Asymptotic Methods In The Theory Of Plates With Mixed Boundary Conditions

Author : Igor Andrianov,Jan Awrejcewicz,Vladyslav Danishevs'kyy,Andrey Ivankov
Publisher : John Wiley & Sons
Page : 281 pages
File Size : 50,9 Mb
Release : 2014-02-06
Category : Science
ISBN : 9781118725146

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Asymptotic Methods in the Theory of Plates with Mixed Boundary Conditions by Igor Andrianov,Jan Awrejcewicz,Vladyslav Danishevs'kyy,Andrey Ivankov Pdf

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.

Author : Lenser Aghalovyan
Publisher : World Scientific
Page : 376 pages
File Size : 40,8 Mb
Release : 2015-03-03
Category : Technology & Engineering
ISBN : 9789814579049

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Asymptotic Theory of Anisotropic Plates and Shells by Lenser Aghalovyan Pdf

A consistent theory for thin anisotropic layered structures is developed starting from asymptotic analysis of 3D equations in linear elasticity. The consideration is not restricted to the traditional boundary conditions along the faces of the structure expressed in terms of stresses, originating a new type of boundary value problems, which is not governed by the classical Kirchhoff-Love assumptions. More general boundary value problems, in particular related to elastic foundations are also studied. The general asymptotic approach is illustrated by a number of particular problems for elastic and thermoelastic beams and plates. For the latter, the validity of derived approximate theories is investigated by comparison with associated exact solution. The author also develops an asymptotic approach to dynamic analysis of layered media composed of thin layers motivated by modeling of engineering structures under seismic excitation. Contents:Plane Problem for a Rectangular Elastic StripThe Winkler-Fuss ModelDirect Asymptotic Integration of 3D Elasticity Equations for Orthotropic PlatesMatching of the Outer Solution and the Boundary Layer for an Orthotropic PlateElastic Plates of General AnisotropyNon-Classical Boundary Value Problems for Anisotropic PlatesTwo-Layer Anisotropic Plates. The Modulus of a Layered FoundationAsymptotic Analysis of the Outer Problem for an Orthotropic ShellBoundary Layer in Orthotropic ShellsNon-Classical Boundary Value Problems for Anisotropic ShellsSpatial Dynamic Problems for Anisotropic Plates Readership: Researchers and specialists in applied mathematics and mechanical engineering, undergraduates and graduate students. Keywords:Asymptotic Theories;Beams;Plates;Shells;Problems of Elasticity Theory;Layered Thermoelastic Thin Structures;Elastic Foundations;Non-Classical Boundary Problems for Anisotropic Beams, Plates and Shells;Singularly Perturbed Systems;Boundary LayerKey Features:The book exposits consistent theory for composite thin walled elastic structures. The obtained results are applied to justification and refinement of ad hoc engineering structural theoriesThe effective solutions of a variety of boundary value problems are obtainedThere is a clear potential for numerous advanced industrial applications

Author : Igor V. Andrianov,Jan Awrejcewicz
Publisher : CRC Press
Page : 409 pages
File Size : 54,5 Mb
Release : 2024-05-20
Category : Mathematics
ISBN : 9781040032770

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Asymptotic Methods for Engineers by Igor V. Andrianov,Jan Awrejcewicz Pdf

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.).

Author : Holm Altenbach,Victor A. Eremeyev,Igor S. Pavlov,Alexey V. Porubov
Publisher : Springer Nature
Page : 473 pages
File Size : 50,7 Mb
Release : 2020-04-22
Category : Technology & Engineering
ISBN : 9783030387082

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Nonlinear Wave Dynamics of Materials and Structures by Holm Altenbach,Victor A. Eremeyev,Igor S. Pavlov,Alexey V. Porubov Pdf

This book marks the 60th birthday of Prof. Vladimir Erofeev – a well-known specialist in the field of wave processes in solids, fluids, and structures. Featuring a collection of papers related to Prof. Erofeev’s contributions in the field, it presents articles on the current problems concerning the theory of nonlinear wave processes in generalized continua and structures. It also discusses a number of applications as well as various discrete and continuous dynamic models of structures and media and problems of nonlinear acoustic diagnostics.

Author : Klaus Hackl,Robert P. Gilbert
Publisher : CRC Press
Page : 148 pages
File Size : 45,7 Mb
Release : 1995-03-06
Category : Mathematics
ISBN : 0582248752

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Asymptotic Theories for Plates and Shells by Klaus Hackl,Robert P. Gilbert Pdf

This Research Note contains papers presented at the SIAM 40th anniversary meeting organised by the editors and held in Los Angeles in 1992. The papers focus on new fundamental results in the theory of plates and shells, with particular emphasis on the treatment of different materials and the nonlinearities involved. Asymptotic methods, such as formal expansions, homogenization, and two-scale convergence, are analytical tools that pervade much of the research. Some of the papers are also concerned with existence results, especially for nonlinear problems, using various functional analytic methods.

Author : Noel Challamel,Julius Kaplunov,Izuru Takewaki
Publisher : John Wiley & Sons
Page : 306 pages
File Size : 49,7 Mb
Release : 2021-06-08
Category : Science
ISBN : 9781119831846

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Modern Trends in Structural and Solid Mechanics 2 by Noel Challamel,Julius Kaplunov,Izuru Takewaki Pdf

This book comprised of three separate volumes presents the recent developments and research discoveries in structural and solid mechanics; it is dedicated to Professor Isaac Elishakoff. This second volume is devoted to the vibrations of solid and structural members. Modern Trends in Structural and Solid Mechanics 2 has broad scope, covering topics such as: exact and approximate vibration solutions of rods, beams, membranes, plates and three-dimensional elasticity problems, Bolotins dynamic edge effect, the principles of plate theories in dynamics, nano- and microbeams, nonlinear dynamics of shear extensible beams, the vibration and aeroelastic stability behavior of cellular beams, the dynamic response of elastoplastic softening oscillators, the complex dynamics of hysteretic oscillators, bridging waves, and the three-dimensional propagation of waves. This book is intended for graduate students and researchers in the field of theoretical and applied mechanics.

Author : Simon Gluzman,Vladimir Mityushev,Wojciech Nawalaniec
Publisher : Academic Press
Page : 328 pages
File Size : 55,5 Mb
Release : 2017-09-20
Category : Mathematics
ISBN : 9780128110478

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Computational Analysis of Structured Media by Simon Gluzman,Vladimir Mityushev,Wojciech Nawalaniec Pdf

Computational Analysis of Structured Media presents a systematical approach to analytical formulae for the effective properties of deterministic and random composites. Schwarz’s method and functional equations yield for use in symbolic-numeric computations relevant to the effective properties. The work is primarily concerned with constructive topics of boundary value problems, complex analysis, and their applications to composites. Symbolic-numerical computations are widely used to deduce new formulae interesting for applied mathematicians and engineers. The main line of presentation is the investigation of two-phase 2D composites with non-overlapping inclusions randomly embedded in matrices. Computational methodology for main classes of problems in structured media Theory of Representative Volume Element Combines exact results, Monte-Carlo simulations and Resummation techniques under one umbrella Contains new analytical formulae obtained in the last ten years and it combines different asymptotic methods with the corresponding computer implementations

Author : Wojciech Pietraszkiewicz,Wojciech Witkowski
Publisher : CRC Press
Page : 574 pages
File Size : 50,7 Mb
Release : 2017-10-30
Category : Technology & Engineering
ISBN : 9781351680486

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Shell Structures: Theory and Applications Volume 4 by Wojciech Pietraszkiewicz,Wojciech Witkowski Pdf

Shells are basic structural elements of modern technology and everyday life. Examples of shell structures in technology include automobile bodies, water and oil tanks, pipelines, silos, wind turbine towers, and nanotubes. Nature is full of living shells such as leaves of trees, blooming flowers, seashells, cell membranes or wings of insects. In the human body arteries, the eye shell, the diaphragm, the skin and the pericardium are all shells as well. Shell Structures: Theory and Applications, Volume 4 contains 132 contributions presented at the 11th Conference on Shell Structures: Theory and Applications (Gdansk, Poland, 11-13 October 2017). The papers reflect a wide spectrum of scientific and engineering problems from theoretical modelling through strength, stability and dynamic behaviour, numerical analyses, biomechanic applications up to engineering design of shell structures. Shell Structures: Theory and Applications, Volume 4 will be of interest to academics, researchers, designers and engineers dealing with modelling and analyses of shell structures. It may also provide supplementary reading to graduate students in Civil, Mechanical, Naval and Aerospace Engineering.

Author : Igor V. Andrianov,Jan Awrejcewicz,Leonid I. Manevitch
Publisher : Springer Science & Business Media
Page : 527 pages
File Size : 48,9 Mb
Release : 2013-06-29
Category : Science
ISBN : 9783540452461

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Asymptotical Mechanics of Thin-Walled Structures by Igor V. Andrianov,Jan Awrejcewicz,Leonid I. Manevitch Pdf

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.

Author : Igor V. Andrianov,Jan Awrejcewicz,Galina A. Starushenko
Publisher : CRC Press
Page : 368 pages
File Size : 55,6 Mb
Release : 2023-06-20
Category : Science
ISBN : 9781000890204

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Approximate Models of Mechanics of Composites by Igor V. Andrianov,Jan Awrejcewicz,Galina A. Starushenko Pdf

1) Provides analytical solutions based on a three-phase model for composites of various structures 2) Identifies computational models to solve problems within all applications of composite materials 3) Constructs higher approximations of the Maxwell formula 4) Proposes efficient analytical algorithms ensuring reliable computational analysis

Author : Holm Altenbach
Publisher : Springer Nature
Page : 531 pages
File Size : 50,9 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 9783031540639

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Selected Problems of Solid Mechanics and Solving Methods by Holm Altenbach Pdf

Author : Dmitrii Korikov,Boris Plamenevskii,Oleg Sarafanov
Publisher : Springer Nature
Page : 404 pages
File Size : 47,8 Mb
Release : 2021-04-01
Category : Mathematics
ISBN : 9783030653729

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Asymptotic Theory of Dynamic Boundary Value Problems in Irregular Domains by Dmitrii Korikov,Boris Plamenevskii,Oleg Sarafanov Pdf

This book considers dynamic boundary value problems in domains with singularities of two types. The first type consists of "edges" of various dimensions on the boundary; in particular, polygons, cones, lenses, polyhedra are domains of this type. Singularities of the second type are "singularly perturbed edges" such as smoothed corners and edges and small holes. A domain with singularities of such type depends on a small parameter, whereas the boundary of the limit domain (as the parameter tends to zero) has usual edges, i.e. singularities of the first type. In the transition from the limit domain to the perturbed one, the boundary near a conical point or an edge becomes smooth, isolated singular points become small cavities, and so on. In an "irregular" domain with such singularities, problems of elastodynamics, electrodynamics and some other dynamic problems are discussed. The purpose is to describe the asymptotics of solutions near singularities of the boundary. The presented results and methods have a wide range of applications in mathematical physics and engineering. The book is addressed to specialists in mathematical physics, partial differential equations, and asymptotic methods.

Author : Igor V. Andrianov,Jan Awrejcewicz,Vladyslav V. Danishevskyy
Publisher : Springer
Page : 329 pages
File Size : 49,5 Mb
Release : 2017-11-09
Category : Science
ISBN : 9783319657868

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Asymptotical Mechanics of Composites by Igor V. Andrianov,Jan Awrejcewicz,Vladyslav V. Danishevskyy Pdf

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.

Author : Holm Altenbach,Victor A. Eremeyev
Publisher : Springer Science & Business Media
Page : 753 pages
File Size : 46,5 Mb
Release : 2011-07-03
Category : Technology & Engineering
ISBN : 9783642218552

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Shell-like Structures by Holm Altenbach,Victor A. Eremeyev Pdf

In this volume scientists and researchers from industry discuss the new trends in simulation and computing shell-like structures. The focus is put on the following problems: new theories (based on two-dimensional field equations but describing non-classical effects), new constitutive equations (for materials like sandwiches, foams, etc. and which can be combined with the two-dimensional shell equations), complex structures (folded, branching and/or self intersecting shell structures, etc.) and shell-like structures on different scales (for example: nano-tubes) or very thin structures (similar to membranes, but having a compression stiffness). In addition, phase transitions in shells and refined shell thermodynamics are discussed. The chapters of this book are the most exciting contributions presented at the EUROMECH 527 Colloquium “Shell-like structures: Non-classical Theories and Applications” held in Wittenberg, Germany.

Author : Jan Awrejcewicz,Igor V. Andrianov,Leonid I. Manevitch
Publisher : Springer Science & Business Media
Page : 321 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642720796

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Asymptotic Approaches in Nonlinear Dynamics by Jan Awrejcewicz,Igor V. Andrianov,Leonid I. Manevitch Pdf

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.