Finite Rotations And Lagrangean Description In The Non Linear Theory Of Shells
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| Author | : A. Libai |
| Publisher | : Elsevier |
| Total Pages | : 429 |
| Release | : 2012-12-02 |
| Genre | : Technology & Engineering |
| ISBN | : 0323150810 |
The Nonlinear Theory of Elastic Shells: One Spatial Dimension presents the foundation for the nonlinear theory of thermoelastic shells undergoing large strains and large rotations. This book discusses several relatively simple equations for practical application. Organized into six chapters, this book starts with an overview of the description of nonlinear elastic shell. This text then discusses the foundation of three-dimensional continuum mechanics that are relevant to the shell theory approach. Other chapters cover several topics, including birods, beamshells, and axishells that begins with a derivation of the equations of motion by a descent from the equations of balance of linear and rotational momentum of a three-dimensional material continuum. This book discusses as well the approach to deriving complete field equations for one- or two-dimensional continua from the integral equations of motion and thermodynamics of a three-dimensional continuum. The final chapter deals with the analysis of unishells. This book is a valuable resource for physicists, mathematicians, and scientists.
| Author | : K. Wisniewski |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 492 |
| Release | : 2010-11-18 |
| Genre | : Technology & Engineering |
| ISBN | : 9048187613 |
The objective of this book is to provide a comprehensive introduction to ?nite rotation shells and to non-linear shell ?nite elements. It is divided into 5 parts: I. Preliminaries (20 pages), II. Shell equations (104 pages), III. Finite rotations for shells (103 pages), IV. Four-node shell elements (189 pages), and V. Numerical examples (41 pages). Additional numerical examples are presented in Parts III and IV. The bibliography includes 270 entries. The book is intended for both teaching and self-study, and emphasizes fundamental aspects and techniques of the subject. Some familiarity with non-linear mechanics and the ?nite element method is assumed. Shell elements are a subject of active research which results in many publications every year and several conferences and sessions are held r- ularly, among them, two large international conferences: \Computation of Shell and Spatial Structures" and \Shell Structures. Theory and - plications" (SSTA). The literature is voluminous, not easy to follow and evaluate, and the subject is di–cult to comprehend. I hope that this will be facilitated by the book. I would like to express my gratitude to several persons who helped me in my professional life, in this way contributing to the book. I thank Prof. R.L. Taylor from the University of California at Berkeley, Prof. B. Schre er from the University of Padua, and Prof. J.T. Santos from the Instituto Superior Tecnico at Lisbon, for hosting and supporting me when I was a post-doctoral researcher.
| Author | : Iosif I. Vorovich |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 404 |
| Release | : 2008-01-08 |
| Genre | : Technology & Engineering |
| ISBN | : 0387227768 |
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.
| Author | : Wojciech Pietraszkiewicz |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 394 |
| Release | : 2013-03-12 |
| Genre | : Science |
| ISBN | : 3642828388 |
The deformation near a material particle of the classical continuum is produced by successive superposition of a rigid-body translation, a pure stretch along principal directions of strain and a rigid-body ro tation of those directions. The rotational part of deformation is par ticularly important in the non-linear analysis of thin-walled solid structures such as ~eams, thin-walled bars, plates and shells, since in this case finite rotations may appear even if the strains are infinite simal. It seems that the research concerning the application of finite ro tations is carried out independently in different fields of structural mechanics. Theoretical and numerical methods developed and the results obtained for a particular type of the structure or for a particular ma terial behaviour not always are used to analyse similar problems for other types of structures or for another material behaviour. Since the research in this field had been growing rapidly, it was decided to organize an informal international meeting, under the auspi ces of the European Mechanics Co~mittee, entitled: Euromech Colloquium 197 "Finite Rotations in Structural Mechanics". The meeting was held on 17 - 20 September 1985 in Jablonna, a small suburbian area of Warsaw.
| Author | : Yavuz Basar |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 201 |
| Release | : 2013-11-11 |
| Genre | : Science |
| ISBN | : 3662042991 |
The aim of the book is the presentation of the fundamental mathematical and physical concepts of continuum mechanics of solids in a unified description so as to bring young researchers rapidly close to their research area. Accordingly, emphasis is given to concepts of permanent interest, and details of minor importance are omitted. The formulation is achieved systematically in absolute tensor notation, which is almost exclusively used in modern literature. This mathematical tool is presented such that study of the book is possible without permanent reference to other works.
| Author | : D. Durban |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 376 |
| Release | : 2006-04-11 |
| Genre | : Technology & Engineering |
| ISBN | : 0306469545 |
The optimal control of flexible structures is an active area of research. The main body of work in this area is concerned with the control of time-dependent displacements and stresses, and assumes linear elastic conditions, namely linear elastic material behavior and small defor- tion. See, e. g. , [1]–[3], the collections of papers [4, 5], and references therein. On the other hand, in the present paper we consider the static optimal control of a structure made of a nonlinear elastic material and und- going large deformation. An important application is the suppression of static or quasi-static elastic deformation in flexible space structures such as parts of satellites by the use of control loads [6]. Solar rad- tion and radiation from other sources induce a temperature field in the structure, which in turn generates an elastic displacement field. The displacements must usually satisfy certain limitations dictated by the allowed working conditions of various orientation-sensitive instruments and antennas in the space vehicle. For example, a parabolic reflector may cease to be effective when undergoing large deflection. The elastic deformation can be reduced by use of control loads, which may be imp- mented via mechanically-based actuators or more modern piezoelectric devices. When the structure under consideration is made of a rubb- like material and is undergoing large deformation, nonlinear material and geometric effects must be taken into account in the analysis.
| Author | : Junuthula Narasimha Reddy |
| Publisher | : |
| Total Pages | : 721 |
| Release | : 2015 |
| Genre | : Finite element method |
| ISBN | : 0199641757 |
The second edition of An Introduction to Nonlinear Finite Element Analysis has the same objective as the first edition, namely, to facilitate an easy and thorough understanding of the details that are involved in the theoretical formulation, finite element model development, and solutions of nonlinear problems. The book offers an easy-to-understand treatment of the subject of nonlinear finite element analysis, which includes element development from mathematical models and numerical evaluation of the underlying physics. The new edition is extensively reorganized and contains substantial amounts of new material. Chapter 1 in the second edition contains a section on applied functional analysis. Chapter 2 on nonlinear continuum mechanics is entirely new. Chapters 3 through 8 in the new edition correspond to Chapter 2 through 8 of the first edition, but with additional explanations, examples, and exercise problems. Material on time dependent problems from Chapter 8 of the first edition is absorbed into Chapters 4 through 8 of the new edition. Chapter 9 is extensively revised and it contains up to date developments in the large deformation analysis of isotropic, composite and functionally graded shells. Chapter 10 of the first edition on material nonlinearity and coupled problems is reorganized in the second edition by moving the material on solid mechanics to Chapter 12 in the new edition and material on coupled problems to the new chapter, Chapter 10, on weak-form Galerkin finite element models of viscous incompressible fluids. Finally, Chapter 11 in the second edition is entirely new and devoted to least-squares finite element models of viscous incompressible fluids. Chapter 12 of the second edition is enlarged to contain finite element models of viscoelastic beams. In general, all of the chapters of the second edition contain additional explanations, detailed example problems, and additional exercise problems. Although all of the progr
| Author | : Debabrata Ray |
| Publisher | : John Wiley & Sons |
| Total Pages | : 996 |
| Release | : 2015-12-14 |
| Genre | : Technology & Engineering |
| ISBN | : 111899695X |
Comprehensively introduces linear and nonlinear structural analysis through mesh generation, solid mechanics and a new numerical methodology called c-type finite element method Takes a self-contained approach of including all the essential background materials such as differential geometry, mesh generation, tensor analysis with particular elaboration on rotation tensor, finite element methodology and numerical analysis for a thorough understanding of the topics Presents for the first time in closed form the geometric stiffness, the mass, the gyroscopic damping and the centrifugal stiffness matrices for beams, plates and shells Includes numerous examples and exercises Presents solutions for locking problems
| Author | : Wojciech Pietraszkiewicz |
| Publisher | : CRC Press |
| Total Pages | : 600 |
| Release | : 2013-09-18 |
| Genre | : Technology & Engineering |
| ISBN | : 1482229080 |
Shells are basic structural elements of modern technology and everyday life. Examples are automobile bodies, water and oil tanks, pipelines, aircraft fuselages, nanotubes, graphene sheets or beer cans. Also nature is full of living shells such as leaves of trees, blooming flowers, seashells, cell membranes, the double helix of DNA or wings of insec
| Author | : J. Chandra |
| Publisher | : SIAM |
| Total Pages | : 196 |
| Release | : 1987-01-01 |
| Genre | : Technology & Engineering |
| ISBN | : 9780898712179 |
