher : Springer
ISBN 13 : 3319286641
Total Pages : 628 pages
Book Rating : 4.48/5 ( download)

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Download or read book Nonsmooth Mechanics written by Bernard Brogliato and published by Springer. This book was released on 2016-02-29 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: Now in its third edition, this standard reference is a comprehensive treatment of nonsmooth mechanical systems refocused to give more prominence to issues connected with control and modelling. It covers Lagrangian and Newton–Euler systems, detailing mathematical tools such as convex analysis and complementarity theory. The ways in which nonsmooth mechanics influence and are influenced by well-posedness analysis, numerical analysis and simulation, modelling and control are explained. Contact/impact laws, stability theory and trajectory-tracking control are given detailed exposition connected by a mathematical framework formed from complementarity systems and measure-differential inclusions. Links are established with electrical circuits with set-valued nonsmooth elements as well as with other nonsmooth dynamical systems like impulsive and piecewise linear systems. Nonsmooth Mechanics (third edition) retains the topical structure familiar from its predecessors but has been substantially rewritten, edited and updated to account for the significant body of results that have emerged in the twenty-first century—including developments in: the existence and uniqueness of solutions; impact models; extension of the Lagrange–Dirichlet theorem and trajectory tracking; and well-posedness of contact complementarity problems with and without friction. Many figures (both new and redrawn to improve the clarity of the presentation) and examples are used to illustrate the theoretical developments. Material introducing the mathematics of nonsmooth mechanics has been improved to reflect the broad range of applications interest that has developed since publication of the second edition. The detail of some mathematical essentials is provided in four appendices. With its improved bibliography of over 1,300 references and wide-ranging coverage, Nonsmooth Mechanics (third edition) is sure to be an invaluable resource for researchers and postgraduates studying the control of mechanical systems, robotics, granular matter and relevant fields of applied mathematics. “The book’s two best features, in my view are its detailed survey of the literature... and its detailed presentation of many examples illustrating both the techniques and their limitations... For readers interested in the field, this book will serve as an excellent introductory survey.” Andrew Lewis in Automatica “It is written with clarity, contains the latest research results in the area of impact problems for rigid bodies and is recommended for both applied mathematicians and engineers.” Panagiotis D. Panagiotopoulos in Mathematical Reviews “The presentation is excellent in combining rigorous mathematics with a great number of examples... allowing the reader to understand the basic concepts.” Hans Troger in Mathematical Abstracts “/i>

Author : Pierre Alart
Publisher : Springer Science & Business Media
ISBN 13 : 0387291954
Total Pages : 318 pages
Book Rating : 4.56/5 ( download)

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Download or read book Nonsmooth Mechanics and Analysis written by Pierre Alart and published by Springer Science & Business Media. This book was released on 2006-06-26 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Yoshihiro Kanno
Publisher : CRC Press
ISBN 13 : 1420094238
Total Pages : 447 pages
Book Rating : 4.37/5 ( download)

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Download or read book Nonsmooth Mechanics and Convex Optimization written by Yoshihiro Kanno and published by CRC Press. This book was released on 2011-04-05 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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 : David Yang Gao
Publisher : Springer Science & Business Media
ISBN 13 : 1461302757
Total Pages : 505 pages
Book Rating : 4.59/5 ( download)

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Download or read book Nonsmooth/Nonconvex Mechanics written by David Yang Gao and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 505 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Michel Fremond
Publisher : Springer Science & Business Media
ISBN 13 : 3662048000
Total Pages : 487 pages
Book Rating : 4.09/5 ( download)

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Download or read book Non-Smooth Thermomechanics written by Michel Fremond and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on practical problems in mechanical engineering, here the author develops the fundamental concepts of non-smooth mechanics and introduces the necessary background material needed to deal with mechanics involving discontinuities and non-smooth constraints.

Author : Francesco dell'Isola
Publisher : Springer
ISBN 13 : 9811037647
Total Pages : 327 pages
Book Rating : 4.41/5 ( download)

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Download or read book Mathematical Modelling in Solid Mechanics written by Francesco dell'Isola and published by Springer. This book was released on 2017-03-10 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling analysis of elasto-plastic structures engineering optimization and design, global optimization and related algorithms The book presents selected papers presented at ETAMM 2016. It includes new and original results written by internationally recognized specialists.

Author : Pinlei Chen
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.06/5 ( download)

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Download or read book A Variational Framework for Mathematically Nonsmooth Problems in Solid and Structure Mechanics written by Pinlei Chen and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: