Mathematical Methods In Electro Magneto Elasticity

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Mathematical Methods in Electro-Magneto-Elasticity

Demosthenis I. Bardzokas,Michael L. Filshtinsky,Leonid A. Filshtinsky
Mathematical Methods in Electro Magneto Elasticity Book PDF

Author : Demosthenis I. Bardzokas,Michael L. Filshtinsky,Leonid A. Filshtinsky
Publisher : Springer Science & Business Media
Page : 539 pages
File Size : 45,9 Mb
Release : 2007-05-19
Category : Technology & Engineering
ISBN : 9783540710318

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Mathematical Methods in Electro-Magneto-Elasticity by Demosthenis I. Bardzokas,Michael L. Filshtinsky,Leonid A. Filshtinsky Pdf

The mechanics of Coupled Fields is a discipline at the edge of modern research connecting Continuum Mechanics with Solid State Physics. This book fills many gaps in the theoretical literature which arise due to the complexity of the problem. A vast number of problems are considered so that the reader can get a clear quantitative and qualitative understanding of the phenomena taking place.

Mathematical Methods in Dynamical Systems

S. Chakraverty,Subrat Kumar Jena
Mathematical Methods in Dynamical Systems Book PDF

Author : S. Chakraverty,Subrat Kumar Jena
Publisher : CRC Press
Page : 508 pages
File Size : 42,9 Mb
Release : 2023-05-19
Category : Mathematics
ISBN : 9781000833805

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Mathematical Methods in Dynamical Systems by S. Chakraverty,Subrat Kumar Jena Pdf

The art of applying mathematics to real-world dynamical problems such as structural dynamics, fluid dynamics, wave dynamics, robot dynamics, etc. can be extremely challenging. Various aspects of mathematical modelling that may include deterministic or uncertain (fuzzy, interval, or stochastic) scenarios, along with integer or fractional order, are vital to understanding these dynamical systems. Mathematical Methods in Dynamical Systems offers problem-solving techniques and includes different analytical, semi-analytical, numerical, and machine intelligence methods for finding exact and/or approximate solutions of governing equations arising in dynamical systems. It provides a singular source of computationally efficient methods to investigate these systems and includes coverage of various industrial applications in a simple yet comprehensive way.

Hygro-Thermo-Magneto-Electro-Elastic Theory of Anisotropic Doubly-Curved Shells

Francesco Tornabene
Hygro Thermo Magneto Electro Elastic Theory of Anisotropic Doubly Curved Shells Book PDF

Author : Francesco Tornabene
Publisher : Società Editrice Esculapio
Page : 1073 pages
File Size : 53,5 Mb
Release : 2023-10-13
Category : Technology & Engineering
ISBN : 9791222459431

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Hygro-Thermo-Magneto-Electro-Elastic Theory of Anisotropic Doubly-Curved Shells by Francesco Tornabene Pdf

This book aims to present in depth several Higher-order Shear Deformation Theories (HSDTs) by means of a unified approach for studying the Hygro-Thermo-Magneto-Electro- Elastic Theory of Anisotropic Doubly-Curved Shells. In particular, a general coupled multifield theory regarding anisotropic shell structures is provided. The three-dimensional multifield problem is reduced in a two-dimensional one following the principles of the Equivalent Single Layer (ESL) approach and the Equivalent Layer-Wise (ELW) approach, setting a proper configuration model. According to the adopted configuration assumptions, several Higher-order Shear Deformation Theories (HSDTs) are obtained. Furthermore, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. The approach presented in this volume is completely general and represents a valid tool to investigate the physical behavior of many arbitrarily shaped structures. An isogeometric mapping procedure is also illustrated to this aim. Special attention is given also to advanced and innovative constituents, such as Carbon Nanotubes (CNTs), Variable Angle Tow (VAT) composites and Functionally Graded Materials (FGMs). In addition, several numerical applications are used to support the theoretical models. Accurate, efficient and reliable numerical techniques able to approximate both derivatives and integrals are considered, which are respectively the Differential Quadrature (DQ) and Integral Quadrature (IQ) methods. The Theory of Composite Thin Shells is derived in a simple and intuitive manner from the theory of thick and moderately thick shells (First-order Shear Deformation Theory or Reissner- Mindlin Theory). In particular, the Kirchhoff-Love Theory and the Membrane Theory for composite shells are shown. Furthermore, the Theory of Composite Arches and Beams is also exposed. In particular, the equations of the Timoshenko Theory and the Euler-Bernoulli Theory are directly deducted from the equations of singly-curved shells of translation and of plates.

Applications of Mathematics and Informatics in Natural Sciences and Engineering

George Jaiani,David Natroshvili
Applications of Mathematics and Informatics in Natural Sciences and Engineering Book PDF

Author : George Jaiani,David Natroshvili
Publisher : Springer Nature
Page : 280 pages
File Size : 40,8 Mb
Release : 2020-11-28
Category : Mathematics
ISBN : 9783030563561

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Applications of Mathematics and Informatics in Natural Sciences and Engineering by George Jaiani,David Natroshvili Pdf

This book presents peer-reviewed papers from the 4th International Conference on Applications of Mathematics and Informatics in Natural Sciences and Engineering (AMINSE2019), held in Tbilisi, Georgia, in September 2019. Written by leading researchers from Austria, France, Germany, Georgia, Hungary, Romania, South Korea and the UK, the book discusses important aspects of mathematics, and informatics, and their applications in natural sciences and engineering. It particularly focuses on Lie algebras and applications, strategic graph rewriting, interactive modeling frameworks, rule-based frameworks, elastic composites, piezoelectrics, electromagnetic force models, limiting distribution, degenerate Ito-SDEs, induced operators, subgaussian random elements, transmission problems, pseudo-differential equations, and degenerate partial differential equations. Featuring theoretical, practical and numerical contributions, the book will appeal to scientists from various disciplines interested in applications of mathematics and informatics in natural sciences and engineering.

Multiscale Solid Mechanics

Holm Altenbach,Victor A. Eremeyev,Leonid A. Igumnov
Multiscale Solid Mechanics Book PDF

Author : Holm Altenbach,Victor A. Eremeyev,Leonid A. Igumnov
Publisher : Springer Nature
Page : 509 pages
File Size : 43,8 Mb
Release : 2020-11-09
Category : Science
ISBN : 9783030549282

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Multiscale Solid Mechanics by Holm Altenbach,Victor A. Eremeyev,Leonid A. Igumnov Pdf

This book provides an overview of the current of the state of the art in the multiscale mechanics of solids and structures. It comprehensively discusses new materials, including theoretical and experimental investigations their durability and strength, as well as fractures and damage

Mathematical Applications in Continuum and Structural Mechanics

Francesco Marmo,Salvatore Sessa,Emilio Barchiesi,Mario Spagnuolo
Mathematical Applications in Continuum and Structural Mechanics Book PDF

Author : Francesco Marmo,Salvatore Sessa,Emilio Barchiesi,Mario Spagnuolo
Publisher : Springer Nature
Page : 275 pages
File Size : 40,9 Mb
Release : 2021-11-30
Category : Technology & Engineering
ISBN : 9783030427078

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Mathematical Applications in Continuum and Structural Mechanics by Francesco Marmo,Salvatore Sessa,Emilio Barchiesi,Mario Spagnuolo Pdf

This book presents a range of research projects focusing on innovative numerical and modeling strategies for the nonlinear analysis of structures and metamaterials. The topics covered concern various analysis approaches based on classical finite element solutions, structural optimization, and analytical solutions in order to present a comprehensive overview of the latest scientific advances. Although based on pioneering research, the contributions are focused on immediate and direct application in practice, providing valuable tools for researchers and practicing professionals alike.

Generalized Differential and Integral Quadrature

Francesco Tornabene
Generalized Differential and Integral Quadrature Book PDF

Author : Francesco Tornabene
Publisher : Società Editrice Esculapio
Page : 689 pages
File Size : 53,6 Mb
Release : 2023-10-17
Category : Technology & Engineering
ISBN : 9791222460543

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Generalized Differential and Integral Quadrature by Francesco Tornabene Pdf

The main aim of this book is to analyze the mathematical fundamentals and the main features of the Generalized Differential Quadrature (GDQ) and Generalized Integral Quadrature (GIQ) techniques. Furthermore, another interesting aim of the present book is to shown that from the two numerical techniques mentioned above it is possible to derive two different approaches such as the Strong and Weak Finite Element Methods (SFEM and WFEM), that will be used to solve various structural problems and arbitrarily shaped structures. A general approach to the Differential Quadrature is proposed. The weighting coefficients for different basis functions and grid distributions are determined. Furthermore, the expressions of the principal approximating polynomials and grid distributions, available in the literature, are shown. Besides the classic orthogonal polynomials, a new class of basis functions, which depend on the radial distance between the discretization points, is presented. They are known as Radial Basis Functions (or RBFs). The general expressions for the derivative evaluation can be utilized in the local form to reduce the computational cost. From this concept the Local Generalized Differential Quadrature (LGDQ) method is derived. The Generalized Integral Quadrature (GIQ) technique can be used employing several basis functions, without any restriction on the point distributions for the given definition domain. To better underline these concepts some classical numerical integration schemes are reported, such as the trapezoidal rule or the Simpson method. An alternative approach based on Taylor series is also illustrated to approximate integrals. This technique is named as Generalized Taylor-based Integral Quadrature (GTIQ) method. The major structural theories for the analysis of the mechanical behavior of various structures are presented in depth in the book. In particular, the strong and weak formulations of the corresponding governing equations are discussed and illustrated. Generally speaking, two formulations of the same system of governing equations can be developed, which are respectively the strong and weak (or variational) formulations. Once the governing equations that rule a generic structural problem are obtained, together with the corresponding boundary conditions, a differential system is written. In particular, the Strong Formulation (SF) of the governing equations is obtained. The differentiability requirement, instead, is reduced through a weighted integral statement if the corresponding Weak Formulation (WF) of the governing equations is developed. Thus, an equivalent integral formulation is derived, starting directly from the previous one. In particular, the formulation in hand is obtained by introducing a Lagrangian approximation of the degrees of freedom of the problem. The need of studying arbitrarily shaped domains or characterized by mechanical and geometrical discontinuities leads to the development of new numerical approaches that divide the structure in finite elements. Then, the strong form or the weak form of the fundamental equations are solved inside each element. The fundamental aspects of this technique, which the author defined respectively Strong Formulation Finite Element Method (SFEM) and Weak Formulation Finite Element Method (WFEM), are presented in the book.

Mathematics Without Boundaries

Panos M. Pardalos,Themistocles M. Rassias
Mathematics Without Boundaries Book PDF

Author : Panos M. Pardalos,Themistocles M. Rassias
Publisher : Springer
Page : 648 pages
File Size : 52,9 Mb
Release : 2014-09-16
Category : Mathematics
ISBN : 9781493911240

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Mathematics Without Boundaries by Panos M. Pardalos,Themistocles M. Rassias Pdf

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.

Mathematical Methods of Electromagnetic Theory

Kurt O. Friedrichs
Mathematical Methods of Electromagnetic Theory Book PDF

Author : Kurt O. Friedrichs
Publisher : American Mathematical Soc.
Page : 159 pages
File Size : 49,8 Mb
Release : 2014-11-12
Category : Science
ISBN : 9781470417116

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Mathematical Methods of Electromagnetic Theory by Kurt O. Friedrichs Pdf

This text provides a mathematically precise but intuitive introduction to classical electromagnetic theory and wave propagation, with a brief introduction to special relativity. While written in a distinctive, modern style, Friedrichs manages to convey the physical intuition and 19th century basis of the equations, with an emphasis on conservation laws. Particularly striking features of the book include: (a) a mathematically rigorous derivation of the interaction of electromagnetic waves with matter, (b) a straightforward explanation of how to use variational principles to solve problems in electro- and magnetostatics, and (c) a thorough discussion of the central importance of the conservation of charge. It is suitable for advanced undergraduate students in mathematics and physics with a background in advanced calculus and linear algebra, as well as mechanics and electromagnetics at an undergraduate level. Apart from minor corrections to the text, the notation was updated in this edition to follow the conventions of modern vector calculus. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.

Mechanics and Physics of Structured Media

Igor Andrianov,Simon Gluzman,Vladimir Mityushev
Mechanics and Physics of Structured Media Book PDF

Author : Igor Andrianov,Simon Gluzman,Vladimir Mityushev
Publisher : Academic Press
Page : 528 pages
File Size : 48,9 Mb
Release : 2022-01-20
Category : Technology & Engineering
ISBN : 9780323906531

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Mechanics and Physics of Structured Media by Igor Andrianov,Simon Gluzman,Vladimir Mityushev Pdf

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

Spectral Method in Multiaxial Random Fatigue

Adam Nieslony,Ewald Macha
Spectral Method in Multiaxial Random Fatigue Book PDF

Author : Adam Nieslony,Ewald Macha
Publisher : Springer Science & Business Media
Page : 148 pages
File Size : 51,6 Mb
Release : 2007-09-04
Category : Technology & Engineering
ISBN : 9783540738237

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Spectral Method in Multiaxial Random Fatigue by Adam Nieslony,Ewald Macha Pdf

This monograph examines the theoretical foundations of the spectral method for fatigue life determination. The authors discuss a rule of description of random loading states with the matrix of power spectral density functions of the stress/strain tensor components. Some chosen criteria of multiaxial fatigue failure are analyzed. The formula proposed in this book enables readers to determine power spectral density of the equivalent history directly from the components of the power spectral density matrix of the multidimensional stochastic process.

Numerical Methods for Nonsmooth Dynamical Systems

Vincent Acary,Bernard Brogliato
Numerical Methods for Nonsmooth Dynamical Systems Book PDF

Author : Vincent Acary,Bernard Brogliato
Publisher : Springer Science & Business Media
Page : 529 pages
File Size : 49,9 Mb
Release : 2008-01-30
Category : Technology & Engineering
ISBN : 9783540753926

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Numerical Methods for Nonsmooth Dynamical Systems by Vincent Acary,Bernard Brogliato Pdf

This book concerns the numerical simulation of dynamical systems whose trajec- ries may not be differentiable everywhere. They are named nonsmooth dynamical systems. They make an important class of systems, rst because of the many app- cations in which nonsmooth models are useful, secondly because they give rise to new problems in various elds of science. Usually nonsmooth dynamical systems are represented as differential inclusions, complementarity systems, evolution va- ational inequalities, each of these classes itself being split into several subclasses. The book is divided into four parts, the rst three parts being sketched in Fig. 0. 1. The aim of the rst part is to present the main tools from mechanics and applied mathematics which are necessary to understand how nonsmooth dynamical systems may be numerically simulated in a reliable way. Many examples illustrate the th- retical results, and an emphasis is put on mechanical systems, as well as on electrical circuits (the so-called Filippov’s systems are also examined in some detail, due to their importance in control applications). The second and third parts are dedicated to a detailed presentation of the numerical schemes. A fourth part is devoted to the presentation of the software platform Siconos. This book is not a textbook on - merical analysis of nonsmooth systems, in the sense that despite the main results of numerical analysis (convergence, order of consistency, etc. ) being presented, their proofs are not provided.

Mathematical Methods in Electromagnetism

M Cessenat
Mathematical Methods in Electromagnetism Book PDF

Author : M Cessenat
Publisher : World Scientific
Page : 396 pages
File Size : 40,6 Mb
Release : 1996-07-13
Category : Electronic
ISBN : 9789814525381

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Mathematical Methods in Electromagnetism by M Cessenat Pdf

This book provides the reader with basic tools to solve problems of electromagnetism in their natural functional frameworks thanks to modern mathematical methods: integral surface methods, and also semigroups, variational methods, etc., well adapted to a numerical approach. As examples of applications of these tools and concepts, we solve several fundamental problems of electromagnetism, stationary or time-dependent: scattering of an incident wave by an obstacle, bounded or not, by gratings; wave propagation in a waveguide, with junctions and cascades. We hope that mathematical notions will allow a better understanding of modelization in electromagnetism and emphasize the essential features related to the geometry and nature of materials. Contents:Mathematical Modelling of the Electromagnetic Field in Continuous Media: Maxwell Equations and Constitutive RelationsMathematical Framework for ElectromagnetismStationary Scattering Problems with Bounded ObstaclesWaveguide ProblemsStationary Scattering Problems on Unbounded ObstaclesEvolution ProblemsAppendix — Differential Geometry for ElectromagnetismReferencesIndexNotations Readership: Applied mathematicians. keywords:Electromagnetism;Mathematical Modeling;Maxwell Equations;Variational Methods;Differential Geometry;Hodge Decomposition;Impedance Operators;Calderon Operators;Waveguides;Scattering;Outgoing Waves;Causal Problems “I would recommend it to anyone interested in the analysis or numerical analysis of Maxwell's equations for its up-to-date and extensive treatment of the problem.” SIAM Reviews

Fracture Mechanics of Piezoelectric Solids with Interface Cracks

Volodymyr Govorukha,Marc Kamlah,Volodymyr Loboda,Yuri Lapusta
Fracture Mechanics of Piezoelectric Solids with Interface Cracks Book PDF

Author : Volodymyr Govorukha,Marc Kamlah,Volodymyr Loboda,Yuri Lapusta
Publisher : Springer
Page : 235 pages
File Size : 51,7 Mb
Release : 2017-03-14
Category : Science
ISBN : 9783319535531

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Fracture Mechanics of Piezoelectric Solids with Interface Cracks by Volodymyr Govorukha,Marc Kamlah,Volodymyr Loboda,Yuri Lapusta Pdf

This book provides a comprehensive study of cracks situated at the interface of two piezoelectric materials. It discusses different electric boundary conditions along the crack faces, in particular the cases of electrically permeable, impermeable, partially permeable, and conducting cracks. The book also elaborates on a new technique for the determination of electromechanical fields at the tips of interface cracks in finite sized piezoceramic bodies of arbitrary shape under different load types. It solves scientific problems of solid mechanics in connection with the investigation of electromechanical fields in piezoceramic bodies with interface cracks, and develops calculation models and solution methods for plane fracture mechanical problems for piecewise homogeneous piezoceramic bodies with cracks at the interfaces. It discusses the “open” crack model, which leads to a physically unrealistic oscillating singularity at the crack tips, and the contact zone model for in-plane straight interface cracks between two dissimilar piezoelectric materials. It also investigates the model of a crack with electro-mechanical pre-fracture zones. The formulated problems are reduced to problems of linear relationship, which correspond to different crack models, and their exact analytical solutions are found. The book presents in detail the expressions for stress and electric displacement intensity factors, as well as for the energy release rate. The influence of the electric permittivity of the crack, the mechanical load and the electric field upon the electro-elastic state, as well as the main fracture mechanical parameters, are analyzed and clearly illustrated. This book addresses postgraduate students, university teachers and researchers dealing with the problems of fracture mechanics of piezoelectric materials, as well as engineers who are active in the analysis of strength and durability of piezoelectric constructions.

Linear and Nonlinear Waves in Microstructured Solids

Igor V. Andrianov,Jan Awrejcewicz,Vladyslav Danishevskyy
Linear and Nonlinear Waves in Microstructured Solids Book PDF

Author : Igor V. Andrianov,Jan Awrejcewicz,Vladyslav Danishevskyy
Publisher : CRC Press
Page : 322 pages
File Size : 42,7 Mb
Release : 2021-04-22
Category : Technology & Engineering
ISBN : 9781000372212

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Linear and Nonlinear Waves in Microstructured Solids by Igor V. Andrianov,Jan Awrejcewicz,Vladyslav Danishevskyy Pdf

This book uses asymptotic methods to obtain simple approximate analytic solutions to various problems within mechanics, notably wave processes in heterogeneous materials. Presenting original solutions to common issues within mechanics, this book builds upon years of research to demonstrate the benefits of implementing asymptotic techniques within mechanical engineering and material science. Focusing on linear and nonlinear wave phenomena in complex micro-structured solids, the book determines their global characteristics through analysis of their internal structure, using homogenization and asymptotic procedures, in line with the latest thinking within the field. The book’s cutting-edge methodology can be applied to optimal design, non-destructive control and in deep seismic sounding, providing a valuable alternative to widely used numerical methods. Using case studies, the book covers topics such as elastic waves in nonhomogeneous materials, regular and chaotic dynamics based on continualisation and discretization and vibration localization in 1D Linear and Nonlinear lattices. The book will be of interest to students, research engineers, and professionals specialising in mathematics and physics as well as mechanical and civil engineering.