Download or read book Asymptotic Methods for Elastic Structures written by Philippe G. Ciarlet and published by Walter de Gruyter. This book was released on 2011-07-20 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Download or read book Plates and Junctions in Elastic Multi structures written by Philippe G. Ciarlet and published by Springer. This book was released on 1990 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Vibration and Coupling of Continuous Systems written by Jacqueline Sanchez Hubert and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Real problems concerning vibrations of elastic structures are among the most fascinating topics in mathematical and physical research as well as in applications in the engineering sciences. This book addresses the student familiar with the elementary mechanics of continua along with specialists. The authors start with an outline of the basic methods and lead the reader to research problems of current interest. An exposition of the method of spectra, asymptotic methods and perturbation is followed by applications to linear problems where elastic structures are coupled to fluids in bounded and unbounded domains, to radiation of immersed bodies, to local vibrations, to thermal effects and many more.
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 Asymptotical Mechanics of Thin Walled Structures written by Igor V. Andrianov and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 Asymptotic Analysis of Spatial Problems in Elasticity written by Magomed F. Mekhtiev and published by Springer. This book was released on 2018-11-11 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents homogeneous solutions in static and dynamical problems of anisotropic theory of elasticity, which are constructed for a hollow cylinder. It also offers an asymptotic process for finding frequencies of natural vibrations of a hollow cylinder, and establishes a qualitative study of several applied theories of the boundaries of applicability. Further the authors develop a general theory for a transversally isotropic spherical shell, which includes methods for constructing inhomogeneous and homogeneous solutions that allow the characteristic features of the stress–strain state of an anisotropic spherical shell to be revealed. Lastly, the book introduces an asymptotic method for integrating the equations of anisotropic theory of elasticity in variable thickness plates and shells. Based on the results of the author and researchers at Baku State University and the Institute of Mathematics and Mechanics, ANAS, the book is intended for specialists in the field of theory of elasticity, theory of plates and shells, and applied mathematics.
Download or read book Shell Structures Theory and Applications written by Wojciech Pietraszkiewicz and published by CRC Press. This book was released on 2005-09-22 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: Shells are basic structural elements of modern technology. Examples of shell structures include automobile bodies, domes, water and oil tanks, pipelines, ship hulls, aircraft fuselages, turbine blades, laudspeaker cones, but also balloons, parachutes, biological membranes, a human skin, a bottle of wine or a beer can. This volume contains full texts of over 100 papers presented by specialists from over 20 countries at the 8th Conference "Shell Structures: Theory and Applications", 12-14 October, 2005 in Jurata (Poland). The aim of the meeting was to bring together scientists, designers, engineers and other specialists in shell structures in order to discuss important results and new ideas in this field. The goal is to pursue more accurate theoretical models, to develop more powerful and versatile methods of analysis, and to disseminate expertise in design and maintenance of shell structures. Among the authors there are many distinguished specialists of shell structures, including the authors of general lectures: I.V. Andrianov (Ukraine), V.A. Eremeyev (Russia), A. Ibrahimbegovic (France), P. Klosowski (Poland), B.H. Kröplin (Germany), E. Ramm (Germany), J.M. Rotter (UK) and D. Steigmann (USA). The subject area of the papers covers various theoretical models and numerical analyses of strength, dynamics, stability, optimization etc. of different types of shell structures, their design and maintenance, as well as modelling of some surface-related mechanical phenomena.
Download or read book Asymptotical Mechanics of Composites written by Igor V. Andrianov and published by Springer. This book was released on 2017-11-09 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Asymptotic Methods In The Buckling Theory Of Elastic Shells written by Andrei L Smirnov and published by World Scientific. This book was released on 2001-10-12 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains solutions to the most typical problems of thin elastic shells buckling under conservative loads. The linear problems of bifurcation of shell equilibrium are considered using a two-dimensional theory of the Kirchhoff-Love type. The explicit approximate formulas obtained by means of the asymptotic method permit one to estimate the critical loads and find the buckling modes.The solutions to some of the buckling problems are obtained for the first time in the form of explicit formulas. Special attention is devoted to the study of the shells of negative Gaussian curvature, the buckling of which has some specific features. The buckling modes localized near the weakest lines or points on the neutral surface are constructed, including the buckling modes localized near the weakly supported shell edge. The relations between the buckling modes and bending of the neutral surface are analyzed. Some of the applied asymptotic methods are standard; the others are new and are used for the first time in this book to study thin shell buckling. The solutions obtained in the form of simple approximate formulas complement the numerical results, and permit one to clarify the physics of buckling.
Download or read book Asymptotic Methods for Engineers written by Igor V. Andrianov and published by CRC Press. This book was released on 2024-05-16 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.).
Download or read book Mathematical Elasticity written by Philippe G. Ciarlet and published by SIAM. This book was released on 2022-01-22 with total page 686 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of Theory of Shells, the third book of a three-volume set, is to show how asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear shell theories: membrane, generalized membrane, and flexural. The book also shows how asymptotic methods justify nonlinear elastic shell theories and gives a detailed presentation of the Koiter equations for a nonlinearly elastic shell. An extended preface and extensive bibliography have been added to highlight the progress that has been made since the volume’s original publication. While each one of the three volumes is self-contained, together the Mathematical Elasticity set provides the only modern treatise on elasticity; introduces contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells; and contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study These classic textbooks are for advanced undergraduates, first-year graduate students, and researchers in pure or applied mathematics or continuum mechanics. They are appropriate for courses in mathematical elasticity, theory of plates and shells, continuum mechanics, computational mechanics, and applied mathematics in general.
Download or read book Asymptotic Theory Of Anisotropic Plates And Shells written by Lenser A Aghalovyan and published by World Scientific. This book was released on 2015-03-03 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Direct Methods for Limit States in Structures and Materials written by Konstantinos Spiliopoulos and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knowing the safety factor for limit states such as plastic collapse, low cycle fatigue or ratcheting is always a major design consideration for civil and mechanical engineering structures that are subjected to loads. Direct methods of limit or shakedown analysis that proceed to directly find the limit states offer a better alternative than exact time-stepping calculations as, on one hand, an exact loading history is scarcely known, and on the other they are much less time-consuming. This book presents the state of the art on various topics concerning these methods, such as theoretical advances in limit and shakedown analysis, the development of relevant algorithms and computational procedures, sophisticated modeling of inelastic material behavior like hardening, non-associated flow rules, material damage and fatigue, contact and friction, homogenization and composites.
Download or read book Plates Laminates And Shells Asymptotic Analysis And Homogenization written by Tomasz Lewinski and published by World Scientific. This book was released on 2000-03-23 with total page 765 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a systematic and comprehensive presentation of the results concerning effective behavior of elastic and plastic plates with periodic or quasiperiodic structure. One of the chapters covers the hitherto available results concerning the averaging problems in the linear and nonlinear shell models.A unified approach to the problems studied is based on modern variational and asymptotic methods, including the methods of variational inequalities as well as homogenization techniques. Duality arguments are also exploited. A significant part of the book deals with problems important for engineering practice, such as: statical analysis of highly nonhomogeneous plates and shells for which common discretization techniques fail to be efficient, assessing stiffness reduction of cracked [00n/900m]s laminates, and assessing ultimate loads for perfectly plastic plates and shells composed of repeated segments. When possible, the homogenization formulas are cast in closed form expressions. The formulas presented in this manner are then used in constructing regularized formulations of the fundamental optimization problems for plates and shells, since the regularization concepts are based on introducing the composite regions for which microstructural properties play the role of new design variables.
Download or read book Mathematical Elasticity written by and published by Elsevier. This book was released on 1997-07-22 with total page 561 pages. Available in PDF, EPUB and Kindle. Book excerpt: The objective of Volume II is to show how asymptotic methods, with the thickness as the small parameter, indeed provide a powerful means of justifying two-dimensional plate theories. More specifically, without any recourse to any a priori assumptions of a geometrical or mechanical nature, it is shown that in the linear case, the three-dimensional displacements, once properly scaled, converge in H1 towards a limit that satisfies the well-known two-dimensional equations of the linear Kirchhoff-Love theory; the convergence of stress is also established.In the nonlinear case, again after ad hoc scalings have been performed, it is shown that the leading term of a formal asymptotic expansion of the three-dimensional solution satisfies well-known two-dimensional equations, such as those of the nonlinear Kirchhoff-Love theory, or the von Kármán equations. Special attention is also given to the first convergence result obtained in this case, which leads to two-dimensional large deformation, frame-indifferent, nonlinear membrane theories. It is also demonstrated that asymptotic methods can likewise be used for justifying other lower-dimensional equations of elastic shallow shells, and the coupled pluri-dimensional equations of elastic multi-structures, i.e., structures with junctions. In each case, the existence, uniqueness or multiplicity, and regularity of solutions to the limit equations obtained in this fashion are also studied.
Download or read book Asymptotic Methods in Mechanics written by Rmi Vaillancourt and published by American Mathematical Soc.. This book was released on 1993-12-21 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic methods constitute an important area of both pure and applied mathematics and have applications to a vast array of problems. This collection of papers is devoted to asymptotic methods applied to mechanical problems, primarily thin structure problems. The first section presents a survey of asymptotic methods and a review of the literature, including the considerable body of Russian works in this area. This part may be used as a reference book or as a textbook for advanced undergraduate or graduate students in mathematics or engineering. The second part presents original papers containing new results. Among the key features of the book are its analysis of the general theory of asymptotic integration with applications to the theory of thin shells and plates, and new results about the local forms of vibrations and buckling of thin shells which have not yet made their way into other monographs on this subject.
