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Author: Igor V. Andrianov
Publisher: CRC Press
ISBN: 1000890309
Category : Science
Languages : en
Pages : 441
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Book Description
Approximate Models of Mechanics of Composites: An Asymptotic Approach is an essential guide to constructing asymptotic models and mathematical methods to correctly identify the mechanical behavior of composites. It provides methodology for predicting and evaluating composite behavior in various structures, leading to accurate mathematical and physical assessments. The book estimates the error of approximations through comparing asymptotic solutions with the results of numerical and analytical solutions to gain a holistic view of the data. The authors have developed asymptotic models based on mathematical and physical rigorous approaches, which include three-phase models of fibrous composites, a modernized three-phase composite model with cylindrical inclusions, and models of two-dimensional composites of hexagonal structure. Also covered are two-phase models of composites related to the Maxwell formula and a percolation transition model for elastic problems based on the self-consistency method and Padé approximations. By obtaining analytical expressions to effectively characterize composite materials, their physical and geometric parameters can be accurately assessed. This book suits engineers and students working in material science, mechanical engineering, physics, and mathematics, as well as composite materials in industries such as construction, transport, aerospace, and chemical engineering.
Author: Igor V. Andrianov
Publisher: CRC Press
ISBN: 1000890309
Category : Science
Languages : en
Pages : 441
Get Book Here
Book Description
Approximate Models of Mechanics of Composites: An Asymptotic Approach is an essential guide to constructing asymptotic models and mathematical methods to correctly identify the mechanical behavior of composites. It provides methodology for predicting and evaluating composite behavior in various structures, leading to accurate mathematical and physical assessments. The book estimates the error of approximations through comparing asymptotic solutions with the results of numerical and analytical solutions to gain a holistic view of the data. The authors have developed asymptotic models based on mathematical and physical rigorous approaches, which include three-phase models of fibrous composites, a modernized three-phase composite model with cylindrical inclusions, and models of two-dimensional composites of hexagonal structure. Also covered are two-phase models of composites related to the Maxwell formula and a percolation transition model for elastic problems based on the self-consistency method and Padé approximations. By obtaining analytical expressions to effectively characterize composite materials, their physical and geometric parameters can be accurately assessed. This book suits engineers and students working in material science, mechanical engineering, physics, and mathematics, as well as composite materials in industries such as construction, transport, aerospace, and chemical engineering.
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: Leonid Berlyand
Publisher: Cambridge University Press
ISBN: 110702823X
Category : Mathematics
Languages : en
Pages : 259
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Book Description
Introduces graduate students to the state of the art in this fast-developing field of applied mathematics.
Author: Uwe Kähler
Publisher: Springer Nature
ISBN: 3031363752
Category : Mathematics
Languages : en
Pages : 696
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Book Description
This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium. The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.
Author: Simon Gluzman
Publisher: Academic Press
ISBN: 0128110473
Category : Mathematics
Languages : en
Pages : 330
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Book Description
Computational Analysis of Structured Media presents a systematical approach to analytical formulae for the effective properties of deterministic and random composites. Schwarz's method and functional equations yield for use in symbolic-numeric computations relevant to the effective properties. The work is primarily concerned with constructive topics of boundary value problems, complex analysis, and their applications to composites. Symbolic-numerical computations are widely used to deduce new formulae interesting for applied mathematicians and engineers. The main line of presentation is the investigation of two-phase 2D composites with non-overlapping inclusions randomly embedded in matrices. - Computational methodology for main classes of problems in structured media - Theory of Representative Volume Element - Combines exact results, Monte-Carlo simulations and Resummation techniques under one umbrella - Contains new analytical formulae obtained in the last ten years and it combines different asymptotic methods with the corresponding computer implementations
Author: Holm Altenbach
Publisher: Springer Nature
ISBN: 3031287444
Category : Technology & Engineering
Languages : en
Pages : 533
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Book Description
This book is published on dedication of Prof. Dr. Igor Sevostianov who passed away in 2021. He was a great Russian-American scientist who made significant contributions in the field of mechanics of heterogeneous media. This book contains research papers from his friends and colleagues in this research field.
Author: Ross McPhedran
Publisher: Elsevier
ISBN: 0128188200
Category : Technology & Engineering
Languages : en
Pages : 318
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Book Description
2D and Quasi-2D Composite and Nanocomposite Materials: Theory, Properties and Photonic Applications covers the theory, characterization and computational modeling of 2D composite materials and shows how they are used for the creation of materials for 3D structures The book covers three major themes: - Properties of 2D and quasi-2D composites are discussed in the context of homogenization theory. Homogenization results are discussed for spatiotemporal material composites assembled from materials which are distributed on a micro-scale in space and in time. - New types of transport phenomena and localization in random media are addressed, with particular attention to the non-reciprocity of transport coefficients. - Plasmonics and magneto-optics are also of particular interest. Magneto-transport and sub-wavelength resolution in electromagnetic and acoustic imaging are further considered. This book is an important resource for materials scientists and engineers working on nanomaterials, photonic composites, and materials theory, modeling and simulations. - Outlines major modelling techniques of 2D nanocomposites for photonic applications - Explores how the properties of 2D nanocomposites make them suitable for use for building 3D structures - Assesses the challenges of using 2D nanocomposites for designing new devices on a mass scale
Author: Paula Cerejeiras
Publisher: Springer Nature
ISBN: 3030875024
Category : Mathematics
Languages : en
Pages : 663
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Book Description
This volume contains the contributions of the participants of the 12th ISAAC congress which was held at the University of Aveiro, Portugal, from July 29 to August 3, 2019. These contributions originate from the following sessions: Applications of dynamical systems theory in biology, Complex Analysis and Partial Differential Equations, Complex Geometry, Complex Variables and Potential Theory, Constructive Methods in the Theory of Composite and Porous Media, Function Spaces and Applications, Generalized Functions and Applications, Geometric & Regularity Properties of Solutions to Elliptic and Parabolic PDEs, Geometries Defined by Differential Forms, Partial Differential Equations on Curved Spacetimes, Partial Differential Equations with Nonstandard Growth, Quaternionic and Clifford Analysis, Recent Progress in Evolution Equations, Wavelet theory and its Related Topics.
Author: Panos M. Pardalos
Publisher: Springer
ISBN: 1493911244
Category : Mathematics
Languages : en
Pages : 648
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Book Description
This volume consists of chapters written by eminent scientists and engineers from the international community and present significant advances in several theories, methods and applications of an interdisciplinary research. These contributions focus on both old and recent developments of Global Optimization Theory, Convex Analysis, Calculus of Variations, Discrete Mathematics and Geometry, as well as several applications to a large variety of concrete problems, including applications of computers to the study of smoothness and analyticity of functions, applications to epidemiological diffusion, networks, mathematical models of elastic and piezoelectric fields, optimal algorithms, stability of neutral type vector functional differential equations, sampling and rational interpolation for non-band-limited signals, recurrent neural network for convex optimization problems and experimental design. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical and Engineering subjects and especially to graduate students who search for the latest information.
Author: Holm Altenbach
Publisher: Springer Nature
ISBN: 3030871851
Category : Technology & Engineering
Languages : en
Pages : 326
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Book Description
This book presents the various approaches in establishment the basic equations of one- and two-dimensional structural elements. In addition, the boundaries of validity of the theories and the estimation of errors in approximate theories are given. Many contributions contain not only new theories, but also new applications, which makes the book interesting for researcher and graduate students.
