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Functional Analysis

Functional Analysis Author Leonid P. Lebedev
ISBN-10 9780306483974
Release 2006-04-29
Pages 254
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This book started its life as a series of lectures given by the second author from the 1970’s onwards to students in their third and fourth years in the Department of Mechanics and Mathematics at Rostov State University. For these lectures there was also an audience of engineers and applied mechanicists who wished to understand the functional analysis used in contemporary research in their fields. These people were not so much interested in functional analysis itself as in its applications; they did not want to be told about functional analysis in its most abstract form, but wanted a guided tour through those parts of the analysis needed for their applications. The lecture notes evolved over the years as the first author started to make more formal typewritten versions incorporating new material. About 1990 the first author prepared an English version and submitted it to Kluwer Academic Publishers for inclusion in the series Solid Mechanics and its Applications. At that state the notes were divided into three long chapters covering linear and nonlinear analysis. As Series Editor, the third author started to edit them. The requirements of lecture notes and books are vastly different. A book has to be complete (in some sense), self contained, and able to be read without the help of an instructor.

Functional analysis

Functional analysis Author L. P. Lebedev
ISBN-10 0792338499
Release 1996
Pages 239
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This is a book for people who want to use functional analysis to justify approximate methods in Mechanics and Inverse Problems. It provides such researchers with the tools they need without having to assimilate or skip through concepts they do not need. The essence of functional analysis is abstraction: from the everyday ideas of 3-dimensional space and distance, one abstracts the concepts of metric space and metric. The properties of this metric are laid down as axioms on which all subsequent arguments are based. The vocabulary of functional analysis consists largely of terms which originally appeared either in geometry or in connection with the real line: set, closed, open, bounded, compact, inner-product, etc.; in functional analysis they are defined abstractly. For the applied mathematician the essential difficulty attending the study of functional analysis is that the pure mathematicians who have developed the field have carried the process of abstraction to increasingly higher levels. In this book the authors have kept the level of abstraction high enough for the majority of applications, and have resisted the temptation to abstract to the limit. The book starts from scratch with a chapter on real numbers and functions. Chapter 2 introduces metric spaces, including the concept of a complete space and Banach's contraction mapping theorem; normed linear spaces, and inner product spaces. An excursion into some boundary value problems in Mechanics leads up to the concept of a generalized solution, and to Sobolev space. A study of approximation in Hilbert space leads to Riesz's representation theorem. An introduction to linear operators is followed by a chapter on the essential, but often misunderstood concept of a compact set. En route the mysteries of weakly closed, weakly convergent, sequential compactness, compact operator, singular value decomposition, etc. are revealed. The final chapter shows how the language of functional analysis is ideally suited to elucidate and justify the regularisation methods for the ill-posed inverse problems exemplified by Fredholm integral equations of the first kind.

IUTAM Symposium on Synthesis in Bio Solid Mechanics

IUTAM Symposium on Synthesis in Bio Solid Mechanics Author Pauli Pedersen
ISBN-10 9780792356158
Release 1999-04-30
Pages 410
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This book contains the edited version of invited lectures presented at the IUTAM-Sym- sium Synthesis in Bio Solid Mechanics, held at Hotel Frederiksdal, Virum (Copenhagen), Denmark, May 24 to May 27, 1998. The symposium was attended by 48 scientist from 14 countries. Biomechanics has been a very active research area in the last 25 years and covers a very broad class of problems. The present symposium concentrated on the solid mechanics - main of biomechanics, where important problems of synthesis presently are an active and challenging part. Characteristics of biomechanical materials are not only the inhomogeneity and anisotropy, but also the capability to change in relation to actual use. These living materials call for new methods of analysis and also new methods for synthesis. By the synthesis in this context is meant design of implants or artificial control of material growth. Bone mechanics is closely related to recent work on analysis and design of microstructural anisotropic materials. Also, recent work in shape design can to some extent be useful in the more complicated problems of biomechanics. Here interface problems play an essential role. The symposium brought together scientists from mechanics, mathematics and medicine.

Inverse Problems in Vibration

Inverse Problems in Vibration Author G.M.L. Gladwell
ISBN-10 9781402027215
Release 2006-01-15
Pages 457
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In the first, 1986, edition of this book, inverse problems in vibration were interpreted strictly: problems concerning the reconstruction of a unique, undamped vibrating system, of a specified type, from specified vibratory behaviour, particularly specified natural frequencies and/or natural mode shapes. In this new edition the scope of the book has been widened to include topics such as isospectral systems- families of systems which all exhibit some specified behaviour; applications of the concept of Toda flow; new, non-classical approaches to inverse Sturm-Liouville problems; qualitative properties of the modes of some finite element models; damage identification. With its emphasis on analysis, on qualitative results, rather than on computation, the book will appeal to researchers in vibration theory, matrix analysis, differential and integral equations, matrix analysis, non-destructive testing, modal analysis, vibration isolation, etc. "This book is a necessary addition to the library of engineers and mathematicians working in vibration theory." Mathematical Reviews

Applied Mechanics Reviews

Applied Mechanics Reviews Author
ISBN-10 UIUC:30112046050990
Release 1996
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Applied Mechanics Reviews has been writing in one form or another for most of life. You can find so many inspiration from Applied Mechanics Reviews also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Applied Mechanics Reviews book for free.

Fracture Mechanics

Fracture Mechanics Author Huy Duong Bui
ISBN-10 9781402048371
Release 2007-01-03
Pages 375
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This book presents, in a unified manner, a variety of topics in Continuum and Fracture Mechanics: energy methods, conservation laws, mathematical methods to solve two-dimensional and three-dimensional crack problems. Moreover, a series of new subjects is presented in a straightforward manner, accessible to under-graduate students. Emphasizing physical or experimental back-grounds, then analysis and theoretical results, this monograph is intended for use by students and researchers in solid mechanics, mechanical engineering and applied mathematics.

Approximating Perfection

Approximating Perfection Author Leonid P. Lebedev
ISBN-10 9781400873258
Release 2015-07-28
Pages 232
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This is a book for those who enjoy thinking about how and why Nature can be described using mathematical tools. Approximating Perfection considers the background behind mechanics as well as the mathematical ideas that play key roles in mechanical applications. Concentrating on the models of applied mechanics, the book engages the reader in the types of nuts-and-bolts considerations that are normally avoided in formal engineering courses: how and why models remain imperfect, and the factors that motivated their development. The opening chapter reviews and reconsiders the basics of calculus from a fully applied point of view; subsequent chapters explore selected topics from solid mechanics, hydrodynamics, and the natural sciences. Emphasis is placed on the logic that underlies modeling in mechanics and the many surprising parallels that exist between seemingly diverse areas. The mathematical demands on the reader are kept to a minimum, so the book will appeal to a wide technical audience.

Inverse Problems in Engineering Mechanics IV

Inverse Problems in Engineering Mechanics IV Author Mana Tanaka
ISBN-10 0080535178
Release 2003-11-19
Pages 544
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This latest collection of proceedings provides a state of the art review of research on inverse problems in engineering mechanics. Inverse problems can be found in many areas of engineering mechanics, and have many successful applications. They are concerned with estimating the unknown input and/or the characteristics of a system given certain aspects of its output. The mathematical challenges of such problems have to be overcome through the development of new computational schemes, regularization techniques, objective functionals, and experimental procedures. The papers within this represent an excellent reference for all in the field. Providing a state of the art review of research on inverse problems in engineering mechanics Contains the latest research ideas and related techniques A recognized standard reference in the field of inverse problems Papers from Asia, Europe and America are all well represented

IUTAM Symposium on Discretization Methods in Structural Mechanics

IUTAM Symposium on Discretization Methods in Structural Mechanics Author H.A. Mang
ISBN-10 STANFORD:36105021928135
Release 1999-03-31
Pages 378
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Proceedings of the IUTAM Symposium held in Vienna, Austria, 2-6 June 1997

IUTAM IFToMM Symposium on Synthesis of Nonlinear Dynamical Systems

IUTAM   IFToMM Symposium on Synthesis of Nonlinear Dynamical Systems Author E. Lavendelis
ISBN-10 UOM:39015050325755
Release 1999-11-30
Pages 294
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Proceedings of the IUTAM/IFToMM Symposium held in Riga, Latvia, 24-28 August 1998

Waves and Nonlinear Processes in Hydrodynamics

Waves and Nonlinear Processes in Hydrodynamics Author John Grue
ISBN-10 UCSD:31822023834229
Release 1996-05-31
Pages 402
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In December 1994 Professor Enok Palm celebrated his 70th birthday and retired after more than forty years of service at the University of Oslo. In view of his outstanding achievements as teacher and scientist a symposium entitled "Waves and Nonlinear Processes in Hydrodynamics" was held in his honour from the 17th to the 19th November 1994 in the locations of The Norwegian Academy of Science and Letters in Oslo. The topics of the symposium were chosen to cover Enok's broad range of scientific work, interests and accomplishments: Marine hydrodynamics, nonlinear wave theory, nonlinear stability, thermal convection and geophys ical fluid dynamics, starting with Enok's present activity, ending with the field where he began his career. This order was followed in the symposium program. The symposium had two opening lectures. The first looked back on the history of hydrodynamic research at the University of Oslo. The second focused on applications of hydrodynamics in the offshore industry today.

Proceedings of the IUTAM Symposium Held in Eindhoven the Netherlands 21 26 April 1996

Proceedings of the IUTAM Symposium Held in Eindhoven  the Netherlands  21 26 April 1996 Author Dick H. van Campen
ISBN-10 0792344294
Release 1997-01-01
Pages 443
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This volume contains 51 contributions presented at the IUTAM Symposium on Interaction between Dynamics and Control in Advanced Mechanical Systems. The Symposium brought together scientists active in various fields of both dynamics and control, and stimulated the interaction of the two with respect to advanced engineering applications. The papers presented address a wide variety of applications ranging from vehicle systems to mechatronic systems. Furthermore, the relevance of more fundamental areas such as control of chaos and optimal control is illuminated. This volume presents a valuable collection of papers and promotes further theoretical and applied investigations with respect to the interaction of dynamics and control. The volume will be of assistance to scientists and engineers working in the fields of dynamics and control.

Advances in turbulence VI

Advances in turbulence VI Author Spyros Gavrilakis
ISBN-10 0792341325
Release 1996
Pages 627
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Advances in Turbulence VI presents an update on the state of turbulence research with some bias towards research in Europe, since it represents an almost complete collection of the paper presentations at the Sixth European Turbulence Conference, sponsored by EUROMECH, ERCOFTAC and COST, and held at the Swiss Federal Institute of Technology in Lausanne, July 2-5, 1996. The problem of transition, together with the structural description of turbulence, and the scaling laws of fully developed turbulence have continued to receive most attention by the research community and much progress has been made since the last European Turbulence Conference in 1994. The volume is thus geared towards specialists in the area of flow turbulence who could not attend the conference, as well as anybody who wishes quickly to assess the most active current research areas and the groups associated with them.

IUTAM Symposium on Rheology of Bodies with Defects

IUTAM Symposium on Rheology of Bodies with Defects Author Jen Wang
ISBN-10 0792352971
Release 1999
Pages 292
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This volume contains the presentations from the IUTAM Symposium on rheology of bodies with defects. The Symposium aimed at building a bridge between macroscopic and microscopic research on damage and fracture behaviour that contributes to the failure of defective bodies made of metal, polymer, composite, and even mortar, concrete, clay and rock-mass, emphasizing the time effects involved in the process. Besides the usual continuum damage mechanics approach, the thermodynamics of non-equilibrium systems approach is also presented, as well as a survey of the study of creep life assessment, especially in relation to polymers.

Inverse problems in the mechanics of materials

Inverse problems in the mechanics of materials Author H. D. Bui
ISBN-10 STANFORD:36105003479115
Release 1994
Pages 204
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Inverse Problems in the Mechanics of Materials concentrates on two timely subjects: Ill-posed inverse problems related to defect identification; and the mechanics of homogeneous and heterogeneous media, including such topics as cracked bodies, solids with interfaces or inclusions, and materials rendered inhomogeneous by irreversible deformation due to their thermomechanical history. These intriguing subjects are not found together in previous publications. Written in a unique, easy-to-read format, Inverse Problems in the Mechanics of Materials provides quick access to current information. It includes up-to-date references and many recent results, particularly in such classical subjects as elasticity, plasticity, and fracture mechanics. The reader discovers numerous recipes for solving inverse problems, and reviews of available methods provide applications to real-life problems in industry.

IUTAM Symposium on Asymptotic Methods for Turbulent Shear Flows at High Reynolds Numbers

IUTAM Symposium on Asymptotic Methods for Turbulent Shear Flows at High Reynolds Numbers Author K. Gersten
ISBN-10 0792341384
Release 1996
Pages 325
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This volume contains the contributions presented at the IUTAM Symposium on Asymptotic Methods for Turbulent Shear Flows, which was the first international conference on the subject. The book provides an overview of the state of the art in this field and presents results found worldwide. Asymptotic theory is here considered as the application of perturbation methods (singular perturbation methods, multiscale methods, rapid distortion theory etc.) to solving the Reynolds- averaged flow equations for turbulent shear flows at high Reynolds numbers. These methods play an important role in turbulence modelling, as is demonstrated by many examples, including turbulence models describing flow separation. It becomes evident that asymptotic methods enable the extraction of a fairly comprehensive set of results from the governing equations without incorporating a specific turbulence model a priori. Furthermore, these methods can be used to quickly eliminate unsatisfactory models. The book contains valuable results for turbulence researchers, in particular for those working in turbulence modelling.

IUTAM Symposium on Variations of Domain and Free Boundary Problems in Solid Mechanics

IUTAM Symposium on Variations of Domain and Free Boundary Problems in Solid Mechanics Author P. Argoul
ISBN-10 STANFORD:36105023112811
Release 1998-11-30
Pages 340
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Proceedings of the IUTAM Symposium held in Paris, France, 22-25 April 1997