Homogenization Methods
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Homogenization Methods
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Author : Rainer Glüge
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-02-20
Homogenization Methods written by Rainer Glüge and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-20 with Technology & Engineering categories.
Almost all materials are inhomogeneous at the microscale. Typical examples are fiber- and grain structures made of anisotropic phases. These cannot be accounted for in detail in engineering calculations. Instead, effective, homogeneous material properties are used. These are obtained from the inhomogeneous structures by homogenization methods. This book provides a structured overview of the analytical homogenization methods, including the most common estimates, bounds, and Fourier methods. The focus is on linear and anisotropic constitutive relationships, like Hookean elasticity and Fourier’s law for thermal conduction. All sections are accompanied by example calculations, including program code that is also available online.
From Creep Damage Mechanics To Homogenization Methods
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Author : Holm Altenbach
language : en
Publisher: Springer
Release Date : 2015-06-03
From Creep Damage Mechanics To Homogenization Methods written by Holm Altenbach and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-03 with Science categories.
This volume presents a collection of contributions on materials modeling, which were written to celebrate the 65th birthday of Prof. Nobutada Ohno. The book follows Prof. Ohno’s scientific topics, starting with creep damage problems and ending with homogenization methods.
Multiscale Methods
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Author : Grigoris Pavliotis
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-18
Multiscale Methods written by Grigoris Pavliotis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-18 with Mathematics categories.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the classical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series Texts in Applied Mathematics (TAM). The development of new courses is a natural consequence of a high level of excitement on the research frontier as newer techniques, such as numerical and s- bolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook - ries is to meet the current and future needs of these advances and to encourage the teaching of new couses. TAM will publish textbooks suitable for use in advanced undergraduate and - ginning graduate courses, and will complement the Applied Mathematical Sciences (AMS) series, which will focus on advanced textbooks and research-level mo- graphs. Pasadena, California J.E. Marsden New York, New York L. Sirovich College Park, Maryland S.S. Antman To my parentsA????? and?o?????? and to my brother?????o. Carry Home.????o???. For my children Natalie, Sebastian, and Isobel.
Shape Optimization By The Homogenization Method
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Author : Gregoire Allaire
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Shape Optimization By The Homogenization Method written by Gregoire Allaire and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
The topic of this book is homogenization theory and its applications to optimal design in the conductivity and elasticity settings. Its purpose is to give a self-contained account of homogenization theory and explain how it applies to solving optimal design problems, from both a theoretical and a numerical point of view. The application of greatest practical interest tar geted by this book is shape and topology optimization in structural design, where this approach is known as the homogenization method. Shape optimization amounts to finding the optimal shape of a domain that, for example, would be of maximal conductivity or rigidity under some specified loading conditions (possibly with a volume or weight constraint). Such a criterion is embodied by an objective function and is computed through the solution of astate equation that is a partial differential equa tion (modeling the conductivity or the elasticity of the structure). Apart from those areas where the loads are applied, the shape boundary is al ways assumed to support Neumann boundary conditions (i. e. , isolating or traction-free conditions). In such a setting, shape optimization has a long history and has been studied by many different methods. There is, therefore, a vast literat ure in this field, and we refer the reader to the following short list of books, and references therein [39], [42], [130], [135], [149], [203], [220], [225], [237], [245], [258].
Homogenization Methods For Multiscale Mechanics
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Author : Chiang C. Mei
language : en
Publisher: World Scientific
Release Date : 2010
Homogenization Methods For Multiscale Mechanics written by Chiang C. Mei and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
In many physical problems several scales present either in space or in time, caused by either inhomogeneity of the medium or complexity of the mechanical process. A fundamental approach is to first construct micro-scale models, and then deduce the macro-scale laws and the constitutive relations by properly averaging over the micro-scale. The perturbation method of multiple scales can be used to derive averaged equations for a much larger scale from considerations of the small scales. In the mechanics of multiscale media, the analytical scheme of upscaling is known as the Theory of Homogenization The authors share the view that the general methods of homogenization should be more widely understood and practiced by applied scientists and engineers. Hence this book is aimed at providing a less abstract treatment of the theory of homogenization for treating inhomogeneous media, and at illustrating its broad range of applications. Each chapter deals with a different class of physical problems. To tackle a new problem, the novel approach of first discussing the physically relevant scales, then identifying the small parameters and their roles in the normalized governing equations is adopted. The details of asymptotic analysis are only explained afterwards.
Handbook Of Food Analysis Methods And Instruments In Applied Food Analysis
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Author : Leo M. L. Nollet
language : en
Publisher: CRC Press
Release Date : 2004
Handbook Of Food Analysis Methods And Instruments In Applied Food Analysis written by Leo M. L. Nollet and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Technology & Engineering categories.
Presents contemporary methods of measuring optical properties, moisture, ash content, and other physical characteristics of food and evaluates techniques used to trace nutrient analytes ranging from peptides, proteins, and enzymes to aroma compounds to carbohydrates and starch.
Homogenization Techniques For Composite Media
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Author : Enrique Sanchez-Palencia
language : en
Publisher:
Release Date : 1987
Homogenization Techniques For Composite Media written by Enrique Sanchez-Palencia and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with categories.
Reactor Physics Methods And Applications
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Author : Tengfei Zhang
language : en
Publisher: Frontiers Media SA
Release Date : 2022-06-29
Reactor Physics Methods And Applications written by Tengfei Zhang and has been published by Frontiers Media SA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-29 with Technology & Engineering categories.
Homogenization And Structural Topology Optimization
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Author : Behrooz Hassani
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Homogenization And Structural Topology Optimization written by Behrooz Hassani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Structural topology optimization is a fast growing field that is finding numerous applications in automotive, aerospace and mechanical design processes. Homogenization is a mathematical theory with applications in several engineering problems that are governed by partial differential equations with rapidly oscillating coefficients Homogenization and Structural Topology Optimization brings the two concepts together and successfully bridges the previously overlooked gap between the mathematical theory and the practical implementation of the homogenization method. The book is presented in a unique self-teaching style that includes numerous illustrative examples, figures and detailed explanations of concepts. The text is divided into three parts which maintains the book's reader-friendly appeal.
Handbook Of Numerical Methods For Hyperbolic Problems
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Author : Remi Abgrall
language : en
Publisher: Elsevier
Release Date : 2017-01-16
Handbook Of Numerical Methods For Hyperbolic Problems written by Remi Abgrall and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-16 with Mathematics categories.
Handbook on Numerical Methods for Hyperbolic Problems: Applied and Modern Issues details the large amount of literature in the design, analysis, and application of various numerical algorithms for solving hyperbolic equations that has been produced in the last several decades. This volume provides concise summaries from experts in different types of algorithms, so that readers can find a variety of algorithms under different situations and become familiar with their relative advantages and limitations. - Provides detailed, cutting-edge background explanations of existing algorithms and their analysis - Presents a method of different algorithms for specific applications and the relative advantages and limitations of different algorithms for engineers or those involved in applications - Written by leading subject experts in each field, the volumes provide breadth and depth of content coverage