Mathematical Models For Elastic Structures
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Mathematical Models For Elastic Structures
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Author : Piero Villaggio
language : en
Publisher: Cambridge University Press
Release Date : 1997-10-28
Mathematical Models For Elastic Structures written by Piero Villaggio and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-10-28 with Technology & Engineering categories.
Elastic structures, conceived as slender bodies able to transmit loads, have been studied by scientists and engineers for centuries. By the seventeenth century several useful theories of elastic structures had emerged, with applications to civil and mechanical engineering problems. In recent years improved mathematical tools have extended applications into new areas such as geomechanics and biomechanics. This book, first published in 1998, offers a critically filtered collection of the most significant theories dealing with elastic slender bodies. It includes mathematical models involving elastic structures, which are used to solve practical problems with particular emphasis on nonlinear problems. This collection of interesting and important problems in elastic structures will appeal to a broad range of scientists, engineers and graduate students working in the area of structural mechanics.
Mathematical Models For Elastic Structures
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Author :
language : en
Publisher: Cambridge University Press
Release Date :
Mathematical Models For Elastic Structures written by and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Phenomenological And Mathematical Modelling Of Structural Instabilities
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Author : Marcello Pignataro
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-07-15
Phenomenological And Mathematical Modelling Of Structural Instabilities written by Marcello Pignataro and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-15 with Computers categories.
The study of structural instability plays a role of primary importance in the field of applied mechanics. Despite the remarkable progresses made in the recent past years, the structural instability remains one of the most challenging topics in applied - chanics. Many problems have bee:: solved in the last decades but still many others remain to be solved satisfactorily. The increasing number of papers published in jo- nals and conferences organized by ECCS, SSRC, IUTAM, and EUROMECH strongly indicates the interest of scientists and engineers in the subject. A careful examination of these publications shows that they tend to fall into one of the two categories. The first is that of practical design direction in which methods for analyzing specific stability problems related to some specific structural typologies are developed. The research works are restricted to determining the critical load, considering that it is sufficient to know the limits of stability range. These studies are invaluable since their aim is to provide solutions to practical problems, to supply the designer with data useful for design and prepare norms, specifications and codes. The second direction is that of theoretical studies, aiming at a mathematical modeling of the instability problems, for a better understanding of the phenomena. In these studies, special emphasis is placed on the behavior of structures after the loss of stability in the post-critical range. This approach is less familiar to designers as its results have not yet become part of current structural design practice.
An Introduction To The Mathematical Theory Of Vibrations Of Elastic Plates
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Author : Raymond David Mindlin
language : en
Publisher: World Scientific
Release Date : 2006
An Introduction To The Mathematical Theory Of Vibrations Of Elastic Plates written by Raymond David Mindlin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Technology & Engineering categories.
This book by the late R D Mindlin is destined to become a classic introduction to the mathematical aspects of two-dimensional theories of elastic plates. It systematically derives the two-dimensional theories of anisotropic elastic plates from the variational formulation of the three-dimensional theory of elasticity by power series expansions. The uniqueness of two-dimensional problems is also examined from the variational viewpoint. The accuracy of the two-dimensional equations is judged by comparing the dispersion relations of the waves that the two-dimensional theories can describe with prediction from the three-dimensional theory. Discussing mainly high-frequency dynamic problems, it is also useful in traditional applications in structural engineering as well as provides the theoretical foundation for acoustic wave devices.
Acoustic Interactions With Submerged Elastic Structures
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Author : A. Guran
language : en
Publisher: World Scientific
Release Date : 2001
Acoustic Interactions With Submerged Elastic Structures written by A. Guran and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Technology & Engineering categories.
The interaction of acoustic fields with submerged elastic structures, both by propagation and scattering, is being investigated at various institutions and laboratories world-wide with ever-increasing sophistication of experiments and analysis. This book offers a collection of contributions from these research centers that represent the present state-of-the-art in the study of acoustic elastic interaction, being on the cutting edge of these investigations. This includes the description of acoustic scattering from submerged elastic objects and shells by the Resonance Scattering Theory of Flax, Dragonette and berall, and the interaction of these phenomena in terms of interface waves. It also includes the use of this theory for the purpose of inverse scattering, i.e. the determination of the scattered objects properties from the received acoustic backscattered signals. The problem of acoustically excited waves in inhomogeneous and anisotropic materials, and of inhomogeneous propagating waves is considered. Vibrations and resonances of elastic shells, including shells with various kinds of internal attachments, are analyzed. Acoustic scattering experiments are described in the time domain, and on the basis of the WignerOCoVille distribution. Acoustic propagation in the water column over elastic boundaries is studied experimentally both in laboratory tanks, and in the field, and is analyzed theoretically. Ultrasonic nondestructive testing, including such aspects like probe modelling, scattering by various types of cracks, receiving probes and calibration by a side-drilled hole is also studied in details. A comprehensive picture of these complex phenomena and other aspects is presented in the book by researchers that are experts in each of these domains, giving up-to-date accounts of the field in all these aspects. Contents: Discrete Spectral Analysis for Solitary Waves (J Engelbrecht et al.); Propagation and Interaction of Waves in Nonlinear-Elastic Solids with Microstructures (V I Erofeyev); Matched Field Processing: A Powerful Tool for the Study of Oceans and Scatterers (A Tolstoy); Progress in Underwater Acoustic Modeling (P C Etter); Reflectivity Response of a Submerged Layer with Density, Sound Velocity and Absorbtion Gradients (R Carb-Fit(r)); Mathematical Aspects of Wave Phenomena in a Wave Guide with Elastic Walls and Operator Polynomials (B P Belinskiy & J P Dauer); On Some General Mathematical Properties of the System Elastic Plate OCo Acoustic Medium (B P Belinskiy); Acoustic Scattering from Finite Length Cylinders Encapped by Two Hemispheres (D Decultot et al.); Acoustic Scattering from a Circular Cylindrical Shell Immersed in Water. Generation and Reradiation of Guided Waves (F L(r)on & G Maze); The Finite Element/Boundary Element Approach to the Radiation and Scattering of Submerged Shells Including Internal Structure or Equipment (R Miller); Resonance Extraction, Phase Matching Method and the Surface Paths for Finite Elastic Cylinders (X-L Bao); Nonlinear Waves in Thermoelastic Solids Undergoing Phase Transitions (J K Knowles). Readership: Nonlinear scientists."
Nonlinear Theory Of Elasticity
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Author : Larry Alan Taber
language : en
Publisher: World Scientific
Release Date : 2004
Nonlinear Theory Of Elasticity written by Larry Alan Taber and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.
Soft biological tissues often undergo large (nearly) elastic deformations that can be analyzed using the nonlinear theory of elasticity. Because of the varied approaches to nonlinear elasticity in the literature, some aspects of the subject may be difficult to appreciate. This book attempts to clarify and unify those treatments, illustrating the advantages and disadvantages of each through various examples in the mechanics of soft tissues. Applications include muscle, arteries, the heart, and embryonic tissues.
Geometric Methods In The Elastic Theory Of Membranes In Liquid Crystal Phases
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Author : Zhong-Can Ou-Yang
language : en
Publisher: World Scientific
Release Date : 1999
Geometric Methods In The Elastic Theory Of Membranes In Liquid Crystal Phases written by Zhong-Can Ou-Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Science categories.
This book contains a comprehensive description of the mechanical equilibrium and deformation of membranes as a surface problem in differential geometry. Following the pioneering work by W Helfrich, the fluid membrane is seen as a nematic or smectic ? A liquid crystal film and its elastic energy form is deduced exactly from the curvature elastic theory of the liquid crystals. With surface variation the minimization of the energy at fixed osmotical pressure and surface tension gives a completely new surface equation in geometry that involves potential interest in mathematics. The investigations of the rigorous solution of the equation that have been carried out in recent years by the authors and their co-workers are presented here, among which the torus and the discocyte (the normal shape of the human red blood cell) may attract attention in cell biology. Within the framework of our mathematical model by analogy with cholesteric liquid crystals, an extensive investigation is made of the formation of the helical structures in a tilted chiral lipid bilayer, which has now become a hot topic in the fields of soft matter and biomembranes.
Modeling Analysis And Control Of Dynamic Elastic Multi Link Structures
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Author : J.E. Lagnese
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Modeling Analysis And Control Of Dynamic Elastic Multi Link Structures written by J.E. Lagnese and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The purpose of this monograph is threefold. First, mathematical models of the transient behavior of some or all of the state variables describing the motion of multiple-link flexible structures will be developed. The structures which we have in mind consist of finitely many interconnected flexible ele ments such as strings, beams, plates and shells or combinations thereof and are representative of trusses, frames, robot arms, solar panels, antennae, deformable mirrors, etc. , currently in use. For example, a typical subsys tem found in almost all aircraft and space vehicles consists of beam, plate and/or shell elements attached to each other in a rigid or flexible manner. Due to limitations on their weights, the elements themselves must be highly flexible, and due to limitations on their initial configuration (i. e. , before de ployment), those aggregates often have to contain several links so that the substructure may be unfolded or telescoped once it is deployed. The point of view we wish to adopt is that in order to understand completely the dynamic response of a complex elastic structure it is not sufficient to con to take into account the sider only its global motion but also necessary flexibility of individual elements and the interaction and transmission of elastic effects such as bending, torsion and axial deformations at junctions where members are connected to each other. The second object of this book is to provide rigorous mathematical analyses of the resulting models.
Mathematical Methods And Models In Composites
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Author : Vladislav Mantic
language : en
Publisher: World Scientific
Release Date : 2013-10-25
Mathematical Methods And Models In Composites written by Vladislav Mantic and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-25 with Technology & Engineering categories.
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.
Mathematical Modelling Of Waves In Multi Scale Structured Media
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Author : Alexander B. Movchan
language : en
Publisher: CRC Press
Release Date : 2017-11-09
Mathematical Modelling Of Waves In Multi Scale Structured Media written by Alexander B. Movchan and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-09 with Mathematics categories.
Mathematical Modelling of Waves in Multi-Scale Structured Media presents novel analytical and numerical models of waves in structured elastic media, with emphasis on the asymptotic analysis of phenomena such as dynamic anisotropy, localisation, filtering and polarisation as well as on the modelling of photonic, phononic, and platonic crystals.