Geometric Methods For Stability Of Nonlinear Elastic Thin Shells
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Geometric Method For Stability Of Non Linear Elastic Thin Shells
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Author : Jordanka Ivanova
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Geometric Method For Stability Of Non Linear Elastic Thin Shells written by Jordanka Ivanova 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 2013-11-27 with Science categories.
PREFACE This book deals with the new developments and applications of the geometric method to the nonlinear stability problem for thin non-elastic shells. There are no other published books on this subject except the basic ones of A. V. Pogorelov (1966,1967,1986), where variational principles defined over isometric surfaces, are postulated, and applied mainly to static and dynamic problems of elastic isotropic thin shells. A. V. Pogorelov (Harkov, Ukraine) was the first to provide in his monographs the geometric construction of the deformed shell surface in a post-critical stage and deriving explicitely the asymptotic formulas for the upper and lower critical loads. In most cases, these formulas were presented in a closed analytical form, and confirmed by experimental data. The geometric method by Pogorelov is one of the most important analytical methods developed during the last century. Its power consists in its ability to provide a clear geometric picture of the postcritical form of a deformed shell surface, successfully applied to a direct variational approach to the nonlinear shell stability problems. Until now most Pogorelov's monographs were written in Russian, which limited the diffusion of his ideas among the international scientific community. The present book is intended to assist and encourage the researches in this field to apply the geometric method and the related results to everyday engineering practice.
Geometric Methods For Stability Of Nonlinear Elastic Thin Shells
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Author : Franco Pastrone
language : en
Publisher:
Release Date : 2002
Geometric Methods For Stability Of Nonlinear Elastic Thin Shells written by Franco Pastrone and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.
Geometric Method For Stability Of Non Linear Elastic Thin Shells
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Author : Jordanka Ivanova
language : en
Publisher: Springer Science & Business Media
Release Date : 2002
Geometric Method For Stability Of Non Linear Elastic Thin Shells written by Jordanka Ivanova 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 2002 with Mathematics categories.
Ivanova (mechanics, Bulgarian Academy of Sciences) and Pastrone (mathematics, Universita di Torino) present this volume on the new developments and application of the geometric method to the nonlinear stability problem for thin non-elastic shells. The geometric method has been treated previously in the 1960s and 1980s in monographs by A. V. Pogorelov (Harkov, Ukraine) but written in Russian only, thus making his ideas inaccessible to much of the international scientific community. The current text requires a basic understanding of introductory surface theory, stability of shells, and partial differential equations. It is intended as a textbook for post-graduate students in structural engineering and applied mathematics, and as a reference for academic and industrial researchers. c. Book News Inc.
Nonlinear Problems Of Elasticity
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Author : Stuart Antman
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Nonlinear Problems Of Elasticity written by Stuart Antman 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 2013-03-14 with Mathematics categories.
The scientists of the seventeenth and eighteenth centuries, led by Jas. Bernoulli and Euler, created a coherent theory of the mechanics of strings and rods undergoing planar deformations. They introduced the basic con cepts of strain, both extensional and flexural, of contact force with its com ponents of tension and shear force, and of contact couple. They extended Newton's Law of Motion for a mass point to a law valid for any deformable body. Euler formulated its independent and much subtler complement, the Angular Momentum Principle. (Euler also gave effective variational characterizations of the governing equations. ) These scientists breathed life into the theory by proposing, formulating, and solving the problems of the suspension bridge, the catenary, the velaria, the elastica, and the small transverse vibrations of an elastic string. (The level of difficulty of some of these problems is such that even today their descriptions are sel dom vouchsafed to undergraduates. The realization that such profound and beautiful results could be deduced by mathematical reasoning from fundamental physical principles furnished a significant contribution to the intellectual climate of the Age of Reason. ) At first, those who solved these problems did not distinguish between linear and nonlinear equations, and so were not intimidated by the latter. By the middle of the nineteenth century, Cauchy had constructed the basic framework of three-dimensional continuum mechanics on the founda tions built by his eighteenth-century predecessors.
Mathematical Elasticity
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Author : Philippe G. Ciarlet
language : en
Publisher: SIAM
Release Date : 2022-01-22
Mathematical Elasticity written by Philippe G. Ciarlet and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-22 with Mathematics categories.
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.
Nonlinear Theory Of Shallow Shells
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Author : Iosif I. Vorovich
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-01-08
Nonlinear Theory Of Shallow Shells written by Iosif I. Vorovich 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 2008-01-08 with Technology & Engineering categories.
This book presents rigorous treatment of boundary value problems in nonlinear theory of shallow shells. The consideration of the problems is carried out using methods of nonlinear functional analysis.
Theory Of Shells
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Author : Philippe G. Ciarlet
language : en
Publisher: Elsevier
Release Date : 2000-05-11
Theory Of Shells written by Philippe G. Ciarlet and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-11 with Mathematics categories.
The objective of Volume III is to lay down the proper mathematical foundations of the two-dimensional theory of shells. To this end, it provides, without any recourse to any a priori assumptions of a geometrical or mechanical nature, a mathematical justification of two-dimensional nonlinear and linear shell theories, by means of asymptotic methods, with the thickness as the "small" parameter.
New Approaches To Structural Mechanics Shells And Biological Structures
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Author : Horace R. Drew
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
New Approaches To Structural Mechanics Shells And Biological Structures written by Horace R. Drew 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 2013-03-09 with Science categories.
This Festschrift marks the retirement of Professor Chris Calladine, FRS after 42 years on the teaching staff of the Department of Engineering, University of Cambridge. It contains a series of papers contributed by his former students, colleagues, and friends. Chris Calladine's research has ranged very widely across the field of struc tural mechanics, with a particular focus on the plastic deformation of solids and structures, and the behaviour of thin-shell structures. His insightful books on Engineering Plasticity and Theory of Shell Structures have been appreciated by many generations of students at Cambridge and elsewhere. His scientific contri bution outside engineering, in molecular structures, is at least as significant, and he is unique among engineers in having co-authored a book on DNA. Also, he has been keenly interested in the research of many students and colleagues, and on many occasions his quick grasp and physical insight have helped a student, and sometimes a colleague, find the nub of the problem without unnecessary effort. Many of the papers contained in this volume gratefully acknowledge this generous contribution. We thank Professor G. M. l. Gladwell for reading through all of the contri butions, Mrs R. Baxter and Mrs o. Constantinides for help in preparing this volume, Godfrey Argent Studio for permission to reproduce Calladine's por trait for the Royal Society, and Dr A. Schouwenburg -from Kluwer- for his assistance. Horace R. Drew Sergio Pellegrino ix CHRIS CALLADINE SOME THOUGHTS ON RESEARCH c. R.
Differential Geometric Methods In The Control Of Partial Differential Equations
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Author : Robert Gulliver
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Differential Geometric Methods In The Control Of Partial Differential Equations written by Robert Gulliver and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
This volume contains selected papers that were presented at the AMS-IMS-SIAM Joint Summer Research Conference on "Differential Geometric Methods in the Control of Partial Differential Equations", which was held at the University of Colorado in Boulder in June 1999. The aim of the conference was to explore the infusion of differential-geometric methods into the analysis of control theory of partial differential equations, particularly in the challenging case of variable coefficients, where the physical characteristics of the medium vary from point to point. While a mutually profitable link has been long established, for at least 30 years, between differential geometry and control of ordinary differential equations, a comparable relationship between differential geometry and control of partial differential equations (PDEs) is a new and promising topic. Very recent research, just prior to the Colorado conference, supported the expectation that differential geometric methods, when brought to bear on classes of PDE modelling and control problems with variable coefficients, will yield significant mathematical advances. The papers included in this volume - written by specialists in PDEs and control of PDEs as well as by geometers - collectively support the claim that the aims of the conference are being fulfilled. In particular, they endorse the belief that both subjects-differential geometry and control of PDEs-have much to gain by closer interaction with one another. Consequently, further research activities in this area are bound to grow.
Inelastic Behaviour Of Plates And Shells
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Author : Luiz Bevilacqua
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Inelastic Behaviour Of Plates And Shells written by Luiz Bevilacqua 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 Technology & Engineering categories.
During the last ten years a considerable volume of inform ation has been accumulated regarding the inelastic behaviour of materials. The increasing number of communications published in specialised journals and also the frequency of meetings in these fields, indicates a considerable research effort aimed at such topics as plasticity, creep, fatigue, visco-plasticity and the like. This fact encouraged a group of Brazilian researchers, stimulated enthusiastically by Professor P. Germain, to submit a proposal for a Symposium on the "Inelastic Behaviour of Plates and Shells" to the General Assembly of IUTAM. Brazil had recently joined IUTAM and the Brazilian Association of Mechanical Sciences was eager to host an IUTAM meeting. In the selection of the subject, it was taken into account, besides a promising number of original contributions, the interest to be raised amongst the Brazilian researchers and engineers, in order to maximise the participation of the host country. The recent steps taken in this country towards the develop ment of the aero-space industry, the construction of nuclear power plants a.nd the off-shore exploration of petroleum have required an intensification of research activities in several fields, structural behaviour of plates and shells being one of the most important. Therefore, the suggested theme would attract the interest or a significant group of Brazilian researchers and engineers and match the necessity for exchanging experience among leading scientists working in those fields.