Download or read book Mathematical Models for Elastic Structures written by Piero Villaggio and published by Cambridge University Press. This book was released on 1997-10-28 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical Theory of Elastic Structures written by Kang Feng and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elasticity theory is a classical discipline. The mathematical theory of elasticity in mechanics, especially the linearized theory, is quite mature, and is one of the foundations of several engineering sciences. In the last twenty years, there has been significant progress in several areas closely related to this classical field, this applies in particular to the following two areas. First, progress has been made in numerical methods, especially the development of the finite element method. The finite element method, which was independently created and developed in different ways by sci entists both in China and in the West, is a kind of systematic and modern numerical method for solving partial differential equations, especially el liptic equations. Experience has shown that the finite element method is efficient enough to solve problems in an extremely wide range of applica tions of elastic mechanics. In particular, the finite element method is very suitable for highly complicated problems. One of the authors (Feng) of this book had the good fortune to participate in the work of creating and establishing the theoretical basis of the finite element method. He thought in the early sixties that the method could be used to solve computational problems of solid mechanics by computers. Later practice justified and still continues to justify this point of view. The authors believe that it is now time to include the finite element method as an important part of the content of a textbook of modern elastic mechanics.

Download or read book Modeling Analysis and Control of Dynamic Elastic Multi Link Structures written by J.E. Lagnese and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Mathematical Models for Elastic Structures written by Piero Villaggio and published by Cambridge University Press. This book was released on 1997-10-28 with total page 694 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the seventeenth century, several useful theories of elastic structures emerged, with applications to civil and mechanical engineering problems. Recent and improved mathematical tools have extended applications into new areas such as mathematical physics, geomechanics, and biomechanics. This book offers a critically filtered collection of the most significant theories dealing with elastic slender bodies. It includes mathematical models involving elastic structures that are used to solve practical problems with particular emphasis on nonlinear problems.

Download or read book Stability of Elastic Multi Link Structures written by Kaïs Ammari and published by Springer Nature. This book was released on 2022-01-16 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt: This brief investigates the asymptotic behavior of some PDEs on networks. The structures considered consist of finitely interconnected flexible elements such as strings and beams (or combinations thereof), distributed along a planar network. Such study is motivated by the need for engineers to eliminate vibrations in some dynamical structures consisting of elastic bodies, coupled in the form of chain or graph such as pipelines and bridges. There are other complicated examples in the automotive industry, aircraft and space vehicles, containing rather than strings and beams, plates and shells. These multi-body structures are often complicated, and the mathematical models describing their evolution are quite complex. For the sake of simplicity, this volume considers only 1-d networks.

Download or read book Theory of Stability of Continuous Elastic Structures written by Mario Como and published by Routledge. This book was released on 2022-01-27 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Theory of Stability of Continuous Elastic Structures presents an applied mathematical treatment of the stability of civil engineering structures. The book's modern and rigorous approach makes it especially useful as a text in advanced engineering courses and an invaluable reference for engineers.

Download or read book Mathematical Modelling in Solid Mechanics written by Francesco dell'Isola and published by Springer. This book was released on 2017-03-10 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents new research results in multidisciplinary fields of mathematical and numerical modelling in mechanics. The chapters treat the topics: mathematical modelling in solid, fluid and contact mechanics nonconvex variational analysis with emphasis to nonlinear solid and structural mechanics numerical modelling of problems with non-smooth constitutive laws, approximation of variational and hemivariational inequalities, numerical analysis of discrete schemes, numerical methods and the corresponding algorithms, applications to mechanical engineering numerical aspects of non-smooth mechanics, with emphasis on developing accurate and reliable computational tools mechanics of fibre-reinforced materials behaviour of elasto-plastic materials accounting for the microstructural defects definition of structural defects based on the differential geometry concepts or on the atomistic basis interaction between phase transformation and dislocations at nano-scale energetic arguments bifurcation and post-buckling analysis of elasto-plastic structures engineering optimization and design, global optimization and related algorithms The book presents selected papers presented at ETAMM 2016. It includes new and original results written by internationally recognized specialists.

Download or read book Mathematical Models for Structural Reliability Analysis written by Fabio Casciati and published by CRC Press. This book was released on 1996-07-24 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Models for Structural Reliability Analysis offers mathematical models for describing load and material properties in solving structural engineering problems. Examples are provided, demonstrating how the models are implemented, and the limitations of the models are clearly stated. Analytical solutions are also discussed, and methods are clearly distinguished from models. The authors explain both theoretical models and practical applications in a clear, concise, and readable fashion.

Download or read book Stability of Elastic Structures written by N.A. Alfutov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject discussed in this book is the stability of thin-walled elastic systems under static loads. The presentation of these problems is based on modern approaches to elastic-stability theory. Special attention is paid to the formulation of elastic-stability criteria, to the statement of column, plate and shell stability problems, to the derivation of basic relationships, and to a discussion of the boundaries of the application of analytic relationships. The author has tried to avoid arcane, nonstandard problems and elaborate and unexpected solutions, which bring real pleasure to connoisseurs, but confuse students and cause bewilderment to some practical engineers. The author has an apprehension that problems which, though interesting, are limited in application can divert the reader's attention from the more prosaic but no less sophisticated general problems of stability theory.

Download or read book Introduction to Mathematical Elasticity written by L. P. Lebedev and published by World Scientific. This book was released on 2009 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides the general reader with an introduction to mathematical elasticity, by means of general concepts in classic mechanics, and models for elastic springs, strings, rods, beams and membranes. Functional analysis is also used to explore more general boundary value problems for three-dimensional elastic bodies, where the reader is provided, for each problem considered, a description of the deformation; the equilibrium in terms of stresses; the constitutive equation; the equilibrium equation in terms of displacements; formulation of boundary value problems; and variational principles, generalized solutions and conditions for solvability.Introduction to Mathematical Elasticity will also be of essential reference to engineers specializing in elasticity, and to mathematicians working on abstract formulations of the related boundary value problems.

Download or read book Mathematical Models of Beams and Cables written by Angelo Luongo and published by John Wiley & Sons. This book was released on 2013-12-02 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear models of elastic and visco-elastic onedimensional continuous structures (beams and cables) are formulated by the authors of this title. Several models of increasing complexity are presented: straight/curved, planar/non-planar, extensible/inextensible, shearable/unshearable, warpingunsensitive/ sensitive, prestressed/unprestressed beams, both in statics and dynamics. Typical engineering problems are solved via perturbation and/or numerical approaches, such as bifurcation and stability under potential and/or tangential loads, parametric excitation, nonlinear dynamics and aeroelasticity. Contents 1. A One-Dimensional Beam Metamodel. 2. Straight Beams. 3. Curved Beams. 4. Internally Constrained Beams. 5. Flexible Cables. 6. Stiff Cables. 7. Locally-Deformable Thin-Walled Beams. 8. Distortion-Constrained Thin-Walled Beams.

Download or read book Mathematical Methods in Elasticity Imaging written by Habib Ammari and published by Princeton University Press. This book was released on 2015-04-05 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first to comprehensively explore elasticity imaging and examines recent, important developments in asymptotic imaging, modeling, and analysis of deterministic and stochastic elastic wave propagation phenomena. It derives the best possible functional images for small inclusions and cracks within the context of stability and resolution, and introduces a topological derivative–based imaging framework for detecting elastic inclusions in the time-harmonic regime. For imaging extended elastic inclusions, accurate optimal control methodologies are designed and the effects of uncertainties of the geometric or physical parameters on stability and resolution properties are evaluated. In particular, the book shows how localized damage to a mechanical structure affects its dynamic characteristics, and how measured eigenparameters are linked to elastic inclusion or crack location, orientation, and size. Demonstrating a novel method for identifying, locating, and estimating inclusions and cracks in elastic structures, the book opens possibilities for a mathematical and numerical framework for elasticity imaging of nanoparticles and cellular structures.

Download or read book Mathematical Modelling of Waves in Multi Scale Structured Media written by Alexander B. Movchan and published by CRC Press. This book was released on 2017-11-09 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book Plates and Junctions in Elastic Multi structures written by Philippe G. Ciarlet and published by . This book was released on 1990-01-01 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first objective of this monograph is to show that the method of asymptotic expansions, with the thickness as the parameter, provides a very effective tool for justifying two-dimensional plate theories, in both the nonlinear and the linear case. Without resorting to any a priori assumption of a geometrical or mechanical nature, it is shown that, the displacements and stresses corresponding to the leading term of the expansion of the 3-dimensional solution do indeed solve the classical equations of 2-dimensional nonlinear plate theories such as the von Kármán equations. The second objective is to extend this analysis to the mathematical modeling of junctions in elastic multi-structures, e.g. typically a structure comprising a '3-dimensional' part, and a '2-dimensional' part. These can be folded plates, H-shaped beams, plates with stiffeners, plates held by rods as in a solar panel, etc. A similar asymptotic analysis provides a systematic way of finding the models for such multi-structures, as the 'thin' part approach. Interestingly, the limit problems found in this way are coupled, multi-dimensional, problems of a new type providing new instances of stiff problems. The book written by one of the leading experts internationally in the field of numerical methods applied to solid mechanics presents an up-to-date report on an active research topic, and will be a useful reference for applied mathematicians and engineers working with elastic multi-structures.

Download or read book Acoustic Interactions with Submerged Elastic Structures written by A. Guran and published by World Scientific. This book was released on 2001 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."

Download or read book Mathematical Modeling written by Christof Eck and published by Springer. This book was released on 2017-04-11 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.

Download or read book Mathematical Modelling in Science and Technology written by Xavier J.R. Avula and published by Elsevier. This book was released on 2014-05-09 with total page 1023 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modelling in Science and Technology: The Fourth International Conference covers the proceedings of the Fourth International Conference by the same title, held at the Swiss Federal Institute of Technology, Zurich, Switzerland on August 15-17, 1983. Mathematical modeling is a powerful tool to solve many complex problems presented by scientific and technological developments. This book is organized into 20 parts encompassing 180 chapters. The first parts present the basic principles, methodology, systems theory, parameter estimation, system identification, and optimization of mathematical modeling. The succeeding parts discuss the features of stochastic and numerical modeling and simulation languages. Considerable parts deal with the application areas of mathematical modeling, such as in chemical engineering, solid and fluid mechanics, water resources, medicine, economics, transportation, and industry. The last parts tackle the application of mathematical modeling in student management and other academic cases. This book will prove useful to researchers in various science and technology fields.