Mathematical Methods And Models In Composites

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Mathematical Methods And Models In Composites

Author : Vladislav Mantic
Publisher : World Scientific
ISBN 13 : 178326411X
Total Pages : 521 pages
Book Rating : 4.7/5 (832 download)

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Book Synopsis Mathematical Methods And Models In Composites by : Vladislav Mantic

Download or read book Mathematical Methods And Models In Composites written by Vladislav Mantic and published by World Scientific. This book was released on 2013-10-25 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a representative selection of the most relevant, innovative, and useful mathematical methods and models applied to the analysis and characterization of composites and their behaviour on micro-, meso-, and macroscale. It establishes the fundamentals for meaningful and accurate theoretical and computer modelling of these materials in the future. Although the book is primarily concerned with fibre-reinforced composites, which have ever-increasing applications in fields such as aerospace, many of the results presented can be applied to other kinds of composites. The topics covered include: scaling and homogenization procedures in composite structures, thin plate and wave solutions in anisotropic materials, laminated structures, instabilities, fracture and damage analysis of composites, and highly efficient methods for simulation of composites manufacturing. The results presented are useful in the design, fabrication, testing, and industrial applications of composite components and structures. The book is written by well-known experts in different areas of applied mathematics, physics, and composite engineering and is an essential source of reference for graduate and doctoral students, as well as researchers. It is also suitable for non-experts in composites who wish to have an overview of both the mathematical methods and models used in this area and the related open problems requiring further research.

Mathematical Methods And Models In Composites (Second Edition)

Author : Vladislav Mantic
Publisher : World Scientific
ISBN 13 : 1800611897
Total Pages : 731 pages
Book Rating : 4.8/5 (6 download)

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Book Synopsis Mathematical Methods And Models In Composites (Second Edition) by : Vladislav Mantic

Download or read book Mathematical Methods And Models In Composites (Second Edition) written by Vladislav Mantic and published by World Scientific. This book was released on 2023-03-10 with total page 731 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Methods and Models in Composites (Second Edition) provides an in-depth treatment of modern and rigorous mathematical methods and models applied to composites modeling on the micro-, meso-, and macro scale. There has been a steady growth in the diversity of such methods and models that are used in the analysis and characterization of composites, their behavior, and their associated phenomena and processes. This second edition expands upon the success of the first edition, and has been substantially revised and updated.Written by well-known experts in different areas of applied mathematics, physics, and composite engineering, this book is mainly focused on continuous fiber reinforced composites and their ever increasing range of applications (for example, in the aerospace industry), though it also covers other kind of composites. The chapters cover a range of topics including, but not limited to: scaling and homogenization procedures in composites, thin plate and wave solutions in anisotropic materials, laminated structures, fiber-reinforced nonlinearly elastic solids, buckling and postbuckling, fracture and damage analysis of composites, and highly efficient methods for simulation of composites manufacturing such as resin transfer molding. The results presented are useful for the design, fabrication, testing and industrial applications of composite components and structures.This book is an essential reference for graduate and doctoral students, as well as researchers in mathematics, physics and composite engineering. Explanations and references in the book are sufficiently detailed so as to provide the necessary background to further investigate the fascinating subject of composites modeling and explore relevant research literature. It is also suitable for non-experts who wish to have an overview of the mathematical methods and models used for composites, and of the open problems in this area that require further research.

Asymptotical Mechanics of Composites

Author : Igor V. Andrianov
Publisher : Springer
ISBN 13 : 3319657860
Total Pages : 333 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Asymptotical Mechanics of Composites by : Igor V. Andrianov

Download or read book Asymptotical Mechanics of Composites written by Igor V. Andrianov and published by Springer. This book was released on 2017-11-09 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Multi-scale Modelling for Structures and Composites

Author : G. Panasenko
Publisher : Springer Science & Business Media
ISBN 13 : 9781402029813
Total Pages : 426 pages
Book Rating : 4.0/5 (298 download)

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Book Synopsis Multi-scale Modelling for Structures and Composites by : G. Panasenko

Download or read book Multi-scale Modelling for Structures and Composites written by G. Panasenko and published by Springer Science & Business Media. This book was released on 2005-02-09 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerous applications of rod structures in civil engineering, aircraft and spacecraft confirm the importance of the topic. On the other hand the majority of books on structural mechanics use some simplifying hypotheses; these hypotheses do not allow to consider some important effects, for instance the boundary layer effects near the points of junction of rods. So the question concerning the limits of applicability of structural mechanics hypotheses and the possibilities of their refinement arise. In this connection the asymptotic analysis of equations of mathematical physics, the equations of elasticity in rod structures (without these hypotheses and simplifying assumptions being imposed) is undertaken in the present book. Moreover, a lot of modern structures are made of composite materials and therefore the material of the rods is not homogeneous. This inhomogeneity of the material can generate some unexpected effects. These effects are analysed in this book. The methods of multi-scale modelling are presented by the homogenization, multi-level asymptotic analysis and the domain decomposition. These methods give an access to a new class of hybrid models combining macroscopic description with "microscopic zooms".

The Theory of Composites

Author : Graeme W. Milton
Publisher : SIAM
ISBN 13 : 1611977487
Total Pages : 761 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis The Theory of Composites by : Graeme W. Milton

Download or read book The Theory of Composites written by Graeme W. Milton and published by SIAM. This book was released on 2022-12-07 with total page 761 pages. Available in PDF, EPUB and Kindle. Book excerpt: Composites have been studied for more than 150 years, and interest in their properties has been growing. This classic volume provides the foundations for understanding a broad range of composite properties, including electrical, magnetic, electromagnetic, elastic and viscoelastic, piezoelectric, thermal, fluid flow through porous materials, thermoelectric, pyroelectric, magnetoelectric, and conduction in the presence of a magnetic field (Hall effect). Exact solutions of the PDEs in model geometries provide one avenue of understanding composites; other avenues include microstructure-independent exact relations satisfied by effective moduli, for which the general theory is reviewed; approximation formulae for effective moduli; and series expansions for the fields and effective moduli that are the basis of numerical methods for computing these fields and moduli. The range of properties that composites can exhibit can be explored either through the model geometries or through microstructure-independent bounds on the properties. These bounds are obtained through variational principles, analytic methods, and Hilbert space approaches. Most interesting is when the properties of the composite are unlike those of the constituent materials, and there has been an explosion of interest in such composites, now known as metamaterials. The Theory of Composites surveys these aspects, among others, and complements the new body of literature that has emerged since the book was written. It remains relevant today by providing historical background, a compendium of numerous results, and through elucidating many of the tools still used today in the analysis of composite properties. This book is intended for applied mathematicians, physicists, and electrical and mechanical engineers. It will also be of interest to graduate students.

Modeling Damage, Fatigue and Failure of Composite Materials

Author : Ramesh Talreja
Publisher : Elsevier
ISBN 13 : 0443184887
Total Pages : 620 pages
Book Rating : 4.4/5 (431 download)

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Book Synopsis Modeling Damage, Fatigue and Failure of Composite Materials by : Ramesh Talreja

Download or read book Modeling Damage, Fatigue and Failure of Composite Materials written by Ramesh Talreja and published by Elsevier. This book was released on 2023-09-23 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modeling Damage, Fatigue and Failure of Composite Materials, Second Edition provides the latest research in the field of composite materials, an area that has attracted a wealth of research, with significant interest in the areas of damage, fatigue, and failure. The book is fully updated, and is a comprehensive source of physics-based models for the analysis of progressive and critical failure phenomena in composite materials. It focuses on materials modeling while also reviewing treatments for analyzing failure in composite structures. Sections review damage development in composite materials such as generic damage and damage accumulation in textile composites and under multiaxial loading. Part Two focuses on the modeling of failure mechanisms in composite materials, with attention given to fiber/matrix cracking and debonding, compression failure, and delamination fracture. Final sections examine the modeling of damage and materials response in composite materials, including micro-level and multi-scale approaches, the failure analysis of composite materials and joints, and the applications of predictive failure models. - Provides a comprehensive source of physics-based models for the analysis of progressive and critical failure phenomena in composite materials - Assesses failure and life prediction in composite materials - Discusses the applications of predictive failure models such as computational approaches to failure analysis - Covers further developments in computational analyses and experimental techniques, along with new applications in aerospace, automotive, and energy (wind turbine blades) fields - Covers delamination and thermoplastic-based composites

Process Modeling in Composites Manufacturing

Author : Suresh G. Advani
Publisher : CRC Press
ISBN 13 : 1466580569
Total Pages : 628 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Process Modeling in Composites Manufacturing by : Suresh G. Advani

Download or read book Process Modeling in Composites Manufacturing written by Suresh G. Advani and published by CRC Press. This book was released on 2010-07-14 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a wealth of literature on modeling and simulation of polymer composite manufacturing processes. However, existing books neglect to provide a systematic explanation of how to formulate and apply science-based models in polymer composite manufacturing processes. Process Modeling in Composites Manufacturing, Second Edition provides tangible m

Multiscale Modeling Approaches for Composites

Author : George Chatzigeorgiou
Publisher : Elsevier
ISBN 13 : 0128233702
Total Pages : 366 pages
Book Rating : 4.1/5 (282 download)

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Book Synopsis Multiscale Modeling Approaches for Composites by : George Chatzigeorgiou

Download or read book Multiscale Modeling Approaches for Composites written by George Chatzigeorgiou and published by Elsevier. This book was released on 2022-01-07 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiscale Modeling Approaches for Composites outlines the fundamentals of common multiscale modeling techniques and provides detailed guidance for putting them into practice. Various homogenization methods are presented in a simple, didactic manner, with an array of numerical examples. The book starts by covering the theoretical underpinnings of tensors and continuum mechanics concepts, then passes to actual micromechanic techniques for composite media and laminate plates. In the last chapters the book covers advanced topics in homogenization, including Green's tensor, Hashin-Shtrikman bounds, and special types of problems. All chapters feature comprehensive analytical and numerical examples (Python and ABAQUS scripts) to better illustrate the theory. - Bridges theory and practice, providing step-by-step instructions for implementing multiscale modeling approaches for composites and the theoretical concepts behind them - Covers boundary conditions, data-exchange between scales, the Hill-Mandel principle, average stress and strain theorems, and more - Discusses how to obtain composite properties using different boundary conditions - Includes access to a companion site, featuring the numerical examples, Python and ABACUS codes discussed in the book

Mathematical Methods and Models in Composites

Author : Vladislav Mantic
Publisher :
ISBN 13 : 9781848167841
Total Pages : 506 pages
Book Rating : 4.1/5 (678 download)

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Book Synopsis Mathematical Methods and Models in Composites by : Vladislav Mantic

Download or read book Mathematical Methods and Models in Composites written by Vladislav Mantic and published by . This book was released on 2013-09-16 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: REVIEW VOLUME

Mathematical Modelling and Biomechanics of the Brain

Author : Corina Drapaca
Publisher : Springer Nature
ISBN 13 : 1493998102
Total Pages : 160 pages
Book Rating : 4.4/5 (939 download)

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Book Synopsis Mathematical Modelling and Biomechanics of the Brain by : Corina Drapaca

Download or read book Mathematical Modelling and Biomechanics of the Brain written by Corina Drapaca and published by Springer Nature. This book was released on 2019-09-06 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph aims to provide a rigorous yet accessible presentation of some fundamental concepts used in modeling brain mechanics and give a glimpse of the insights and advances that have arisen as a result of the nascent interaction of the mathematical and neurosurgical sciences. It begins with some historical perspective and a brief synopsis of the biomedical/biological manifestations of the clinical conditions/diseases considered. Each chapter proceeds with a discussion of the various mathematical models of the problems considered, starting with the simplest models and proceeding to more complex models where necessary. A detailed list of relevant references is provided at the end of each chapter. With the beginning research student in mind, the chapters have been crafted to be as self-contained as possible while addressing different clinical conditions and diseases. The book is intended as a brief introduction to both theoreticians and experimentalists interested in brain mechanics, with directions and guidance for further reading, for those who wish to pursue particular topics in greater depth. It can also be used as a complementary textbook in a graduate level course for neuroscientists and neuroengineers.

Finite Element Analysis of Composite Laminates

Author : O.O. Ochoa
Publisher : Springer Science & Business Media
ISBN 13 : 9780792311256
Total Pages : 234 pages
Book Rating : 4.3/5 (112 download)

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Book Synopsis Finite Element Analysis of Composite Laminates by : O.O. Ochoa

Download or read book Finite Element Analysis of Composite Laminates written by O.O. Ochoa and published by Springer Science & Business Media. This book was released on 1992-09-30 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Composite materials are increasingly used in aerospace, underwater, and automotive structures. To take advantage of the full potential of composite materials, structural analysts and designers must have accurate mathematical models and design methods at their disposal. The objective of this monograph is to present the laminated plate theories and their finite element models to study the deformation, strength and failure of composite structures. Emphasis is placed on engineering aspects, such as the analytical descriptions, effective analysis tools, modeling of physical features, and evaluation of approaches used to formulate and predict the response of composite structures. The first chapter presents an overview of the text. Chapter 2 is devoted to the introduction of the definitions and terminology used in composite materials and structures. Anisotropic constitutive relations and Iaminate plate theories are also reviewed. Finite element models of laminated composite plates are presented in Chapter 3. Numerical evaluation of element coefficient matrices, post-computation of strains and stresses, and sample examples of laminated plates in bending and vibration are discussed. Chapter 4 introduces damage and failure criteria in composite laminates. Finally, Chapter 5 is dedicated to case studies involving various aspects and types of composite structures. Joints, cutouts, woven composites, environmental effects, postbuckling response and failure of composite laminates are discussed by considering specific examples.

Mathematical Modelling in Science and Technology

Author : Xavier J.R. Avula
Publisher : Elsevier
ISBN 13 : 1483190595
Total Pages : 1023 pages
Book Rating : 4.4/5 (831 download)

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Book Synopsis Mathematical Modelling in Science and Technology by : Xavier J.R. Avula

Download or read book Mathematical Modelling in Science and Technology written by Xavier J.R. Avula and published by Elsevier. This book was released on 2014-05-09 with total page 1023 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modelling in Science and Technology: The Fourth International Conference covers the proceedings of the Fourth International Conference by the same title, held at the Swiss Federal Institute of Technology, Zurich, Switzerland on August 15-17, 1983. Mathematical modeling is a powerful tool to solve many complex problems presented by scientific and technological developments. This book is organized into 20 parts encompassing 180 chapters. The first parts present the basic principles, methodology, systems theory, parameter estimation, system identification, and optimization of mathematical modeling. The succeeding parts discuss the features of stochastic and numerical modeling and simulation languages. Considerable parts deal with the application areas of mathematical modeling, such as in chemical engineering, solid and fluid mechanics, water resources, medicine, economics, transportation, and industry. The last parts tackle the application of mathematical modeling in student management and other academic cases. This book will prove useful to researchers in various science and technology fields.

Computational Modeling of Polymer Composites

Author : Samit Roy
Publisher : CRC Press
ISBN 13 : 1466586508
Total Pages : 296 pages
Book Rating : 4.4/5 (665 download)

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Book Synopsis Computational Modeling of Polymer Composites by : Samit Roy

Download or read book Computational Modeling of Polymer Composites written by Samit Roy and published by CRC Press. This book was released on 2013-09-05 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a better understanding of the theories associated with finite element models of elastic and viscoelastic response of polymers and polymer composites. It covers computational modeling and life-prediction of polymers and polymeric composites in aggressive environments. It begins with a review of mathematical preliminaries, equations of anisotropic elasticity, and then presents finite element analysis of viscoelasticity and the diffusion process in polymers and polymeric composites. The book provides a reference for engineers and scientists and can be used as a textbook in graduate courses.

The Structural Integrity of Carbon Fiber Composites

Author : Peter W. R Beaumont
Publisher : Springer
ISBN 13 : 3319461206
Total Pages : 954 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis The Structural Integrity of Carbon Fiber Composites by : Peter W. R Beaumont

Download or read book The Structural Integrity of Carbon Fiber Composites written by Peter W. R Beaumont and published by Springer. This book was released on 2016-11-26 with total page 954 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together a diverse compilation of inter-disciplinary chapters on fundamental aspects of carbon fiber composite materials and multi-functional composite structures: including synthesis, characterization, and evaluation from the nano-structure to structure meters in length. The content and focus of contributions under the umbrella of structural integrity of composite materials embraces topics at the forefront of composite materials science and technology, the disciplines of mechanics, and development of a new predictive design methodology of the safe operation of engineering structures from cradle to grave. Multi-authored papers on multi-scale modelling of problems in material design and predicting the safe performance of engineering structure illustrate the inter-disciplinary nature of the subject. The book examines topics such as Stochastic micro-mechanics theory and application for advanced composite systems Construction of the evaluation process for structural integrity of material and structure Nano- and meso-mechanics modelling of structure evolution during the accumulation of damage Statistical meso-mechanics of composite materials Hierarchical analysis including "age-aware," high-fidelity simulation and virtual mechanical testing of composite structures right up to the point of failure. The volume is ideal for scientists, engineers, and students interested in carbon fiber composite materials, and other composite material systems.

Introduction to Mathematical Modeling and Computer Simulations

Author : Vladimir Mityushev
Publisher : CRC Press
ISBN 13 : 1351998757
Total Pages : 202 pages
Book Rating : 4.3/5 (519 download)

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Book Synopsis Introduction to Mathematical Modeling and Computer Simulations by : Vladimir Mityushev

Download or read book Introduction to Mathematical Modeling and Computer Simulations written by Vladimir Mityushev and published by CRC Press. This book was released on 2018-02-19 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Mathematical Modeling and Computer Simulations is written as a textbook for readers who want to understand the main principles of Modeling and Simulations in settings that are important for the applications, without using the profound mathematical tools required by most advanced texts. It can be particularly useful for applied mathematicians and engineers who are just beginning their careers. The goal of this book is to outline Mathematical Modeling using simple mathematical descriptions, making it accessible for first- and second-year students.

Variational Methods for Structural Optimization

Author : Andrej Cherkaev
Publisher : Springer Science & Business Media
ISBN 13 : 1461211883
Total Pages : 561 pages
Book Rating : 4.4/5 (612 download)

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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.

Mathematical Methods in Linguistics

Author : Barbara B.H. Partee
Publisher : Springer Science & Business Media
ISBN 13 : 9789027722454
Total Pages : 692 pages
Book Rating : 4.7/5 (224 download)

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Book Synopsis Mathematical Methods in Linguistics by : Barbara B.H. Partee

Download or read book Mathematical Methods in Linguistics written by Barbara B.H. Partee and published by Springer Science & Business Media. This book was released on 1990-04-30 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary set theory accustoms the students to mathematical abstraction, includes the standard constructions of relations, functions, and orderings, and leads to a discussion of the various orders of infinity. The material on logic covers not only the standard statement logic and first-order predicate logic but includes an introduction to formal systems, axiomatization, and model theory. The section on algebra is presented with an emphasis on lattices as well as Boolean and Heyting algebras. Background for recent research in natural language semantics includes sections on lambda-abstraction and generalized quantifiers. Chapters on automata theory and formal languages contain a discussion of languages between context-free and context-sensitive and form the background for much current work in syntactic theory and computational linguistics. The many exercises not only reinforce basic skills but offer an entry to linguistic applications of mathematical concepts. For upper-level undergraduate students and graduate students in theoretical linguistics, computer-science students with interests in computational linguistics, logic programming and artificial intelligence, mathematicians and logicians with interests in linguistics and the semantics of natural language.