Functional Analysis
Functional Analysis

Author: Leonid P. Lebedev

Publisher: Springer Science & Business Media

Published: 2006-04-29

Total Pages: 259

ISBN-13: 0306483971

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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.

Thin-Walled Composite Beams
Thin-Walled Composite Beams

Author: Liviu Librescu

Publisher: Springer Science & Business Media

Published: 2006-01-15

Total Pages: 627

ISBN-13: 1402042035

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Annotation This is the first monograph devoted to the foundation of the theory of composite anisotropic thin-walled beams and to its applications in various problems involving the aeronautical/aerospace, helicopter, naval and mechanical structures. Throughout the theoretical part, an effort was made to provide the treatment of the subject by using the equations of the 3-D elasticity theory. Non-classical effects such as transverse shear, warping constraint, anisotropy of constituent materials yielding the coupling of twist-bending (lateral), bending (transversal)-extension have been included and their implications have been thoroughly analyzed. Thermal effects have been included and in order to be able to circumvent their deleterious effects, functionally graded materials have been considered in their construction. Implications of the application of the tailoring technique and of the active feedback control on free vibration, dynamic response, instability and aeroelasticity of such structures have been amply investigated. Special care was exercised throughout this work to address and validate the adopted solution methodologies and the obtained results against those available in the literature and obtained via numerical or experimental means.

Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows
Direct Methods for Solving the Boltzmann Equation and Study of Nonequilibrium Flows

Author: V.V. Aristov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 305

ISBN-13: 9401008663

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This book is concerned with the methods of solving the nonlinear Boltz mann equation and of investigating its possibilities for describing some aerodynamic and physical problems. This monograph is a sequel to the book 'Numerical direct solutions of the kinetic Boltzmann equation' (in Russian) which was written with F. G. Tcheremissine and published by the Computing Center of the Russian Academy of Sciences some years ago. The main purposes of these two books are almost similar, namely, the study of nonequilibrium gas flows on the basis of direct integration of the kinetic equations. Nevertheless, there are some new aspects in the way this topic is treated in the present monograph. In particular, attention is paid to the advantages of the Boltzmann equation as a tool for considering nonequi librium, nonlinear processes. New fields of application of the Boltzmann equation are also described. Solutions of some problems are obtained with higher accuracy. Numerical procedures, such as parallel computing, are in vestigated for the first time. The structure and the contents of the present book have some com mon features with the monograph mentioned above, although there are new issues concerning the mathematical apparatus developed so that the Boltzmann equation can be applied for new physical problems. Because of this some chapters have been rewritten and checked again and some new chapters have been added.

Plate and Panel Structures of Isotropic, Composite and Piezoelectric Materials, Including Sandwich Construction
Plate and Panel Structures of Isotropic, Composite and Piezoelectric Materials, Including Sandwich Construction

Author: Jack R. Vinson

Publisher: Springer Science & Business Media

Published: 2005-06-15

Total Pages: 424

ISBN-13: 1402031114

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Plates and panels are primary components in many structures including space vehicles, aircraft, automobiles, buildings, bridge decks, ships and submarines. The ability to design, analyse, optimise and select the proper materials for these structures is a necessity for structural designers, analysts and researchers. This text consists of four parts. The first deals with plates of isotropic (metallic and polymeric) materials. The second involves composite material plates, including anisotropy and laminate considerations. The third section treats sandwich constructions of various types, and the final section gives an introduction to plates involving piezoelectric materials, in which the "smart" or "intelligent" materials are used as actuators or sensors. In each section, the formulations encompass plate structures subjected to static loads, dynamic loads, buckling, thermal/moisture environments, and minimum weight structural optimisation. This is a textbook for a graduate course, an undergraduate senior course and a reference. Many homework problems are given in various chapters.

Self-Consistent Methods for Composites
Self-Consistent Methods for Composites

Author: S.K. Kanaun

Publisher: Springer Science & Business Media

Published: 2007-12-20

Total Pages: 390

ISBN-13: 1402066643

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This timely text is the first monograph to develop self-consistent methods and apply these to the solution of problems of electromagnetic and elastic wave propagation in matrix composites and polycrystals. Predictions are compared with experimental data and exact solutions. Explicit equations and efficient numerical algorithms for calculating the velocities and attenuation coefficients of the mean (coherent) wave fields propagating in composites and polycrystals are presented.

Elasticity of Transversely Isotropic Materials
Elasticity of Transversely Isotropic Materials

Author: Haojiang Ding

Publisher: Springer Science & Business Media

Published: 2006-07-09

Total Pages: 443

ISBN-13: 1402040342

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This book aims to provide a comprehensive introduction to the theory and applications of the mechanics of transversely isotropic elastic materials. There are many reasons why it should be written. First, the theory of transversely isotropic elastic materials is an important branch of applied mathematics and engineering science; but because of the difficulties caused by anisotropy, the mathematical treatments and descriptions of individual problems have been scattered throughout the technical literature. This often hinders further development and applications. Hence, a text that can present the theory and solution methodology uniformly is necessary. Secondly, with the rapid development of modern technologies, the theory of transversely isotropic elasticity has become increasingly important. In addition to the fields with which the theory has traditionally been associated, such as civil engineering and materials engineering, many emerging technologies have demanded the development of transversely isotropic elasticity. Some immediate examples are thin film technology, piezoelectric technology, functionally gradient materials technology and those involving transversely isotropic and layered microstructures, such as multi-layer systems and tribology mechanics of magnetic recording devices. Thus a unified mathematical treatment and presentation of solution methods for a wide range of mechanics models are of primary importance to both technological and economic progress.

Nonlinear and Stochastic Dynamics of Compliant Offshore Structures
Nonlinear and Stochastic Dynamics of Compliant Offshore Structures

Author: Seon Mi Han

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 281

ISBN-13: 9401599122

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The purpose of this monograph is to show how a compliant offshore structure in an ocean environment can be modeled in two and three di mensions. The monograph is divided into five parts. Chapter 1 provides the engineering motivation for this work, that is, offshore structures. These are very complex structures used for a variety of applications. It is possible to use beam models to initially study their dynamics. Chapter 2 is a review of variational methods, and thus includes the topics: princi ple of virtual work, D'Alembert's principle, Lagrange's equation, Hamil ton's principle, and the extended Hamilton's principle. These methods are used to derive the equations of motion throughout this monograph. Chapter 3 is a review of existing transverse beam models. They are the Euler-Bernoulli, Rayleigh, shear and Timoshenko models. The equa tions of motion are derived and solved analytically using the extended Hamilton's principle, as outlined in Chapter 2. For engineering purposes, the natural frequencies of the beam models are presented graphically as functions of normalized wave number and geometrical and physical pa rameters. Beam models are useful as representations of complex struc tures. In Chapter 4, a fluid force that is representative of those that act on offshore structures is formulated. The environmental load due to ocean current and random waves is obtained using Morison's equa tion. The random waves are formulated using the Pierson-Moskowitz spectrum with the Airy linear wave theory.

Reanalysis of Structures
Reanalysis of Structures

Author: Uri Kirsch

Publisher: Springer Science & Business Media

Published: 2008-02-24

Total Pages: 308

ISBN-13: 1402081987

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This book deals with various computational procedures for multiple repeated analyses (reanalysis) of structures, and presents them in a unified approach. It meets the need for a general text covering the basic concepts and methods as well as recent developments in this area. To clarify the presentation, many illustrative examples and numerical results are demonstrated. Previous books on structural analysis do not cover most of the material presented here.

Contact Mechanics
Contact Mechanics

Author: J.A.C. Martins

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 442

ISBN-13: 9401711542

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This volume contains 44 papers presented at the Third Contact Mechanics International Symposium (CMIS 2001) held in Praia da Consola9ao, Peniche (portugal), June 17-21,2001. This Symposium was the direct continuation of the first two CMIS held in Lausanne (1992) and in Carry-Le-Rouet (1994). Other related meetings, in what concerns scientific topics and participants, took place in the nineties at La Grande Motte (1990), Vadstena (1996), Ferrara (1997), Munich (1998) and Grenoble (1999). The Symposium aimed at gathering researchers with interests in a wide range of topics in theoretical, computational and experimental contact mechanics. The call for papers mentioned topics in tribology, mathematical formulations and analysis, numerical methods in non-smooth mechanics, impact problems, instabilities and technological problems. The total number of participants was 102, from Universities and Research Institutes of 19 countries. The Scientific Committee reviewed 102 submitted abstracts, and the final program consisted of 6 main lectures, 43 oral communications and 36 poster presentations (see Appendix A). The papers in this book correspond to almost all the main lectures and oral communications, and they are assembled in 5 chapters: • Dynamics and Impact • Instabilities, Oscillations and Waves • Contact Models, Results and Applications • Mathematical Analysis • Numerical Methods. We thank all the authors for their valuable contributions to this volume. We are indebted to the members of the Scientific Committee for their help in refereeing the submitted abstracts and manuscripts. We also thank the Series editor, Prof. Graham Gladwell, for his assistance in the revision process.

Inelastic Analysis of Structures under Variable Loads
Inelastic Analysis of Structures under Variable Loads

Author: Dieter Weichert

Publisher: Springer Science & Business Media

Published: 2001-11-30

Total Pages: 400

ISBN-13: 9781402003820

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The question whether a structure or a machine component can carry the applied loads, and with which margin of safety, or whether it will become unserviceable due to collapse or excessive inelastic deformations, has always been a major concern for civil and mechanical engineers. The development of methods to answer this technologically crucial question without analysing the evolution of the system under varying loads, has a long tradition that can be traced back even to the times of emerging mechanical sciences in the early 17th century. However, the scientific foundations of the theories underlying these methods, nowadays frequently called "direct", were established sporadically in the Thirties of the 20th century and systematically and rigorously in the Fifties. Further motivations for the development of direct analysis techniques in applied mechanics of solids and structures arise from the circumstance that in many engineering situations the external actions fluctuate according to time histories not a priori known except for some essential features, e.g. variation intervals. In such situations the critical events (or "limit states") to consider, besides plastic collapse, are incremental collapse (or "ratchetting") and alternating plastic yielding, namely lack of "shakedown". Non evolutionary, direct methods for ultimate limit state analysis of structures subjected to variably-repeated external actions are the objectives of most papers collected in this book, which also contains a few contributions on related topics.