Modern Mechanics and Mathematics

Mechanics and mathematics have been two complementary partners since the time of the founding masters, Newton, Euler and Lagrange and great names such as Legendre, Poisson, Jacobi, Hamilton, Gauss, Cauchy, Fourier, Poincaré, Liapunov and Einstein. In the history of science, developments in mathematics and mechanics have always been intertwined; on the one hand, analysis of mechanical phenomena depends on the powerful tools of mathematics; on the other hand, revolutionary mathematical methods and concepts were often developed by mechanicians in order to meet their own needs.  These methods and concepts often stimulated new developments in mathematics.  For example, in the modern mathematical theory of convex analysis, the fundamental concepts of sub-differential and super-potentials were originally introduced by J.J. Moreau in the study of friction.  Today, the theory of convex analysis, with its diverse applications in the modern calculus of variations, potential theory, mathematical programming, nonlinear functional analysis, partial differential equations, non-convex dynamical systems, control theory, numerical analysis, economics and game theory, has become a well-established and fruitful fundamental mathematical discipline.  Moreover, some very active interdisciplinary fields, such as the theory of variational inequalities, nonlinear semi-group theory, and critical point theory are also closely related to the notion of the non-differentiable super-potentials. These fields, moreover, serve as a foundation for modern theoretical mechanics and computational mechanics.  Applications to mechanics have proven to be an exciting and fruitful endeavor. 

This book series is intended to bridge the gap between mathematics and engineering sciences by providing multi-disciplinary publication media in modern mechanics and mathematics. An Editorial Advisory Board consisting of internationally distinguished researchers supports the Editors.

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Editors

David Y. Gao Department of Mathematics  Virginia  Polytechnic Institute and State University  Blacksburg, VA 24061, USA Tel: +1-540-231-2768  Fax:  +1-540-231-5960  E-mail: mailto:%20gao@math.vt.edu http://www.math.vt.edu/people/gao/ applied mathematics, optimization, mechanics

Martin Ostoja-Starzewski Department of Mechanical Science & Engineering, University of Illinois Urbana, IL 61801, USA Tel: 217-265-0900 Fax: 217-244-9980 E-mail: martinos@uiuc.edu http://www.mechse.uiuc.edu/research/martinos/ random media, (thermo)mechanics, stochastic mechanics, waves

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Editorial Advisory Board 

Jan Awrejcewicz (Technical University of Łódź, Poland)

http://www.p.lodz.pl/k16/awrejcewicz/index_awrej.html)

nonlinear mechanics, multibody dynamics, biomechanics

A.S. Fokas (University of Cambridge)

http://www.damtp.cam.ac.uk/user/tf227/)

applied mathematics and fluid mechanics

Dominique Jeulin (Ecole des Mines de Paris, France)

http://cmm.ensmp.fr/~jeulin/

mathematical morphology, probability theory in mechanics, image analysis and stereology, continuum-discrete problems

Irena Lasiecka (University of Virgina, USA)

http://www.math.virginia.edu/Faculty/Lasiecka/

PDEs and related control theory

Qishao Lu (Beijing University of Aeronautics and Astronautics, China)

http://www.ss.buaa.edu.cn/syscontrol/luqishao.htm

nonlinear dynamics, biomechanics

Gérard A. Maugin (Institut d'Alembert, Université Pierre et Marie Curie, France)

http://www.lmm.jussieu.fr/MEMBRES/MAUGIN/directeur.html

continuum mechanics and thermodynamics, configurational forces and materials mechanics, nonlinear waves

Ray W. Ogden (University of Glasgow, UK)

http://www.maths.gla.ac.uk/~rwo/

solid mechanics, nonlinear elasticity, biomechanics

Meir (Fiki) Shillor (Oaklnad University, USA)

http://personalwebs.oakland.edu/~shillor/

applied analysis and solid mechanics

Andrzej Święch (Georgia Institute of Technology, USA)

http://www.math.gatech.edu/~swiech/

nonlinear PDEs, optimal control, differential games, stochastic PDE, mathematical fluid dynamics

Roger Temam (Indiana University, USA and Paris, France)

http://mypage.iu.edu/~temam/home_F.htm

functional, applied and numerical analysis. PDE, continuum mechanics, fluid mechanics, turbulence and chaos

Kok Lay Teo (Curtin University of Technology, Perth, Australia),

http://www.maths.curtin.edu.au/staff/teo/index.cfm dynamical systems,

optimization and control

Stéphane Zaleski (Institut d'Alembert, Université Pierre et Marie Curie, France)

http://www.lmm.jussieu.fr/~zaleski/zaleski.html fluid mechanics 

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Books in this Series:

forthcoming

New Models and Analytical Methods in Tribology by Ilya Kudish

Modern Mechanics and Mathematics Volume: 8

Classical and Generalized Models of Elastic Rods

Price: $129.95

ISBN: 9781420086492

ISBN 10: 1420086499

CAT #: C6499

Pub Date: 11/14/2008

Dorin Iesan

Reflecting new developments in the study of Saint-Venant’s problem, the book focuses on the deformation of elastic cylinders for three models of continuum: classical elastic continuum, Cosserat elastic body, and porous elastic material.(...more)

Modern Mechanics and Mathematics Volume: 7

Microstructural Randomness and Scaling in Mechanics of Materials

Price: $89.96

ISBN: 9781584884170

ISBN 10: 1584884177

CAT #: C4174

Pub Date: 8/13/2007

Martin Ostoja-Starzewski

An area at the intersection of solid mechanics, materials science, and stochastic mathematics, mechanics of materials often necessitates a stochastic approach to grasp the effects of spatial randomnes (...more)

Modern Mechanics and Mathematics Volume: 6

Introduction to Asymptotic Methods

Price: $85.46

ISBN: 9781584886778

ISBN 10: 1584886773

CAT #: C6773

Pub Date: 5/3/2006

Jan Awrejcewicz; Vadim A. Krysko

Among the theoretical methods for solving many problems of applied mathematics, physics, and technology, asymptotic methods often provide results that lead to obtaining more effective algorithms of nu   (...more)

Modern Mechanics and Mathematics Volume: 5

Hybrid and Incompatible Finite Element Methods

Price: $107.96

ISBN: 9781584882763

ISBN 10: 158488276X

CAT #: C276X

Pub Date: 11/4/2005

Theodore H.H. Pian; Chang-Chun Wu

While the theory and application of finite elements methods can be extended to incompatible, hybrid, and mixed element methods, important issues, such as determining the reliability of the solution of   (...more)

Modern Mechanics and Mathematics Volume: 4

Continuum Mechanics and Plasticity

Price: $116.96

ISBN: 9781584883630

ISBN 10: 1584883634

CAT #: C3634

Pub Date: 12/20/2004

Han-Chin Wu

Tremendous advances in computer technologies and methods have precipitated a great demand for refinements in the constitutive models of plasticity. Such refinements include the development of a model    (...more)

Modern Mechanics and Mathematics Volume: 3

Beyond Perturbation: Introduction to the Homotopy Analysis Method

Price: $107.96

ISBN: 9781584884071

ISBN 10: 158488407X

CAT #: C407X

Pub Date: 10/27/2003

Shijun Liao

Solving nonlinear problems is inherently difficult, and the stronger the nonlinearity, the more intractable solutions become. Analytic approximations often break down as nonlinearity becomes strong, a   (...more)

Modern Mechanics and Mathematics Volume: 2

Mechanics of Elastic Composites

Price: $134.96

ISBN: 9781584884422

ISBN 10: 1584884428

CAT #: C4428

Pub Date: 9/15/2003

Nicolaie Dan Cristescu; Eduard-Marius Craciun; Eugen Soós

Composite materials play a fundamental role in many modern engineering applications and have been the focus of much research and development in recent years. Mechanics of Elastic Composites is a compr (...more)

Modern Mechanics and Mathematics Volume: 1