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Problems Of Nonlinear Deformation
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Book Synopsis Problems of Nonlinear Deformation by : E.I. Grigolyuk
Download or read book Problems of Nonlinear Deformation written by E.I. Grigolyuk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Interest in nonlinear problems in mechanics has been revived and intensified by the capacity of digital computers. Consequently, a question offundamental importance is the development of solution procedures which can be applied to a large class of problems. Nonlinear problems with a parameter constitute one such class. An important aspect of these problems is, as a rule, a question of the variation of the solution when the parameter is varied. Hence, the method of continuing the solution with respect to a parameter is a natural and, to a certain degree, universal tool for analysis. This book includes details of practical problems and the results of applying this method to a certain class of nonlinear problems in the field of deformable solid mechanics. In the Introduction, two forms of the method are presented, namely continu ous continuation, based on the integration of a Cauchy problem with respect to a parameter using explicit schemes, and discrete continuation, implementing step wise processes with respect to a parameter with the iterative improvement of the solution at each step. Difficulties which arise in continuing the solution in the neighbourhood of singular points are discussed and the problem of choosing the continuation parameter is formulated.
Book Synopsis Non-Linear Elastic Deformations by : R. W. Ogden
Download or read book Non-Linear Elastic Deformations written by R. W. Ogden and published by Courier Corporation. This book was released on 2013-04-26 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic in the field covers application of theory of finite elasticity to solution of boundary-value problems, analysis of mechanical properties of solid materials capable of large elastic deformations. Problems. References.
Book Synopsis Problems of Nonlinear Deformation by :
Download or read book Problems of Nonlinear Deformation written by and published by . This book was released on 1991 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlinear Problems of Elasticity by : Stuart Antman
Download or read book Nonlinear Problems of Elasticity written by Stuart Antman and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Problems in Machine Design by : Eliahu Zahavi
Download or read book Nonlinear Problems in Machine Design written by Eliahu Zahavi and published by CRC Press. This book was released on 2000-12-28 with total page 435 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern machine design challenges engineers with a myriad of nonlinear problems, among them fatigue, friction, plasticity, and excessive deformation. Today's advanced numerical computer programs bring optimal solutions to these complex problems within reach, but not without a trained and experienced overseer. Nonlinear Problems in Machine Des
Book Synopsis Nonlinear Mechanics, Second Edition by : Demeter G. Fertis
Download or read book Nonlinear Mechanics, Second Edition written by Demeter G. Fertis and published by CRC Press. This book was released on 1998-12-21 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complicated problems in nonlinear mechanics pose a challenge - many cannot be solved with existing closed-form methods. You would probably like easier methods for obtaining analytical and numerically exact solutions for finite elements, updated or total Lagrangian formulation, and arc-length methods of nonlinear elastic problem solving. Nonlinear Mechanics, Second Edition gives you what you want - convenient methods of analysis and valuable data for comparison. This is the only book to offer a comprehensive treatment of structural components with variable thickness and a variable modulus of elasticity. It is also the only one to cover closed-form solutions for the dynamic and inelastic analysis of members and plates that are subjected to small and large deformations by including axial and vertical restraints. The author uses exact and approximate solutions for static, dynamic, and inelastic analysis. It also discusses aspects of nonlinear vibration of elastically supported beams, nonlinear response of nonuniform rotor blades, and a new concept of airfoil design. With more than 30% updated and new material, this edition is revised and reorganized to meet the needs of both academia and industry. Easy-to-follow equation derivations, example problems, step-by-step procedures, and iterative approaches create a thorough reference that fills present needs and equips you for the challenges of the future.
Book Synopsis Nonlinear Analysis of Structures by : Muthukrishnan Sathyamoorthy
Download or read book Nonlinear Analysis of Structures written by Muthukrishnan Sathyamoorthy and published by CRC Press. This book was released on 1997-10-28 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Analysis of Structures presents a complete evaluation of the nonlinear static and dynamic behavior of beams, rods, plates, trusses, frames, mechanisms, stiffened structures, sandwich plates, and shells. These elements are important components in a wide variety of structures and vehicles such as spacecraft and missiles, underwater vessels and structures, and modern housing. Today's engineers and designers must understand these elements and their behavior when they are subjected to various types of loads. Coverage includes the various types of nonlinearities, stress-strain relations and the development of nonlinear governing equations derived from nonlinear elastic theory. This complete guide includes both mathematical treatment and real-world applications, with a wealth of problems and examples to support the text. Special topics include a useful and informative chapter on nonlinear analysis of composite structures, and another on recent developments in symbolic computation. Designed for both self-study and classroom instruction, Nonlinear Analysis of Structures is also an authoritative reference for practicing engineers and scientists. One of the world's leaders in the study of nonlinear structural analysis, Professor Sathyamoorthy has made significant research contributions to the field of nonlinear mechanics for twenty-seven years. His foremost contribution to date has been the development of a unique transverse shear deformation theory for plates undergoing large amplitude vibrations and the examination of multiple mode solutions for plates. In addition to his notable research, Professor Sathyamoorthy has also developed and taught courses in the field at universities in India, Canada, and the United States.
Book Synopsis Non-Linear Theory of Elasticity and Optimal Design by : L.W. Ratner
Download or read book Non-Linear Theory of Elasticity and Optimal Design written by L.W. Ratner and published by Elsevier. This book was released on 2003-11-12 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: In order to select an optimal structure among possible similar structures, one needs to compare the elastic behavior of the structures. A new criterion that describes elastic behavior is the rate of change of deformation. Using this criterion, the safe dimensions of a structure that are required by the stress distributed in a structure can be calculated. The new non-linear theory of elasticity allows one to determine the actual individual limit of elasticity/failure of a structure using a simple non-destructive method of measurement of deformation on the model of a structure while presently it can be done only with a destructive test for each structure. For building and explaining the theory, a new logical structure was introduced as the basis of the theory. One of the important physical implications of this logic is that it describes mathematically the universal domain of the possible stable physical relations.
Book Synopsis Nonlinear Mechanics for Composite Heterogeneous Structures by : Georgios A. Drosopoulos
Download or read book Nonlinear Mechanics for Composite Heterogeneous Structures written by Georgios A. Drosopoulos and published by CRC Press. This book was released on 2022-04-26 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Mechanics for Composite Heterogeneous Structures applies both classical and multi-scale finite element analysis to the non-linear, failure response of composite structures. These traditional and modern computational approaches are holistically presented, providing insight into a range of non-linear structural analysis problems. The classical methods include geometric and material non-linearity, plasticity, damage and contact mechanics. The cutting-edge formulations include cohesive zone models, the Extended Finite Element Method (XFEM), multi-scale computational homogenization, localization of damage, neural networks and data-driven techniques. This presentation is simple but efficient, enabling the reader to understand, select and apply appropriate methods through programming code or commercial finite element software. The book is suitable for undergraduate studies as a final year textbook and for MSc and PhD studies in structural, mechanical, aerospace engineering and material science, among others. Professionals in these fields will also be strongly benefited. An accompanying website provides MATLAB codes for two-dimensional finite element problems with contact, multi-scale (FE2) and non-linear XFEM analysis, data-driven and machine learning simulations.
Book Synopsis Advances in Computational Nonlinear Mechanics by : I.S. Doltsinis
Download or read book Advances in Computational Nonlinear Mechanics written by I.S. Doltsinis and published by Springer. This book was released on 2014-05-04 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced computational methods in nonlinear mechanics of solids and fluids are dealt with in this volume. Contributions consider large deformations of structures and solids, problems in nonlinear dynamics, aspects of earthquake analysis, coupled problems, convection-dominated phenomena, and compressible and incompressible viscous flows. Selected applications indicate the relevance of the analysis to the demands of industry and science. The contributors are from research institutions well-known for their work in this field.
Book Synopsis Nonlinear Finite Element Analysis of Solids and Structures by : René de Borst
Download or read book Nonlinear Finite Element Analysis of Solids and Structures written by René de Borst and published by John Wiley & Sons. This book was released on 2012-07-25 with total page 481 pages. Available in PDF, EPUB and Kindle. Book excerpt: Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist René de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature. Key features: Combines the two previous volumes into one heavily revised text with obsolete material removed, an improved layout and updated references and notations Extensive new material on more recent developments in computational mechanics Easily readable, engineering oriented, with no more details in the main text than necessary to understand the concepts. Pseudo-code throughout makes the link between theory and algorithms, and the actual implementation. Accompanied by a website (www.wiley.com/go/deborst) with a Python code, based on the pseudo-code within the book and suitable for solving small-size problems. Non-linear Finite Element Analysis of Solids and Structures, 2nd Edition is an essential reference for practising engineers and researchers that can also be used as a text for undergraduate and graduate students within computational mechanics.
Book Synopsis Nonlinear Finite Element Methods by : Peter Wriggers
Download or read book Nonlinear Finite Element Methods written by Peter Wriggers and published by Springer Science & Business Media. This book was released on 2008-09-24 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element methods have become ever more important to engineers as tools for design and optimization, now even for solving non-linear technological problems. However, several aspects must be considered for finite-element simulations which are specific for non-linear problems: These problems require the knowledge and the understanding of theoretical foundations and their finite-element discretization as well as algorithms for solving the non-linear equations. This book provides the reader with the required knowledge covering the complete field of finite element analyses in solid mechanics. It is written for advanced students in engineering fields but serves also as an introduction into non-linear simulation for the practising engineer.
Book Synopsis Amplification of Nonlinear Strain Waves in Solids by : Alexey V. Porubov
Download or read book Amplification of Nonlinear Strain Waves in Solids written by Alexey V. Porubov and published by World Scientific. This book was released on 2003 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats two problems simultaneously: sequential analytical consideration of nonlinear strain wave amplification and selection in wave guides and in a medium; demonstration of the use of even particular analytical solutions to nonintegrable equations in a design of numerical simulation of unsteady nonlinear wave processes. The text includes numerous detailed examples of the strain wave amplification and selection caused by the influence of an external medium, microstructure, moving point defects, and thermal phenomena. The main features of the book are: (1) nonlinear models of the strain wave evolution in a rod subjected by various dissipative/active factors; (2) an analytico-numerical approach for solutions to the governing nonlinear partial differential equations with dispersion and dissipation. This book is essential for introducing readers in mechanics, mechanical engineering, and applied mathematics to the concept of long nonlinear strain wave in one-dimensional wave guides. It is also suitable for self-study by professionals in all areas of nonlinear physics.
Book Synopsis Nonlinear Boundary Value Problems in Science and Engineering by : C. Rogers
Download or read book Nonlinear Boundary Value Problems in Science and Engineering written by C. Rogers and published by Academic Press. This book was released on 1989-11-14 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Overall, our object has been to provide an applications-oriented text that is reasonably self-contained. It has been used as the basis for a graduate-level course both at the University of Waterloo and at the Centro Studie Applicazioni in Tecnologie Avante, Bari, Italy. The text is aimed, in the main, at applied mathematicians with a strong interest in physical applications or at engineers working in theoretical mechanics.
Book Synopsis Mechanics of Deformable Solids by : Issam Doghri
Download or read book Mechanics of Deformable Solids written by Issam Doghri and published by Springer Science & Business Media. This book was released on 2000-07-13 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: Three subjects of major interest in one textbook: linear elasticity, mechanics of structures in linear isotropic elasticity, and nonlinear mechanics including computational algorithms. After the simplest possible, intuitive approach there follows the mathematical formulation and analysis, with computational methods occupying a good portion of the book. There are several worked-out problems in each chapter and additional exercises at the end of the book, plus mathematical expressions are bery often given in more than one notation. The book is intended primarily for students and practising engineers in mechanical and civil engineering, although students and experts from applied mathematics, materials science and other related fields will also find it useful.
Book Synopsis Introduction to Nonlinear Finite Element Analysis by : Nam-Ho Kim
Download or read book Introduction to Nonlinear Finite Element Analysis written by Nam-Ho Kim and published by Springer Science & Business Media. This book was released on 2014-11-21 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. Please visit the author's website for supplemental material, including PowerPoint presentations and MATLAB codes, at http://www2.mae.ufl.edu/nkim/INFEM/
Book Synopsis Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells by : Jan Awrejcewicz
Download or read book Nonclassical Thermoelastic Problems in Nonlinear Dynamics of Shells written by Jan Awrejcewicz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "A unique feature of this book is the nice blend of engineering vividness and mathematical rigour. [...] The authors are to be congratulated for their valuable contribution to the literature in the area of theoretical thermoelasticity and vibration of plates." Journal of Sound and Vibration
