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Mathematical Modelling Of Solids With Nonregular Boundaries
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Book Synopsis Mathematical Modelling of Solids with Nonregular Boundaries by : A.B. Movchan
Download or read book Mathematical Modelling of Solids with Nonregular Boundaries written by A.B. Movchan and published by CRC Press. This book was released on 2020-07-26 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modelling of Solids with Nonregular Boundaries demonstrates the use of asymptotic methods and other analytical techniques for investigating problems in solid mechanics. Applications to solids with nonregular boundaries are described in detail, providing precise and rigorous treatment of current methods and techniques. The book addresses problems in fracture mechanics of inhomogeneous media and illustrates applications in strength analysis and in geophysics. The rigorous approach allows the reader to explicitly analyze the stress-strain state in continuous media with cavities or inclusions, in composite materials with small defects, and in elastic solids with sharp inclusions. Effective asymptotic procedures for eigenvalue problems in domains with small defects are clearly outlined, and methods for analyzing singularly perturbed boundary value problems are examined. Introductory material is provided in the first chapter of Mathematical Modelling of Solids with Nonregular Boundaries, which presents a survey of relevant and necessary information, including equations of linear elasticity and formulations of the boundary value problems. Background information - in the form of definitions and general solutions - is also provided on elasticity problems in various bounded and unbounded domains. This book is an excellent resource for students, applied scientists, and engineers.
Book Synopsis Free Boundary Problems Involving Solids by : J M Chadam
Download or read book Free Boundary Problems Involving Solids written by J M Chadam and published by CRC Press. This book was released on 1993-02-22 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of three volumes containing the proceedings of the International Colloquium 'Free Boundary Problems: Theory and Applications', held in Montreal from June 13 to June 22, 1990. The main theme of this volume is the concept of free boundary problems associated with solids. The first free boundary problem, the freezing of water - the Stefan problem - is the prototype of solidification problems which form the main part of this volume. The two sections treting this subject cover a large variety of topics and procedures, ranging from a theoretical mathematical treatment of solvability to numerical procedures for practical problems. Some new and interesting problems in solid mechanics are discussed in the first section while in the last section the important new subject of solid-solid-phase transition is examined.
Book Synopsis Reconstruction of Small Inhomogeneities from Boundary Measurements by : Habib Ammari
Download or read book Reconstruction of Small Inhomogeneities from Boundary Measurements written by Habib Ammari and published by Springer Science & Business Media. This book was released on 2004-08-03 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to provide a systematic exposition of promising techniques for the reconstruction of small inhomogeneities from boundary measurements. In particular, theoretical results and numerical procedures for the inverse problems for the conductivity equation, the Lamé system, as well as the Helmholtz equation are discussed in a readable and informative manner. The general approach developed in this book is based on layer potential techniques and modern asymptotic analysis of partial differential equations. The book is particularly suitable for graduate students in mathematics.
Book Synopsis Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation by : Zohar Yosibash
Download or read book Singularities in Elliptic Boundary Value Problems and Elasticity and Their Connection with Failure Initiation written by Zohar Yosibash and published by Springer Science & Business Media. This book was released on 2011-12-02 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory and self-contained book gathers as much explicit mathematical results on the linear-elastic and heat-conduction solutions in the neighborhood of singular points in two-dimensional domains, and singular edges and vertices in three-dimensional domains. These are presented in an engineering terminology for practical usage. The author treats the mathematical formulations from an engineering viewpoint and presents high-order finite-element methods for the computation of singular solutions in isotropic and anisotropic materials, and multi-material interfaces. The proper interpretation of the results in engineering practice is advocated, so that the computed data can be correlated to experimental observations. The book is divided into fourteen chapters, each containing several sections. Most of it (the first nine Chapters) addresses two-dimensional domains, where only singular points exist. The solution in a vicinity of these points admits an asymptotic expansion composed of eigenpairs and associated generalized flux/stress intensity factors (GFIFs/GSIFs), which are being computed analytically when possible or by finite element methods otherwise. Singular points associated with weakly coupled thermoelasticity in the vicinity of singularities are also addressed and thermal GSIFs are computed. The computed data is important in engineering practice for predicting failure initiation in brittle material on a daily basis. Several failure laws for two-dimensional domains with V-notches are presented and their validity is examined by comparison to experimental observations. A sufficient simple and reliable condition for predicting failure initiation (crack formation) in micron level electronic devices, involving singular points, is still a topic of active research and interest, and is addressed herein. Explicit singular solutions in the vicinity of vertices and edges in three-dimensional domains are provided in the remaining five chapters. New methods for the computation of generalized edge flux/stress intensity functions along singular edges are presented and demonstrated by several example problems from the field of fracture mechanics; including anisotropic domains and bimaterial interfaces. Circular edges are also presented and the author concludes with some remarks on open questions. This well illustrated book will appeal to both applied mathematicians and engineers working in the field of fracture mechanics and singularities.
Book Synopsis Mathematical Modelling of Waves in Multi-Scale Structured Media by : Alexander B. Movchan
Download or read book Mathematical Modelling of Waves in Multi-Scale Structured Media written by Alexander B. Movchan and published by CRC Press. This book was released on 2017-11-09 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modelling of Waves in Multi-Scale Structured Media presents novel analytical and numerical models of waves in structured elastic media, with emphasis on the asymptotic analysis of phenomena such as dynamic anisotropy, localisation, filtering and polarisation as well as on the modelling of photonic, phononic, and platonic crystals.
Book Synopsis Asymptotic Models of Fields in Dilute and Densely Packed Composites by : A B Movchan
Download or read book Asymptotic Models of Fields in Dilute and Densely Packed Composites written by A B Movchan and published by World Scientific. This book was released on 2002-11-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a systematic study of asymptotic models of continuum mechanics for composite structures, which are either dilute (for example, two-phase composite structures with small inclusions) or densely packed (in this case inclusions may be close to touching). It is based on the results of recent research and includes a comprehensive analysis of dipole and multipole fields associated with defects in solids. The text covers static problems of elasticity in dilute composites as well as spectral problems. Applications of the mathematical models included in the book are in damage mechanics and in problems of design of composite structures that can be used as filters or polarisers of elastic waves. Dipole tensors are defined in Chapter 1 both for scalar boundary value problems for the Laplacian and for vector problems of elasticity. In Chapter 2 the dipole tensors are used in spectral problems involving domains with small defects. Chapter 3 introduces a multipole method for static problems (both electrostatics and elasticity) in composite structures containing doubly periodic arrays of circular inclusions. Chapter 4 presents a multipole method for eigenvalue problems of electromagnetism and elasticity. Contents:Long and Close Range Interaction within Elastic StructuresDipole Tensors in Spectral Problems of ElasticityMultipole Methods and Homogenisation in Two-Dimensions Readership: Graduate students and researchers in applied mathematics and mechanics who are interested in asymptotic theory of partial differential equations, spectral theory, and mathematical models of composite structures. Reviews:“The material is interesting and based on results of recent research.”Mathematical Reviews
Author :Antonio André Novotny Publisher :Springer Science & Business Media ISBN 13 :3642352456 Total Pages :324 pages Book Rating :4.6/5 (423 download)
Book Synopsis Topological Derivatives in Shape Optimization by : Antonio André Novotny
Download or read book Topological Derivatives in Shape Optimization written by Antonio André Novotny and published by Springer Science & Business Media. This book was released on 2012-12-14 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topological derivative is defined as the first term (correction) of the asymptotic expansion of a given shape functional with respect to a small parameter that measures the size of singular domain perturbations, such as holes, inclusions, defects, source-terms and cracks. Over the last decade, topological asymptotic analysis has become a broad, rich and fascinating research area from both theoretical and numerical standpoints. It has applications in many different fields such as shape and topology optimization, inverse problems, imaging processing and mechanical modeling including synthesis and/or optimal design of microstructures, fracture mechanics sensitivity analysis and damage evolution modeling. Since there is no monograph on the subject at present, the authors provide here the first account of the theory which combines classical sensitivity analysis in shape optimization with asymptotic analysis by means of compound asymptotic expansions for elliptic boundary value problems. This book is intended for researchers and graduate students in applied mathematics and computational mechanics interested in any aspect of topological asymptotic analysis. In particular, it can be adopted as a textbook in advanced courses on the subject and shall be useful for readers interested on the mathematical aspects of topological asymptotic analysis as well as on applications of topological derivatives in computation mechanics.
Book Synopsis Mathematical Models for Structural Reliability Analysis by : Fabio Casciati
Download or read book Mathematical Models for Structural Reliability Analysis written by Fabio Casciati and published by CRC Press. This book was released on 1996-07-24 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Models for Structural Reliability Analysis offers mathematical models for describing load and material properties in solving structural engineering problems. Examples are provided, demonstrating how the models are implemented, and the limitations of the models are clearly stated. Analytical solutions are also discussed, and methods are clearly distinguished from models. The authors explain both theoretical models and practical applications in a clear, concise, and readable fashion.
Book Synopsis Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions by : Igor Andrianov
Download or read book Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions written by Igor Andrianov and published by John Wiley & Sons. This book was released on 2014-02-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Methods in the Theory of Plates with MixedBoundary Conditions comprehensively covers the theoreticalbackground of asymptotic approaches and their use in solvingmechanical engineering-oriented problems of structural members,primarily plates (statics and dynamics) with mixed boundary conditions. The first part of this book introduces the theory and applicationof asymptotic methods and includes a series of approaches that havebeen omitted or not rigorously treated in the existing literature.These lesser known approaches include the method of summation andconstruction of the asymptotically equivalent functions, methods ofsmall and large delta, and the homotopy perturbations method. The second part of the book contains original results devoted tothe solution of the mixed problems of the theory of plates,including statics, dynamics and stability of the studied objects.In addition, the applicability of the approaches presented to otherrelated linear or nonlinear problems is addressed. Key features: • Includes analytical solving of mixed boundary valueproblems • Introduces modern asymptotic and summationprocedures • Presents asymptotic approaches for nonlinear dynamics ofrods, beams and plates • Covers statics, dynamics and stability of plates withmixed boundary conditions • Explains links between the Adomian and homotopyperturbation approaches Asymptotic Methods in the Theory of Plates with MixedBoundary Conditions is a comprehensive reference forresearchers and practitioners working in the field of Mechanics ofSolids and Mechanical Engineering, and is also a valuable resourcefor graduate and postgraduate students from Civil and MechanicalEngineering.
Book Synopsis IUTAM Symposium on Transformation Problems in Composite and Active Materials by : Yehia A. Bahei-El-Din
Download or read book IUTAM Symposium on Transformation Problems in Composite and Active Materials written by Yehia A. Bahei-El-Din and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The field of composite materials has seen substantial development in the past decade, New composite systems are being continually developed for various applications. Among such systems are metal, intermetallic, and superalloy matrix composites, carbon-carbon composites as well as polymer matrix composites. At the same time, a new discipline has emerged of active or smart materials, which are often constructed as composite or heterogeneous media and structures. One unifying theme in these diverse systems is the influence that uncoupled and coupled eigenfields or transformation fields exert on the various types of overall response, as well as on the respective phase responses. Problems of this kind are currently considered by different groups which may not always appreciate the similarities of the problems involved. The purpose of the IUTAM Symposium on Transformation Problems in Composite and Active Materials held in Cairo, Egypt from March 10 to 12, 1997 was to bring together representatives of the different groups so that they may interact and explore common aspects of these seemingly different problem areas. New directions in micromechanics research in both composite and active materials were also explored in the symposium. Specifically, invited lectures in the areas of inelastic behavior of composite materials, shape memory effects, functionally graded materials, transformation problems in composite structures, and adaptive structures were delivered and discussed during the three-day meeting. This book contains the printed contributions to the IUTAM Symposium.
Download or read book Applied mechanics reviews written by and published by . This book was released on 1948 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Cellular and Porous Materials by : Andreas Öchsner
Download or read book Cellular and Porous Materials written by Andreas Öchsner and published by John Wiley & Sons. This book was released on 2008-11-21 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing the reader with a solid understanding of the fundamentals as well as an awareness of recent advances in properties and applications of cellular and porous materials, this handbook and ready reference covers all important analytical and numerical methods for characterizing and predicting thermal properties. In so doing it directly addresses the special characteristics of foam-like and hole-riddled materials, combining theoretical and experimental aspects for characterization purposes.
Book Synopsis Mathematical Analysis for Modeling by : Judah Rosenblatt
Download or read book Mathematical Analysis for Modeling written by Judah Rosenblatt and published by CRC Press. This book was released on 1998-12-28 with total page 882 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Analysis for Modeling is intended for those who want to understand the substance of mathematics, rather than just having familiarity with its techniques. It provides a thorough understanding of how mathematics is developed for and applies to solving scientific and engineering problems. The authors stress the construction of mathematical descriptions of scientific and engineering situations, rather than rote memorizations of proofs and formulas. Emphasis is placed on algorithms as solutions to problems and on insight rather than formal derivations.
Book Synopsis Modelling Mathematical Methods and Scientific Computation by : Nicola Bellomo
Download or read book Modelling Mathematical Methods and Scientific Computation written by Nicola Bellomo and published by CRC Press. This book was released on 1994-12-22 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addressed to engineers, scientists, and applied mathematicians, this book explores the fundamental aspects of mathematical modelling in applied sciences and related mathematical and computational methods. After providing the general framework needed for mathematical modelling-definitions, classifications, general modelling procedures, and validation methods-the authors deal with the analysis of discrete models. This includes modelling methods and related mathematical methods. The analysis of models is defined in terms of ordinary differential equations. The analysis of continuous models, particularly models defined in terms of partial differential equations, follows. The authors then examine inverse type problems and stochastic modelling. Three appendices provide a concise guide to functional analysis, approximation theory, and probability, and a diskette included with the book includes ten scientific programs to introduce the reader to scientific computation at a practical level.
Book Synopsis Variational Methods for Structural Optimization by : Andrej Cherkaev
Download or read book Variational Methods for Structural Optimization written by Andrej Cherkaev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book bridges a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in sufficiently simple form as to make them available for practical use.
Book Synopsis Polarization and Moment Tensors by : Habib Ammari
Download or read book Polarization and Moment Tensors written by Habib Ammari and published by Springer Science & Business Media. This book was released on 2007-06-16 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents important recent developments in mathematical and computational methods used in impedance imaging and the theory of composite materials. By augmenting the theory with interesting practical examples and numerical illustrations, the exposition brings simplicity to the advanced material. An introductory chapter covers the necessary basics. An extensive bibliography and open problems at the end of each chapter enhance the text.
Book Synopsis Differential Geometric Methods in the Control of Partial Differential Equations by : Robert Gulliver
Download or read book Differential Geometric Methods in the Control of Partial Differential Equations written by Robert Gulliver and published by American Mathematical Soc.. This book was released on 2000 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains selected papers that were presented at the AMS-IMS-SIAM Joint Summer Research Conference on "Differential Geometric Methods in the Control of Partial Differential Equations", which was held at the University of Colorado in Boulder in June 1999. The aim of the conference was to explore the infusion of differential-geometric methods into the analysis of control theory of partial differential equations, particularly in the challenging case of variable coefficients, where the physical characteristics of the medium vary from point to point. While a mutually profitable link has been long established, for at least 30 years, between differential geometry and control of ordinary differential equations, a comparable relationship between differential geometry and control of partial differential equations (PDEs) is a new and promising topic. Very recent research, just prior to the Colorado conference, supported the expectation that differential geometric methods, when brought to bear on classes of PDE modelling and control problems with variable coefficients, will yield significant mathematical advances. The papers included in this volume - written by specialists in PDEs and control of PDEs as well as by geometers - collectively support the claim that the aims of the conference are being fulfilled. In particular, they endorse the belief that both subjects-differential geometry and control of PDEs-have much to gain by closer interaction with one another. Consequently, further research activities in this area are bound to grow.
