Asymptotic Theories For Plates And Shells

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Asymptotic Theories for Plates and Shells

Author : Klaus Hackl
Publisher : CRC Press
ISBN 13 : 9780582248755
Total Pages : 148 pages
Book Rating : 4.2/5 (487 download)

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Book Synopsis Asymptotic Theories for Plates and Shells by : Klaus Hackl

Download or read book Asymptotic Theories for Plates and Shells written by Klaus Hackl and published by CRC Press. This book was released on 1995-03-06 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Asymptotic Theory Of Anisotropic Plates And Shells

Author : Lenser A Aghalovyan
Publisher : World Scientific
ISBN 13 : 9814579041
Total Pages : 377 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Asymptotic Theory Of Anisotropic Plates And Shells by : Lenser A Aghalovyan

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.

Theories of Plates and Shells

Author : Reinhold Kienzler
Publisher : Springer Science & Business Media
ISBN 13 : 3540399054
Total Pages : 258 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Theories of Plates and Shells by : Reinhold Kienzler

Download or read book Theories of Plates and Shells written by Reinhold Kienzler and published by Springer Science & Business Media. This book was released on 2013-06-01 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plate and shell theories experienced a renaissance in recent years. The potentials of smart materials, the challenges of adaptive structures, the demands of thin-film technologies and more on the one hand and the availability of newly developed mathematical tools, the tremendous increase in computer facilities and the improvement of commercial software packages on the other caused a reanimation of the scientific interest. In the present book the contributions of the participants of the EUROMECH Colloquium 444 "Critical Review of the Theories of Plates and Shells and New Applications" have been collected. The aim was to discuss the common roots of different plate and shell approaches, to review the current state of the art, and to develop future lines of research. Contributions were written by scientists with civil and mechanical engineering as well as mathematical and physical background.

Asymptotic Theories for Plates and Shells

Author : Robert P. Gilbert
Publisher : Halsted Press
ISBN 13 : 9780470234952
Total Pages : 144 pages
Book Rating : 4.2/5 (349 download)

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Book Synopsis Asymptotic Theories for Plates and Shells by : Robert P. Gilbert

Download or read book Asymptotic Theories for Plates and Shells written by Robert P. Gilbert and published by Halsted Press. This book was released on 1995-01-01 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Analysis of Shells, Plates, and Beams

Author : Holm Altenbach
Publisher : Springer Nature
ISBN 13 : 3030474917
Total Pages : 470 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Analysis of Shells, Plates, and Beams by : Holm Altenbach

Download or read book Analysis of Shells, Plates, and Beams written by Holm Altenbach and published by Springer Nature. This book was released on 2020-06-03 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book commemorates the 75th birthday of Prof. George Jaiani – Georgia’s leading expert on shell theory. He is also well known outside Georgia for his individual approach to shell theory research and as an organizer of meetings, conferences and schools in the field. The collection of papers presented includes articles by scientists from various countries discussing the state of the art and new trends in the theory of shells, plates, and beams. Chapter 20 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.

Plates, Laminates, and Shells

Author : T. Lewi?ski
Publisher : World Scientific
ISBN 13 : 9789810232061
Total Pages : 768 pages
Book Rating : 4.2/5 (32 download)

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Book Synopsis Plates, Laminates, and Shells by : T. Lewi?ski

Download or read book Plates, Laminates, and Shells written by T. Lewi?ski and published by World Scientific. This book was released on 2000 with total page 768 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 0n/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.

Theory of Shells

Author : Philippe G. Ciarlet
Publisher : Elsevier
ISBN 13 : 0080511236
Total Pages : 662 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Theory of Shells by : Philippe G. Ciarlet

Download or read book Theory of Shells written by Philippe G. Ciarlet and published by Elsevier. This book was released on 2000-05-11 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Asymptotical Mechanics of Thin-Walled Structures

Author : Igor V. Andrianov
Publisher : Springer Science & Business Media
ISBN 13 : 354045246X
Total Pages : 527 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Asymptotical Mechanics of Thin-Walled Structures by : Igor V. Andrianov

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.

Thin Plates and Shells

Author : Eduard Ventsel
Publisher : CRC Press
ISBN 13 : 0203908724
Total Pages : 683 pages
Book Rating : 4.2/5 (39 download)

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Book Synopsis Thin Plates and Shells by : Eduard Ventsel

Download or read book Thin Plates and Shells written by Eduard Ventsel and published by CRC Press. This book was released on 2001-08-24 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting recent principles of thin plate and shell theories, this book emphasizes novel analytical and numerical methods for solving linear and nonlinear plate and shell dilemmas, new theories for the design and analysis of thin plate-shell structures, and real-world numerical solutions, mechanics, and plate and shell models for engineering applications. It includes computer processes for finite difference, finite element, boundary element, and boundary collocation methods as well as other variational and numerical methods. It also contains end-of-chapter examples and problem/solution sets, a catalog of solutions for cylindrical and spherical shells, and tables of the most commonly used plates and shells.

Plates, Laminates And Shells: Asymptotic Analysis And Homogenization

Author : Tomasz Lewinski
Publisher : World Scientific
ISBN 13 : 9814497177
Total Pages : 765 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Plates, Laminates And Shells: Asymptotic Analysis And Homogenization by : Tomasz Lewinski

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.

Plates and Shells

Author : Michel Fortin
Publisher : American Mathematical Soc.
ISBN 13 : 9780821873281
Total Pages : 292 pages
Book Rating : 4.8/5 (732 download)

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Book Synopsis Plates and Shells by : Michel Fortin

Download or read book Plates and Shells written by Michel Fortin and published by American Mathematical Soc.. This book was released on 1999-06-23 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume features the proceedings from the Summer Seminar of the Canadian Mathematical Society held at Universite Laval. The purpose of the seminar was to gather both mathematicians and engineers interested in the theory or application of plates and shells, or more generally, in the modelisation of thin structures. From this, it was hoped that a better understanding of the problem would emerge for both groups of professionals. New aspects from the mathematical point of view and new applications posing new challenges are reported. This volume offers a snapshot of the state of the art of this rapidly evolving topic.

Asymptotic Methods in the Buckling Theory of Elastic Shells

Author : P. E. Tovstik
Publisher : World Scientific
ISBN 13 : 9789812794567
Total Pages : 368 pages
Book Rating : 4.7/5 (945 download)

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Book Synopsis Asymptotic Methods in the Buckling Theory of Elastic Shells by : P. E. Tovstik

Download or read book Asymptotic Methods in the Buckling Theory of Elastic Shells written by P. E. Tovstik and published by World Scientific. This book was released on 2001 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 1. Equations of thin elastic shell theory. 1.1. Elements of surface theory. 1.2. Equilibrium equations and boundary conditions. 1.3. Errors of 2D shell theory of Kirchhoff-Love type. 1.4. Membrane stress state. 1.5. Technical shell theory equations. 1.6. Technical theory equations in the other cases. 1.7. Shallow shells. 1.8. Initial imperfections. 1.9. Cylindrical shells. 1.10. The potential energy of shell deformation. 1.11. Problems and exercises -- 2. Basic equations of shell buckling. 2.1. Types of elastic shell buckling. 2.2. The buckling equations. 2.3. The buckling equations for a membrane state. 2.4. buckling equations of the general stress state. 2.5. Problems and exercises -- 3. Simple buckling problems. 3.1. Buckling of a shallow convex shell. 3.2. Shallow shell buckling modes. 3.3. The non-uniqueness of buckling modes. 3.4. A circular cylindrical shell under axial compression. 3.5. A circular cylindrical shell under external pressure. 3.6. Estimates of critical load. 3.7. Problems and examples -- 4. Buckling modes localized near parallels. 4.1. Local shell buckling modes. 4.2. Construction algorithm of buckling modes. 4.3. Buckling modes of convex shells of revolution. 4.4. Buckling of shells of revolution without torsion. 4.5. Buckling of shells of revolution under torsion. 4.6. Problems and exercises -- 5. Non-homogeneous axial compression of cylindrical shells. 5.1. Buckling modes localized near generatrix. 5.2. Reconstruction of the asymptotic expansions. 5.3. Axial compression and bending of cylindrical shell. 5.4. The influence of internal pressure. 5.5. Buckling of a non-circular cylindrical shell. 5.6. Cylindrical shell with curvature of variable sign. 5.7. Problems and exercises -- 6. Buckling modes localized at a point. 6.1. Local buckling of convex shells. 6.2. Construction of the buckling mode. 6.3. Ellipsoid of revolution under combined load. 6.4. Cylindrical shell under axial compression. 6.5. Construction of the buckling modes. 6.6. Problems and exercises -- 7. Semi-momentless buckling modes. 7.1. Basic equations and boundary conditions. 7.2. Buckling modes for a conic shell. 7.3. Effect of initial membrane stress resultants. 7.4 Semi-momentless buckling modes of cylindrical shells. 7.5. Problems and exercises -- 8. Effect of boundary conditions on semi-momentless modes. 8.1. Construction algorithm for semi-momentless solutions. 8.2. Semi-momentless solutions. 8.3. Edge effect solutions. 8.4. Separation of boundary conditions. 8.5. The effect of boundary conditions on the critical load. 8.6. Boundary conditions and buckling of a cylindrical shell. 8.7. Conic shells under external pressure. 8.8. Problems and exercises -- 9. Torsion and bending of cylindrical and conic shells. 9.1. Torsion of cylindrical shells. 9.2. Cylindrical shell under combined loading. 9.3. A shell with non-constant parameters under torsion. 9.4. Bending of a cylindrical shell. 9.5. The torsion and bending of a conic shell. 9.6. Problems and exercises -- 10. Nearly cylindrical and conic shells. 10.1. Basic relations. 10.2. Boundary problem in the zeroth approximation. 10.3. Buckling of a nearly cylindrical shell. 10.4. Torsion of a nearly cylindrical shell. 10.5. Problems and exercises -- 11. Shells of revolution of negative Gaussian curvature. 11.1. Initial equations and their solutions. 11.2. Separation of the boundary conditions. 11.3. Boundary problem in the zeroth approximation. 11.4. Buckling modes without torsion. 11.5. The case of the neutral surface bending. 11.6. The buckling of a torus sector. 11.7. Shell with Gaussian curvature of variable sign. 11.8. Problems and exercises -- 12. Surface bending and shell buckling. 12.1. The transformation of potential energy. 12.2. Pure bending buckling mode of shells of revolution. 12.3. The buckling of a weakly supported shell of revolution. 12.4. Weakly supported cylindrical and conical shells. 12.5. Weakly supported shells of negative Gaussian curvature. 12.6. Problems and exercises -- 13. Buckling modes localized at an edge. 13.1. Rectangular plates under compression. 13.2. Cylindrical shells and panels under axial compression. 13.3. Cylindrical panel with a weakly supported edge. 13.4. Shallow shell with a weak edge support. 13.5. Modes of shells of revolution localized near an edge. 13.6. Buckling modes with turning points. 13.7. Modes localized near the weakest point on an edge. 13.8. Problems and exercises -- 14. Shells of revolution under general stress state. 14.1. The basic equations and edge effect solutions. 14.2. Buckling with pseudo-bending modes. 14.3. The cases of significant effect of pre-buckling strains. 14.4. The weakest parallel coinciding with an edge. 14.5. Problems and exercises.

Mathematical Elasticity, Volume II

Author : Philippe G. Ciarlet
Publisher :
ISBN 13 : 9781611976793
Total Pages : 0 pages
Book Rating : 4.9/5 (767 download)

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Book Synopsis Mathematical Elasticity, Volume II by : Philippe G. Ciarlet

Download or read book Mathematical Elasticity, Volume II written by Philippe G. Ciarlet and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematical Elasticity set contains three self-contained volumes that together provide the only modern treatise on elasticity. They introduce contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells. Each volume contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. An extended preface and extensive bibliography have been added to each volume to highlight the progress that has been made since the original publication. The first book, Three-Dimensional Elasticity, covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. In volume two, Theory of Plates, asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear plate and shallow shell theories. The objective of Theory of Shells, the final volume, is to show how asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear shell theories: membrane, generalized membrane, and flexural. 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.

Shell Structures, Theory and Applications

Author : Wojciech Pietraszkiewicz
Publisher : CRC Press
ISBN 13 : 9780415383905
Total Pages : 656 pages
Book Rating : 4.3/5 (839 download)

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Book Synopsis Shell Structures, Theory and Applications by : Wojciech Pietraszkiewicz

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.

Mathematical Elasticity, Volume III

Author : Philippe G. Ciarlet
Publisher :
ISBN 13 : 9781611976816
Total Pages : 0 pages
Book Rating : 4.9/5 (768 download)

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Book Synopsis Mathematical Elasticity, Volume III by : Philippe G. Ciarlet

Download or read book Mathematical Elasticity, Volume III written by Philippe G. Ciarlet and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematical Elasticity set contains three self-contained volumes that together provide the only modern treatise on elasticity. They introduce contemporary research on three-dimensional elasticity, the theory of plates, and the theory of shells. Each volume contains proofs, detailed surveys of all mathematical prerequisites, and many problems for teaching and self-study. An extended preface and extensive bibliography have been added to each volume to highlight the progress that has been made since the original publication. The first book, Three-Dimensional Elasticity, covers the modeling and mathematical analysis of nonlinear three-dimensional elasticity. In volume two, Theory of Plates, asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear plate and shallow shell theories. The objective of Theory of Shells, the final volume, is to show how asymptotic methods provide a rigorous mathematical justification of the classical two-dimensional linear shell theories: membrane, generalized membrane, and flexural. 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.

Shell-like Structures

Author : Holm Altenbach
Publisher : Springer
ISBN 13 : 3319422774
Total Pages : 293 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Shell-like Structures by : Holm Altenbach

Download or read book Shell-like Structures written by Holm Altenbach and published by Springer. This book was released on 2016-08-09 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents mathematical and mechanical aspects of the theory of plates and shells, applications in civil, aero-space and mechanical engineering, as well in other areas. The focus relates to the following problems:• comprehensive review of the most popular theories of plates and shells,• relations between three-dimensional theories and two-dimensional ones,• presentation of recently developed new refined plates and shells theories (for example, the micropolar theory or gradient-type theories),• modeling of coupled effects in shells and plates related to electromagnetic and temperature fields, phase transitions, diffusion, etc.,• applications in modeling of non-classical objects like, for example, nanostructures,• presentation of actual numerical tools based on the finite element approach.

Recent Approaches in the Theory of Plates and Plate-Like Structures

Author : Holm Altenbach
Publisher : Springer
ISBN 13 : 9783030871871
Total Pages : 0 pages
Book Rating : 4.8/5 (718 download)

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Book Synopsis Recent Approaches in the Theory of Plates and Plate-Like Structures by : Holm Altenbach

Download or read book Recent Approaches in the Theory of Plates and Plate-Like Structures written by Holm Altenbach and published by Springer. This book was released on 2022-12-31 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the various approaches in establishment the basic equations of one- and two-dimensional structural elements. In addition, the boundaries of validity of the theories and the estimation of errors in approximate theories are given. Many contributions contain not only new theories, but also new applications, which makes the book interesting for researcher and graduate students.