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Asymptotical Mechanics Of Composites
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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 329 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.
Book Synopsis Approximate Models of Mechanics of Composites by : Igor V. Andrianov
Download or read book Approximate Models of Mechanics of Composites written by Igor V. Andrianov and published by CRC Press. This book was released on 2024-06-20 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Asymptotical Mechanics of Thin-Walled Structures by : Igor V. Andrianov
Download or read book Asymptotical Mechanics of Thin-Walled Structures written by Igor V. Andrianov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book a detailed and systematic treatment of asymptotic methods in the theory of plates and shells is presented. The main features of the book are the basic principles of asymptotics and their applications, traditional approaches such as regular and singular perturbations, as well as new approaches such as the composite equations approach. The book introduces the reader to the field of asymptotic simplification of the problems of the theory of plates and shells and will be useful as a handbook of methods of asymptotic integration. Providing a state-of-the-art review of asymptotic applications, this book will be useful as an introduction to the field for novices as well as a reference book for specialists.
Book Synopsis Capacity and Transport in Contrast Composite Structures by : A. A. Kolpakov
Download or read book Capacity and Transport in Contrast Composite Structures written by A. A. Kolpakov and published by CRC Press. This book was released on 2009-11-24 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Is it possible to apply a network model to composites with conical inclusions? How does the energy pass through contrast composites? Devoted to the analysis of transport problems for systems of densely packed, high-contrast composite materials, Capacity and Transport in Contrast Composite Structures: Asymptotic Analysis and Applications answers questions such as these and presents new and modified asymptotic methods for real-world applications in composite materials development. A mathematical discussion of phenomena related to natural sciences and engineering, this book covers historical developments and new progress in mathematical calculations, computer techniques, finite element computer programs, and presentation of results of numerical computations. The "transport problem"—which is described with scalar linear elliptic equations—implies problems of thermoconductivity, diffusion, and electrostatics. To address this "problem," the authors cover asymptotic analysis of partial differential equations, material science, and the analysis of effective properties of electroceramics. Providing numerical calculations of modern composite materials that take into account nonlinear effects, the book also: Presents results of numerical analysis, demonstrating specific properties of distributions of local fields in high-contrast composite structures and systems of closely placed bodies Assesses whether total flux, energy, and capacity exhaust characteristics of the original continuum model Illustrates the expansion of the method for systems of bodies to highly filled contrast composites This text addresses the problem of loss of high-contrast composites, as well as transport and elastic properties of thin layers that cover or join solid bodies. The material presented will be particularly useful for applied mathematicians interested in new methods, and engineers dealing with prospective materials and design methods.
Book Synopsis Asymptotic Models of Fields in Dilute and Densely Packed Composites by : A B Movchan
Download or read book Asymptotic Models of Fields in Dilute and Densely Packed Composites written by A B Movchan and published by World Scientific. This book was released on 2002-11-06 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a systematic study of asymptotic models of continuum mechanics for composite structures, which are either dilute (for example, two-phase composite structures with small inclusions) or densely packed (in this case inclusions may be close to touching). It is based on the results of recent research and includes a comprehensive analysis of dipole and multipole fields associated with defects in solids. The text covers static problems of elasticity in dilute composites as well as spectral problems. Applications of the mathematical models included in the book are in damage mechanics and in problems of design of composite structures that can be used as filters or polarisers of elastic waves. Dipole tensors are defined in Chapter 1 both for scalar boundary value problems for the Laplacian and for vector problems of elasticity. In Chapter 2 the dipole tensors are used in spectral problems involving domains with small defects. Chapter 3 introduces a multipole method for static problems (both electrostatics and elasticity) in composite structures containing doubly periodic arrays of circular inclusions. Chapter 4 presents a multipole method for eigenvalue problems of electromagnetism and elasticity. Contents:Long and Close Range Interaction within Elastic StructuresDipole Tensors in Spectral Problems of ElasticityMultipole Methods and Homogenisation in Two-Dimensions Readership: Graduate students and researchers in applied mathematics and mechanics who are interested in asymptotic theory of partial differential equations, spectral theory, and mathematical models of composite structures. Reviews:“The material is interesting and based on results of recent research.”Mathematical Reviews
Book Synopsis Asymptotic Methods for Engineers by : Igor V. Andrianov
Download or read book Asymptotic Methods for Engineers written by Igor V. Andrianov and published by CRC Press. This book was released on 2024-05-20 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic Methods for Engineers is based on the authors’ many years of practical experience in the application of asymptotic methods to solve engineering problems. This book is devoted to modern asymptotic methods (AM), which is widely used in engineering, applied sciences, physics, and applied mathematics. Avoiding complex formal calculations and justifications, the book’s main goal is to describe the main ideas and algorithms. Moreover, not only is there a presentation of the main AM, but there is also a focus on demonstrating their unity and inseparable connection with the methods of summation and asymptotic interpolation. The book will be useful for students and researchers from applied mathematics and physics and of interest to doctoral and graduate students, university and industry professors from various branches of engineering (mechanical, civil, electro-mechanical, etc.).
Book Synopsis Stressed Composite Structures by : A.G. Kolpakov
Download or read book Stressed Composite Structures written by A.G. Kolpakov and published by Springer Science & Business Media. This book was released on 2012-11-08 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: The mechanics of structures with initial stresses is a traditional part of structural mechanics. It is closely related to the important problem of stability of structures. The basic concepts of elastic stability of structures go back to works by Euler (1759) and Bryan (1889). Later, it was found that the problem of deformation of solids with initial stresses is related to variational principles and nonlinear problems in elasticity; see Trefftz (1933), Marguerre (1938), Prager (1947), Hill (1958), Washuzu (1982). Historical detail up to the 1940s can be found in the book by Timoshenko (1953). Observing the basic concepts of the traditional mechanics of stressed structures, we agree that these are suitable for uniform structural elements (plates, beams, and so on) made of homogeneous materials, but not for complex structures (such as a network plate or a lattice mast) or structures made of composite materials (such as fiber reinforced or textile materials). Many concepts of the classical theory, such as a cross section or neutral plane (axis), correspond to no mechanical objects if we consider an inhomogeneous structure. As a result, we come to the conclusion that it would be useful to have a theory of thin inhomogeneous structures developed on the basis of 3-D elasticity theory with no simplifying assumptions (with no a priori hypothesis).
Book Synopsis Mechanics and Physics of Structured Media by : Igor Andrianov
Download or read book Mechanics and Physics of Structured Media written by Igor Andrianov and published by Academic Press. This book was released on 2022-01-20 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Nonlinear Mechanics for Composite Heterogeneous Structures by : Georgios A. Drosopoulos
Download or read book Nonlinear Mechanics for Composite Heterogeneous Structures written by Georgios A. Drosopoulos and published by CRC Press. This book was released on 2022-04-26 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Mechanics for Composite Heterogeneous Structures applies both classical and multi-scale finite element analysis to the non-linear, failure response of composite structures. These traditional and modern computational approaches are holistically presented, providing insight into a range of non-linear structural analysis problems. The classical methods include geometric and material non-linearity, plasticity, damage and contact mechanics. The cutting-edge formulations include cohesive zone models, the Extended Finite Element Method (XFEM), multi-scale computational homogenization, localization of damage, neural networks and data-driven techniques. This presentation is simple but efficient, enabling the reader to understand, select and apply appropriate methods through programming code or commercial finite element software. The book is suitable for undergraduate studies as a final year textbook and for MSc and PhD studies in structural, mechanical, aerospace engineering and material science, among others. Professionals in these fields will also be strongly benefited. An accompanying website provides MATLAB codes for two-dimensional finite element problems with contact, multi-scale (FE2) and non-linear XFEM analysis, data-driven and machine learning simulations.
Book Synopsis Homogenisation: Averaging Processes in Periodic Media by : N.S. Bakhvalov
Download or read book Homogenisation: Averaging Processes in Periodic Media written by N.S. Bakhvalov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi, .... si j'avait su comment en revenir, One service mathematics has rendered the je n'y semis point all,,: human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent: therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non !inearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Book Synopsis Mechanics Of Composite Structures by : V.V. Vasiliev
Download or read book Mechanics Of Composite Structures written by V.V. Vasiliev and published by CRC Press. This book was released on 2017-10-05 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book compiles techniques used to analyze composite structural elements ranging from beams through plates to stiffened shells. The content is suitable for graduate-level students with a basic background in mechanics of composite materials. Moreover, this book will be placed in an active spot on the bookshelves of composite structures designers as well as researchers.
Book Synopsis Mechanics of Composite Materials, 1983 by : American Society of Mechanical Engineers. Winter Meeting
Download or read book Mechanics of Composite Materials, 1983 written by American Society of Mechanical Engineers. Winter Meeting and published by . This book was released on 1983 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Mechanics of Elastic Composites by : Nicolaie Dan Cristescu
Download or read book Mechanics of Elastic Composites written by Nicolaie Dan Cristescu and published by CRC Press. This book was released on 2003-09-15 with total page 699 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive, reader-friendly treatment of the theory behind modern elastic composite materials. The treatment includes recently developed results and methods drawn from research papers published in Eastern Europe that until now were unavailable in many western countries. Among the book's many notable features is the inclusion of more than 400 problems, many of which are solved at the end of the book. Mechanics of Elastic Composites is an outstanding textbook for graduate-level course work and a valuable reference for engineers and researchers. Developed over many years by leading experts in the field, this book will remain an important contribution to the literature for years to come.
Book Synopsis Asymptotic Multiple Scale Method in Time Domain by : Jan Awrejcewicz
Download or read book Asymptotic Multiple Scale Method in Time Domain written by Jan Awrejcewicz and published by CRC Press. This book was released on 2022-05-10 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers up novel research which uses analytical approaches to explore nonlinear features exhibited by various dynamic processes. Relevant to disciplines across engineering and physics, the asymptotic method combined with the multiple scale method is shown to be an efficient and intuitive way to approach mechanics. Beginning with new material on the development of cutting-edge asymptotic methods and multiple scale methods, the book introduces this method in time domain and provides examples of vibrations of systems. Clearly written throughout, it uses innovative graphics to exemplify complex concepts such as nonlinear stationary and nonstationary processes, various resonances and jump pull-in phenomena. It also demonstrates the simplification of problems through using mathematical modelling, by employing the use of limiting phase trajectories to quantify nonlinear phenomena. Particularly relevant to structural mechanics, in rods, cables, beams, plates and shells, as well as mechanical objects commonly found in everyday devices such as mobile phones and cameras, the book shows how each system is modelled, and how it behaves under various conditions. It will be of interest to engineers and professionals in mechanical engineering and structural engineering, alongside those interested in vibrations and dynamics. It will also be useful to those studying engineering maths and physics.
Book Synopsis Mechanical Response of Composites by : Pedro P. Camanho
Download or read book Mechanical Response of Composites written by Pedro P. Camanho and published by Springer Science & Business Media. This book was released on 2008-06-20 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Themethodologyfordesigninghigh-performancecompositestructuresisstill evo- ing. The complexity of the response of composite materials and the dif?culties in predicting the composite material properties from the basic properties of the c- stituents result in the need for a well-planned and exhaustive test program. The recommended practice to mitigate the technological risks associated with advanced composite materials is to substantiate the performance and durability of the design in a sequence of steps known as the Building Block Approach. The Building Block Approach ensures that cost and performance objectives are met by testing greater numbers of smaller, less expensive specimens. In this way, technology risks are assessed early in the program. In addition, the knowledge acquired at a given level of structural complexity is built up before progressing to a level of increased complexity. Achieving substantiation of structural performance by testing alone can be p- hibitively expensive because of the number of specimens and components required to characterize all material systems, loading scenarios and boundary conditions. Building Block Approachprogramscan achieve signi?cant cost reductionsby se- ing a synergy between testing and analysis. The more the development relies on analysis, the less expensive it becomes. The use of advanced computational models for the prediction of the mechanical response of composite structures can replace some of the mechanical tests and can signi?cantly reduce the cost of designing with composites while providing to the engineers the information necessary to achieve an optimized design.
Book Synopsis Mechanics of Periodically Heterogeneous Structures by : L.I. Manevitch
Download or read book Mechanics of Periodically Heterogeneous Structures written by L.I. Manevitch and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Rigorous presentation of Mathematical Homogenization Theory is the subject of numerous publications. This book, however, is intended to fill the gap in the analytical and numerical performance of the corresponding asymptotic analysis of the static and dynamic behaviors of heterogenous systems. Numerous concrete applications to composite media, heterogeneous plates and shells are considered. A lot of details, numerical results for cell problem solutions, calculations of high-order terms of asymptotic expansions, boundary layer analysis etc., are included.
Book Synopsis Finite Element Analysis of Composite Materials by : Ever J. Barbero
Download or read book Finite Element Analysis of Composite Materials written by Ever J. Barbero and published by CRC Press. This book was released on 2007-08-03 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designing structures using composite materials poses unique challenges due especially to the need for concurrent design of both material and structure. Students are faced with two options: textbooks that teach the theory of advanced mechanics of composites, but lack computational examples of advanced analysis; and books on finite element analysis that may or may not demonstrate very limited applications to composites. But now there is third option that makes the other two obsolete: Ever J. Barbero's Finite Element Analysis of Composite Materials. By layering detailed theoretical and conceptual discussions with fully developed examples, this text supplies the missing link between theory and implementation. In-depth discussions cover all of the major aspects of advanced analysis, including three-dimensional effects, viscoelasticity, edge effects, elastic instability, damage, and delamination. More than 50 complete examples using mainly ANSYSTM, but also including some use of MATLAB®, demonstrate how to use the concepts to formulate and execute finite element analyses and how to interpret the results in engineering terms. Additionally, the source code for each example is available for download online. Cementing applied computational and analytical experience to a firm foundation of basic concepts and theory, Finite Element Analysis of Composite Materials offers a modern, practical, and versatile classroom tool for today's engineering classroom.
