Modeling Nonlinear Problems In The Mechanics Of Strings And Rods PDF Download
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| Author | : Oliver M. O'Reilly |
| Publisher | : Springer |
| Total Pages | : 434 |
| Release | : 2017-03-10 |
| Genre | : Mathematics |
| ISBN | : 331950598X |
Download Modeling Nonlinear Problems in the Mechanics of Strings and Rods Book in PDF, ePub and Kindle
This book presents theories of deformable elastic strings and rods and their application to broad classes of problems. Readers will gain insights into the formulation and analysis of models for mechanical and biological systems. Emphasis is placed on how the balance laws interplay with constitutive relations to form a set of governing equations. For certain classes of problems, it is shown how a balance of material momentum can play a key role in forming the equations of motion. The first half of the book is devoted to the purely mechanical theory of a string and its applications. The second half of the book is devoted to rod theories, including Euler’s theory of the elastica, Kirchhoff ’s theory of an elastic rod, and a range of Cosserat rod theories. A variety of classic and recent applications of these rod theories are examined. Two supplemental chapters, the first on continuum mechanics of three-dimensional continua and the second on methods from variational calculus, are included to provide relevant background for students. This book is suited for graduate-level courses on the dynamics of nonlinearly elastic rods and strings.
| Author | : M. Khalid Jawed |
| Publisher | : Springer |
| Total Pages | : 127 |
| Release | : 2018-05-04 |
| Genre | : Technology & Engineering |
| ISBN | : 3319769650 |
Download A Primer on the Kinematics of Discrete Elastic Rods Book in PDF, ePub and Kindle
This primer discusses a numerical formulation of the theory of an elastic rod, known as a discrete elastic rod, that was recently developed in a series of papers by Miklós Bergou et al. Their novel formulation of discrete elastic rods represents an exciting new method to simulate and analyze the behavior of slender bodies that can be modeled using an elastic rod. The formulation has been extensively employed in computer graphics and is highly cited. In the primer, we provide relevant background from both discrete and classical differential geometry so a reader familiar with classic rod theories can appreciate, comprehend, and use Bergou et al.’s computational efficient formulation of a nonlinear rod theory. The level of coverage is suitable for graduate students in mechanics and engineering sciences.
| Author | : S.S Antman |
| Publisher | : Springer |
| Total Pages | : 752 |
| Release | : 2012-12-22 |
| Genre | : Mathematics |
| ISBN | : 9781475741483 |
Download Nonlinear Problems of Elasticity Book in PDF, ePub and Kindle
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.
| Author | : Stanisław Zawiślak |
| Publisher | : Springer Nature |
| Total Pages | : 311 |
| Release | : 2021-08-01 |
| Genre | : Technology & Engineering |
| ISBN | : 3030767876 |
Download Graph-Based Modelling in Science, Technology and Art Book in PDF, ePub and Kindle
This book presents interdisciplinary, cutting-edge and creative applications of graph theory and modeling in science, technology, architecture and art. Topics are divided into three parts: the first one examines mechanical problems related to gears, planetary gears and engineering installations; the second one explores graph-based methods applied to medical analyses as well as biological and chemical modeling; and the third part includes various topics e.g. drama analysis, aiding of design activities and network visualisation. The authors represent several countries in Europe and America, and their contributions show how different, useful and fruitful the utilization of graphs in modelling of engineering systems can be. The book has been designed to serve readers interested in the subject of graph modelling and those with expertise in related areas, as well as members of the worldwide community of graph modelers.
| Author | : Stuart Antman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 762 |
| Release | : 2013-03-14 |
| Genre | : Mathematics |
| ISBN | : 1475741472 |
Download Nonlinear Problems of Elasticity Book in PDF, ePub and Kindle
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.
| Author | : Ivana Kovacic |
| Publisher | : Springer |
| Total Pages | : 316 |
| Release | : 2019-07-24 |
| Genre | : Technology & Engineering |
| ISBN | : 3030236927 |
Download IUTAM Symposium on Exploiting Nonlinear Dynamics for Engineering Systems Book in PDF, ePub and Kindle
This is the proceedings of the IUTAM Symposium on Exploiting Nonlinear Dynamics for Engineering Systems that was held in Novi Sad, Serbia, from July 15th to 19th, 2018. The appearance of nonlinear phenomena used to be perceived as dangerous, with a general tendency to avoid them or control them. This perception has led to intensive research using various approaches and tailor-made tools developed over decades. However, the Nonlinear Dynamics of today is experiencing a profound shift of paradigm since recent investigations rely on a different strategy which brings good effects of nonlinear phenomena to the forefront. This strategy has a positive impact on different fields in science and engineering, such as vibration isolation, energy harvesting, micro/nano-electro-mechanical systems, etc. Therefore, the ENOLIDES Symposium was devoted to demonstrate the benefits and to unlock the potential of exploiting nonlinear dynamical behaviour in these but also in other emerging fields of science and engineering. This proceedings is useful for researchers in the fields of nonlinear dynamics of mechanical systems and structures, and in Mechanical and Civil Engineering.
| Author | : Giuseppe Rega |
| Publisher | : Springer Nature |
| Total Pages | : 505 |
| Release | : 2022-06-04 |
| Genre | : Technology & Engineering |
| ISBN | : 3030941957 |
Download 50+ Years of AIMETA Book in PDF, ePub and Kindle
The book retraces the history of the Italian Association of Theoretical and Applied Mechanics (AIMETA) since its establishment in 1965. AIMETA is the official Italian association of mechanics adhering to IUTAM (International Union of Theoretical and Applied Mechanics), which organizes and coordinates a meaningful number of research activities, the most important of which are the biennial National Congress and the internationally renowned journal “Meccanica”, published by Springer. Besides collecting and organizing all related important data and information, as far as possible, by distinguishing among the five scientific areas – general mechanics, solids, structures, fluids, machines – encompassed by AIMETA, the history of the association is assumed as a proper perspective to overview the evolution of theoretical and applied mechanics in Italy over about the last fifty years. This is accomplished in the first part of the book. with also a specific focus on the mechanics of solids and structures, where the biographies of a meaningful number of recognized Italian scholars of mechanics in all areas are also provided, along with testimonials and memories by a few senior people meaningfully involved with AIMETA and Italian mechanics. The second part gives an account, although unavoidably incomplete, of recent developments of mechanical sciences in Italy, as reflected also in the activities of AIMETA and with reference to the international context. Contributions by a number of invited senior scholars, still very active, consist of overviews on some scientific themes in the various areas, summaries of achievements of research groups, expressions of research viewpoints, prospects for future developments.
| Author | : S.S Antman |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2012-02-25 |
| Genre | : Mathematics |
| ISBN | : 9780387501024 |
Download Nonlinear Problems of Elasticity Book in PDF, ePub and Kindle
Enlarged, updated, and extensively revised, this second edition illuminates specific problems of nonlinear elasticity, emphasizing the role of nonlinear material response. Opening chapters discuss strings, rods, and shells, and applications of bifurcation theory and the calculus of variations to problems for these bodies. Subsequent chapters cover tensors, three-dimensional continuum mechanics, three-dimensional elasticity , general theories of rods and shells, and dynamical problems. Each chapter includes interesting, challenging, and tractable exercises.
| Author | : Gérard A. Maugin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 337 |
| Release | : 2010-03-24 |
| Genre | : Mathematics |
| ISBN | : 1441956956 |
Download Mechanics of Generalized Continua Book in PDF, ePub and Kindle
In their 1909 publication Théorie des corps déformables, Eugène and François Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers. The included contributions provide a detailed survey of the most recent theoretical developments in the field of generalized continuum mechanics and can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics.
| Author | : Rehan Shah |
| Publisher | : |
| Total Pages | : 0 |
| Release | : 2022 |
| Genre | : |
| ISBN | : |
Download Nonlinear Mechanics of Elastic Rods Constrained to Deform on Rigid Tubular Surfaces Book in PDF, ePub and Kindle
Slender, elastic rod-like structures on or inside constrained rigid surfaces are prevalent in a wide range of engineering (drill strings in borewells, pipelines under the seabed, ocean cables), medical (stents in angioplasty of arteries), biological (DNA toroidal condensates, bacterial flagella), electronic (carbon nanotubes) and robotic (soft robots for in-pipe inspection) applications. The tendency of such rods to deform by bending, twisting, buckling or coiling into complex geometrical shapes when subjected to applied end loads can be investigated using techniques from mathematical modelling and nonlinear dynamics. However, despite some work being done in this field, a comprehensive study analysing the bifurcations and configurations of surface-constrained elastic rods is still lacking. Past research on the subject has primarily used the special Cosserat director theory of rods to exclusively obtain specialised sinusoidal, helical or localised homoclinic solutions. In light of this, the purpose of this thesis is to employ a more comprehensive variational theory of elastic two-strand braids to investigate the post-buckling behaviour of end-loaded rods subject to cylindrical and toroidal surface constraints. Methods comprising the calculus of variations and Lagrangian and Hamiltonian mechanics are utilised to procure more general types of solutions to various nonlinear boundary value problems, using both analytical and numerical approaches. The key results obtained include the determination of critical compressive and torsional buckling loads for straight rods on a cylinder and an open torus, physically realistic and purely helical solutions for helical rods on a cylinder, critical surface lift-off loads and threshold twist values for heavy rods on a cylinder and applied torsion and twist-bend instability solutions for curved rods on a closed torus. The work also comprises the development of two, new frictional contact models to investigate physically meaningful problems for rods lying on frictional rigid surfaces and a self-contained Euler-Lagrange theoretical formulation to acquire all governing equations from a single constraint-inclusive energy functional.
