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Author: Igor Andrianov
Publisher: Academic Press
ISBN: 0323906532
Category : Technology & Engineering
Languages : en
Pages : 528
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Book Description
Mechanics and Physics of Structured Media: Asymptotic and Integral Methods of Leonid Filshtinsky provides unique information on the macroscopic properties of various composite materials and the mathematical techniques key to understanding their physical behaviors. The book is centered around the arguably monumental work of Leonid Filshtinsky. His last works provide insight on fracture in electromagnetic-elastic systems alongside approaches for solving problems in mechanics of solid materials. Asymptotic methods, the method of complex potentials, wave mechanics, viscosity of suspensions, conductivity, vibration and buckling of functionally graded plates, and critical phenomena in various random systems are all covered at length. Other sections cover boundary value problems in fracture mechanics, two-phase model methods for heterogeneous nanomaterials, and the propagation of acoustic, electromagnetic, and elastic waves in a one-dimensional periodic two-component material. - Covers key issues around the mechanics of structured media, including modeling techniques, fracture mechanics in various composite materials, the fundamentals of integral equations, wave mechanics, and more - Discusses boundary value problems of materials, techniques for predicting elasticity of composites, and heterogeneous nanomaterials and their statistical description - Includes insights on asymptotic methods, wave mechanics, the mechanics of piezo-materials, and more - Applies homogenization concepts to various physical systems
Author: Igor Andrianov
Publisher: Academic Press
ISBN: 0323906532
Category : Technology & Engineering
Languages : en
Pages : 528
Get Book Here
Book Description
Mechanics and Physics of Structured Media: Asymptotic and Integral Methods of Leonid Filshtinsky provides unique information on the macroscopic properties of various composite materials and the mathematical techniques key to understanding their physical behaviors. The book is centered around the arguably monumental work of Leonid Filshtinsky. His last works provide insight on fracture in electromagnetic-elastic systems alongside approaches for solving problems in mechanics of solid materials. Asymptotic methods, the method of complex potentials, wave mechanics, viscosity of suspensions, conductivity, vibration and buckling of functionally graded plates, and critical phenomena in various random systems are all covered at length. Other sections cover boundary value problems in fracture mechanics, two-phase model methods for heterogeneous nanomaterials, and the propagation of acoustic, electromagnetic, and elastic waves in a one-dimensional periodic two-component material. - Covers key issues around the mechanics of structured media, including modeling techniques, fracture mechanics in various composite materials, the fundamentals of integral equations, wave mechanics, and more - Discusses boundary value problems of materials, techniques for predicting elasticity of composites, and heterogeneous nanomaterials and their statistical description - Includes insights on asymptotic methods, wave mechanics, the mechanics of piezo-materials, and more - Applies homogenization concepts to various physical systems
Author: A.P.S. Selvadurai
Publisher: Elsevier
ISBN: 1483164136
Category : Technology & Engineering
Languages : en
Pages : 513
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Book Description
Mechanics of Structured Media
Author: Gerald Jay Sussman
Publisher: MIT Press
ISBN: 0262028964
Category : Science
Languages : en
Pages : 580
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Book Description
The new edition of a classic text that concentrates on developing general methods for studying the behavior of classical systems, with extensive use of computation. We now know that there is much more to classical mechanics than previously suspected. Derivations of the equations of motion, the focus of traditional presentations of mechanics, are just the beginning. This innovative textbook, now in its second edition, concentrates on developing general methods for studying the behavior of classical systems, whether or not they have a symbolic solution. It focuses on the phenomenon of motion and makes extensive use of computer simulation in its explorations of the topic. It weaves recent discoveries in nonlinear dynamics throughout the text, rather than presenting them as an afterthought. Explorations of phenomena such as the transition to chaos, nonlinear resonances, and resonance overlap to help the student develop appropriate analytic tools for understanding. The book uses computation to constrain notation, to capture and formalize methods, and for simulation and symbolic analysis. The requirement that the computer be able to interpret any expression provides the student with strict and immediate feedback about whether an expression is correctly formulated. This second edition has been updated throughout, with revisions that reflect insights gained by the authors from using the text every year at MIT. In addition, because of substantial software improvements, this edition provides algebraic proofs of more generality than those in the previous edition; this improvement permeates the new edition.
Author: Albrecht Bertram
Publisher: Springer Science & Business Media
ISBN: 354085715X
Category : Science
Languages : en
Pages : 301
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Book Description
Many materials or media in nature and technology possess a microstructure which determines their macroscopic behaviour. The knowledge of the relevant mechanisms is often more comprehensive on the micro than on the macro scale. On the other hand, not all information on the micro level is relevant for the understanding of this macro behaviour. Therefore, averaging and homogenization methods are needed to select only the specific information from the micro scale, which influences the macro scale. These methods also open the possibility to design or to influence microstructures with the objective to optimize their macro behaviour. This book presents the development of new methods in this interdisciplinary field of macro- micro-interactions of different engineering branches like mechanical and process engineering, applied mathematics, theoretical, and computational physics. In particular, solids with microstructures and particle systems are considered.
Author: Sacha Friedli
Publisher: Cambridge University Press
ISBN: 1107184827
Category : Mathematics
Languages : en
Pages : 643
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Book Description
A self-contained, mathematical introduction to the driving ideas in equilibrium statistical mechanics, studying important models in detail.
Author: Alexander B. Movchan
Publisher: CRC Press
ISBN: 1351651420
Category : Mathematics
Languages : en
Pages : 317
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Book Description
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.
Author: Fusao Oka
Publisher: CRC Press
ISBN: 0203871049
Category : Technology & Engineering
Languages : en
Pages : 628
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Book Description
The last decades have shown a remarkable increase in the number of heavy rains, typhoons and earthquakes. These natural phenomena are the main causes for geohazards. As a result the mitigation of geohazards has become a major research topic in geotechnical engineering, and in recent years simulation-based predictions and monitoring tools have been
Author: Igor V. Andrianov
Publisher: Springer
ISBN: 3319657860
Category : Science
Languages : en
Pages : 333
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Book Description
In this book the authors show that it is possible to construct efficient computationally oriented models of multi-parameter complex systems by using asymptotic methods, which can, owing to their simplicity, be directly used for controlling processes arising in connection with composite material systems. The book focuses on this asymptotic-modeling-based approach because it allows us to define the most important out of numerous parameters describing the system, or, in other words, the asymptotic methods allow us to estimate the sensitivity of the system parameters. Further, the book addresses the construction of nonlocal and higher-order homogenized models. Local fields on the micro-level and the influence of so-called non-ideal contact between the matrix and inclusions are modeled and investigated. The book then studies composites with non-regular structure and cluster type composite conductivity, and analyzes edge effects in fiber composite materials. Transition of load from a fiber to a matrix for elastic and viscoelastic composites, various types of fiber composite fractures, and buckling of fibers in fiber-reinforced composites is also investigated. Last but not least, the book includes studies on perforated membranes, plates, and shells, as well as the asymptotic modeling of imperfect nonlinear interfaces.
Author: Rainer Glüge
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110793520
Category : Science
Languages : en
Pages : 198
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Book Description
Almost all materials posses a microstructure, which cannot be accounted for in detail in structural engineering calculations. Instead, effective material properties are used. These are obtained by homogenization methods. This book provides
Author: Bernard Cambou
Publisher: John Wiley & Sons
ISBN: 1118623088
Category : Science
Languages : en
Pages : 263
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Book Description
Nearly all solids are compised of grains. However most studies treat materials as a continious solid. The book applies analysis used on loose granular materials to dense grainular materials. This title’s main focus is devoted to static or dynamic loadings applied to dense materials, although rapid flows and widely dispersed media are also mentioned briefly. Three essential areas are covered: Local variable analysis: Contact forces, displacements and rotations, orientation of contacting particles and fabric tensors are all examples of local variables. Their statistical distributions, such as spatial distribution and possible localization, are analyzed, taking into account experimental results or numerical simulations. Change of scales procedures: Also known as “homogenization techniques”, these procedures make it possible to construct continuum laws to be used in a continuum mechanics approach or performing smaller scale analyses. Numerical modeling: Several methods designed to calculate approximate solutions of dynamical equations together with unilateral contact and frictional laws are presented, including molecular dynamics, the distinct element method and non-smooth contact dynamics. Numerical examples are given and the quality of numerical approximations is discussed.
