Asymptotical Mechanics of Composites

by Igor V. Andrianov

Author	: Igor V. Andrianov
Publisher	: Springer
Total Pages	: 333
Release	: 2017-11-09
Genre	: Science
ISBN	: 3319657860

GET BOOK

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.

Approximate Models of Mechanics of Composites

by Igor V. Andrianov

Author	: Igor V. Andrianov
Publisher	: CRC Press
Total Pages	: 441
Release	: 2024-06-20
Genre	: Science
ISBN	: 1000890309

GET BOOK

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.

Asymptotic Methods for Engineers

by Igor V. Andrianov

Author	: Igor V. Andrianov
Publisher	: CRC Press
Total Pages	: 409
Release	: 2024-05-20
Genre	: Mathematics
ISBN	: 104003277X

GET BOOK

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.).

Asymptotical Mechanics of Thin-Walled Structures

by Igor V. Andrianov

Author	: Igor V. Andrianov
Publisher	: Springer Science & Business Media
Total Pages	: 527
Release	: 2013-06-29
Genre	: Science
ISBN	: 354045246X

GET BOOK

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.

Asymptotic Models Of Fields In Dilute And Densely Packed Composites

by A B Movchan

Author	: A B Movchan
Publisher	: World Scientific
Total Pages	: 203
Release	: 2002-11-06
Genre	: Science
ISBN	: 1783261250

GET BOOK

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.

Mechanics of Composite Materials

by G. P. Sendeckyj

Author	: G. P. Sendeckyj
Publisher	: Elsevier
Total Pages	: 520
Release	: 2016-06-03
Genre	: Technology & Engineering
ISBN	: 1483216683

GET BOOK

Composite Materials, Volume 2: Mechanics of Composite Materials deals with the prediction of the deformation behavior and strength of composite materials. The book discusses the basic concepts in micromechanics, definition of effective moduli, and the influence of the number of fibers through-the-thickness within a single composite layer on the effective properties. The text also describes the exact moduli of anisotropie laminates; the elastic behavior of composites; and the viscoelastic behavior and analysis of composite materials. The elastoplastic behavior of composites, and the application of statistical theories for the determination of thermal, electrical, and magnetic properties of heterogeneous materials are also considered. The book further tackles the finite deformations of ideal fiber-reinforced composites; wave propagation and vibrations in directionally reinforced composites; and the phenomenological anisotropie failure criterion. The text also looks into the photoelastic investigation of composites. Civil engineers, mechanical engineers, aerospace engineers, and people involved in the study of non-metallic materials will find the book invaluable.

Nonlinear Mechanics for Composite Heterogeneous Structures

by Georgios A. Drosopoulos

Author	: Georgios A. Drosopoulos
Publisher	: CRC Press
Total Pages	: 286
Release	: 2022-04-26
Genre	: Science
ISBN	: 1000579077

GET BOOK

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.

Asymptotic Multiple Scale Method in Time Domain

by Jan Awrejcewicz

Author	: Jan Awrejcewicz
Publisher	: CRC Press
Total Pages	: 506
Release	: 2022-05-10
Genre	: Mathematics
ISBN	: 1000581276

GET BOOK

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.

Mathematical Methods And Models In Composites

by Vladislav Mantic

Author	: Vladislav Mantic
Publisher	: World Scientific
Total Pages	: 521
Release	: 2013-10-25
Genre	: Technology & Engineering
ISBN	: 178326411X

GET BOOK

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.