Igor V. Andrianov's Books

Asymptotical Mechanics of Thin-Walled Structures

By: Igor V. Andrianov,Jan Awrejcewicz,Leonid I. Manevitch

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Asymptotical Mechanics of Thin-Walled Structures

By: Igor V. Andrianov,Jan Awrejcewicz,Leonid I. Manevitch

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.

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Page Count

527

Publisher

Springer Science & Business Media

Published Date

ISBN 10

354045246X

ISBN 13

9783540452461

Linear and Nonlinear Waves in Microstructured Solids

Homogenization and Asymptotic Approaches

By: Igor V. Andrianov,Jan Awrejcewicz,Vladyslav Danishevskyy

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Linear and Nonlinear Waves in Microstructured Solids

Homogenization and Asymptotic Approaches

By: Igor V. Andrianov,Jan Awrejcewicz,Vladyslav Danishevskyy

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.

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Page Count

251

Publisher

CRC Press

Published Date

ISBN 10

1000372197

ISBN 13

9781000372199

Asymptotical Mechanics of Composites

Modelling Composites without FEM

By: Igor V. Andrianov,Jan Awrejcewicz,Vladyslav V. Danishevskyy

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Asymptotical Mechanics of Composites

Modelling Composites without FEM

By: Igor V. Andrianov,Jan Awrejcewicz,Vladyslav V. Danishevskyy

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.

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Page Count

333

Publisher

Springer

Published Date

ISBN 10

3319657860

ISBN 13

9783319657868

Asymptotic Approaches in Nonlinear Dynamics

New Trends and Applications

By: Jan Awrejcewicz,Igor V. Andrianov,Leonid I. Manevitch

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Asymptotic Approaches in Nonlinear Dynamics

New Trends and Applications

By: Jan Awrejcewicz,Igor V. Andrianov,Leonid I. Manevitch

This book covers developments in the theory of oscillations from diverse viewpoints, reflecting the fields multidisciplinary nature. It introduces the state-of-the-art in the theory and various applications of nonlinear dynamics. It also offers the first treatment of the asymptotic and homogenization methods in the theory of oscillations in combination with Pad approximations. With its wealth of interesting examples, this book will prove useful as an introduction to the field for novices and as a reference for specialists.

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Page Count

321

Publisher

Springer Science & Business Media

Published Date

ISBN 10

364272079X

ISBN 13

9783642720796

Approximate Models of Mechanics of Composites

An Asymptotic Approach

By: Igor V. Andrianov,Jan Awrejcewicz,Galina A. Starushenko

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Approximate Models of Mechanics of Composites

An Asymptotic Approach

By: Igor V. Andrianov,Jan Awrejcewicz,Galina A. Starushenko

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.

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Page Count

441

Publisher

CRC Press

Published Date

ISBN 10

1000890309

ISBN 13

9781000890303

Asymptotology

Ideas, Methods, and Applications

By: Igor V. Andrianov,Leonid I. Manevitch

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Asymptotology

Ideas, Methods, and Applications

By: Igor V. Andrianov,Leonid I. Manevitch

Asymptotic methods belong to the, perhaps, most romantic area of modern mathematics. They are widely known and have been used in me chanics, physics and other exact sciences for many, many decades. But more than this, asymptotic ideas are found in all branches of human knowledge, indeed in all areas of life. In this broader context they have not and perhaps cannot be fully formalized. However, they are mar velous, they leave room for fantasy, guesses and intuition; they bring us very near to the border of the realm of art. Many books have been written and published about asymptotic meth ods. Most of them presume a mathematically sophisticated reader. The authors here attempt to describe asymptotic methods on a more accessi ble level, hoping to address a wider range of readers. They have avoided the extreme of banishing formulae entirely, as done in some popular science books that attempt to describe mathematical methods with no mathematics. This is impossible (and not wise). Rather, the authors have tried to keep the mathematics at a moderate level. At the same time, using simple examples, they think they have been able to illustrate all the key ideas of asymptotic methods and approaches, to depict in de tail the results of their application to various branches of knowledg- from astronomy, mechanics, and physics to biology, psychology and art. The book is supplemented by several appendices, one of which con tains the profound ideas of R. G.

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Page Count

262

Publisher

Springer Science & Business Media

Published Date

ISBN 10

144199162X

ISBN 13

9781441991621

Asymptotic Methods for Engineers

By: Igor V. Andrianov,Jan Awrejcewicz

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Asymptotic Methods for Engineers

By: Igor V. Andrianov,Jan Awrejcewicz

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.).

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Page Count

265

Publisher

CRC Press

Published Date

ISBN 10

1040032710

ISBN 13

9781040032718

Book's by Igor V. Andrianov

Asymptotical Mechanics of Thin-Walled Structures

Asymptotical Mechanics of Thin-Walled Structures

Linear and Nonlinear Waves in Microstructured Solids

Linear and Nonlinear Waves in Microstructured Solids

Asymptotical Mechanics of Composites

Asymptotical Mechanics of Composites

Asymptotic Approaches in Nonlinear Dynamics

Asymptotic Approaches in Nonlinear Dynamics

Approximate Models of Mechanics of Composites

Approximate Models of Mechanics of Composites

Asymptotology

Asymptotology

Asymptotic Methods for Engineers

Asymptotic Methods for Engineers

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