Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions comprehensively covers the theoretical background of asymptotic approaches and their use in solving mechanical engineering-oriented problems of structural members, primarily plates (statics and dynamics) with mixed boundary conditions. The first part of this book introduces the theory and application of asymptotic methods and includes a series of approaches that have been omitted or not rigorously treated in the existing literature. These lesser known approaches include the method of summation and construction of the asymptotically equivalent functions, methods of small and large delta, and the homotopy perturbations method. The second part of the book contains original results devoted to the solution of the mixed problems of the theory of plates, including statics, dynamics and stability of the studied objects. In addition, the applicability of the approaches presented to other related linear or nonlinear problems is addressed. Key features: • Includes analytical solving of mixed boundary value problems • Introduces modern asymptotic and summation procedures • Presents asymptotic approaches for nonlinear dynamics of rods, beams and plates • Covers statics, dynamics and stability of plates with mixed boundary conditions • Explains links between the Adomian and homotopy perturbation approaches Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions is a comprehensive reference for researchers and practitioners working in the field of Mechanics of Solids and Mechanical Engineering, and is also a valuable resource for graduate and postgraduate students from Civil and Mechanical Engineering.
The Korean War (1950-1953) was the first - and only - full-scale air war in the jet age. It was in the skies of North Korea where Soviet and American pilots came together in fierce aerial clashes. The best pilots of the opposing systems, the most powerful air forces, and the most up-to-date aircraft in the world in this period of history came together in pitched air battles. The analysis of the air war showed that the powerful United States Air Force and its allies were unable to achieve complete superiority in the air and were unable to fulfill all the tasks they'd been given. Soviet pilots and Soviet jet fighters, which were in no way inferior to their opponents and in certain respects were even superior to them, was the reason for this. The combat experience and new tactical aerial combat tactics, which were tested for the first time in the skies of Korea, have been eagerly studied and applied by modern air forces around the world today. This book fully discusses the Soviet participation in the Korean War and presents a view of this war from the opposite side, which is still not well known in the West from the multitude of publications by Western historians. The reason for this, of course, is the fact that Soviet records pertaining to the Korean War were for a long time highly classified, since Soviet air units were fighting in the skies of North Korea "incognito", so to speak or even more so to write about this was strictly forbidden in the Soviet Union right up to its ultimate collapse. The given work is in essence the first major work in the post-Soviet era. First published in a small edition in Russian in 1998, it was republished in Russia in 2007. For the first time, the Western reader can become acquainted with the most detailed and informative work existing on the course of the air war from the Soviet side, now in English language. The work rests primarily on the recollections of veterans of this war on the so-called 'Red' side - Soviet fighter pilots, who took direct part in this war on the side of North Korea. Their stories have been supplemented with an enormous amount of archival documents, as well as the work of Western historians. The author presents a literal day-by-day chronicle of the aerial combats and combat work of Soviet fighter regiments in the period between 1950 and 1953, and dedicates this work to all the men on both sides who fought and died in the Korean air war.
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.
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.
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.
This monograph discusses cosmological inflation and provides exact and slow roll solutions. It also reviews new and advanced approaches of exact solutions construction with canonical scalar fields, including application of generating functions methods, the superpotential and many others. This book presents the reduction of the Friedmann equation to the Abel equation, which is a very useful tool in cosmology. It offers new solutions and discusses its properties.Additionally, it touches upon the role of phantom scalar field cosmology and analyzes phantonical models. It describes brane cosmology with scalar fields, providing exact solutions construction using the superpotential method as well as Darboux transformations.This book provides detailed calculations throughout.
The common view of indigenous Arctic cultures, even among scholarly observers, has long been one of communities continually in ecological harmony with their natural environment. In Arctic Adaptations, Igor Krupnik dismisses the textbook notion of traditional societies as static. Using information from years of field research, interviews with native Siberians, and archaeological site visits, Krupnik demonstrates that these societies are characterized not by stability but by dynamism and significant evolutionary breaks. Their apparent state of ecological harmony is, in fact, a conscious survival strategy resulting from "a prolonged and therefore successful process of human adaptation in one of the most extreme inhabited environments in the world." As their physical and cultural environment has changed--fluctuating reindeer and caribou herds, unpredictable weather patterns, introduction of firearms and better seacraft--Arctic communities have adapted by developing distinctive subsistence practices, social structures, and ethics regarding utilization of natural resources. Krupnik's pioneering work represents a dynamic marriage of ethnography and ecology, and makes accessible to Western scholars crucial findings and archival data previously unavailable because of political and language barriers.
This book discusses the theoretical foundations of the structural modeling method applied to metamaterials. This method takes into account the parameters of the crystal lattice, the size of the medium particles, as well as their shape and constants of force interactions between them. It provides mathematical models of metamaterials that offer insights into the qualitative influence of the local structure on the effective elastic moduli of the considered medium and into performing theoretical estimations of these quantities. This book is useful for researchers working in the fields of solid mechanics, physical acoustics, and condensed matter physics, as well as for graduate and postgraduate students studying mathematical modeling methods.
Advanced Methods of Structural Analysis aims to help its readers navigate through the vast field of structural analysis. The book aims to help its readers master the numerous methods used in structural analysis by focusing on the principal concepts, as well as the advantages and disadvantages of each method. The end result is a guide to mastering the many intricacies of the plethora of methods of structural analysis. The book differentiates itself from other volumes in the field by focusing on the following: • Extended analysis of beams, trusses, frames, arches and cables • Extensive application of influence lines for analysis of structures • Simple and effective procedures for computation of deflections • Introduction to plastic analysis, stability, and free vibration analysis Authors Igor A. Karnovsky and Olga Lebed have crafted a must-read book for civil and structural engineers, as well as researches and students with an interest in perfecting structural analysis. Advanced Methods of Structural Analysis also offers numerous example problems, accompanied by detailed solutions and discussion of the results.
In this book, the authors derive the theory of elastic depolarizing collisions and describe their importance in some nonlinear electromagnetic phenomena in gaseous media. The formation of photon echo and a description of its various types in gaseous media are then presented. The authors show that the characteristics of the corresponding signals depend essentially on elastic depolarizing collisions. They also consider the advantages of a new kind of photon echo spectroscopy: polarization photon echo-spectroscopy. A high-level, specialized treatment, Depolarizing Collisions in Nonlinear Electrodynamics will appeal to researchers and advanced graduates in nonlinear optics and quantum electronics.
The ‘‘Aral Sea Encyclopedia’’ is the first one in the new series of encyclopedias about the seas of the former Soviet Union. Preparing it we faced certain difficulties. The thing is that this encyclopedia is a monument to the sea that is disappearing during our lifetime. The world community considers the situation with the Aral Sea and all changes that occurred in its whereabouts in the recent decades as one of the most serious, if not disastrous anthropogenic environmental crises of the 20th century. Before 1960, this was a water-abundant sea-lake that was fourth among world lakes after the Caspian Sea (USSR, Iran), the Great Lakes (USA, Canada) and Victoria Lake (Africa). This was a real ‘‘pearl’’ among the sands of the largest deserts, the Karakums and the Kyzylkums. Navigation between the sea ports Muinak and Aralsk and fisheries famous for the Aral breams, barbells, sturgeons, shemaya, and others were developed here. One could find beautiful recreational zones and beaches here. The deltas of the Amudarya, the major river of Central Asia, and the Syrdarya bringing their waters into the Aral Sea were famous for their biodiversity, fishery, muskrat rearing, reed prod- tion. The local population found occupations related to the water infrastructure.
This exhaustive work in three volumes with featuring cross-reference system provides a thorough overview of ultra-high temperature materials – from elements and chemical compounds to alloys and composites. Topics included are physical (crystallographic, thermodynamic, thermo-physical, electrical, optical, physico-mechanical, nuclear) and chemical (solid-state diffusion, interaction with chemical elements and compounds, interaction with gases, vapours and aqueous solutions) properties of the individual physico-chemical phases and multi-phase materials with melting (or sublimation) points over or about 2500 °C. The first volume focuses on carbon (graphite/graphene) and refractory metals (W, Re, Os, Ta, Mo, Nb, Ir). The second and third volumes are dedicated solely to refractory (ceramic) compounds (oxides, nitrides, carbides, borides, silicides) and to the complex materials – refractory alloys, carbon and ceramic composites, respectively. It will be of interest to researchers, engineers, postgraduate, graduate and undergraduate students in various disciplines alike. The reader is provided with the full qualitative and quantitative assessment for the materials, which could be applied in various engineering devices and environmental conditions at ultra-high temperatures, on the basis of the latest updates in the field of physics, chemistry, materials science, nanotechnology and engineering.
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.).
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 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.).
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.
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.
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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