Three Dimensional Contact Problems
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| Author | : A.M. Alexandrov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 422 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 940109893X |
A systematic treatment, based on Green's functions and integral equations, is given to the analytical and numerical methods and results for a great number of 3-D contact problems for elastic bodies. Semi-bounded elastic bodies (layer, cylinder, space with cylindrical or spherical cavity, 3-D wedge, special cases of which are half- and quarter-spaces, cone) and finite elastic bodies (circular plate, finite cylinder, spherical layer, spherical lens, sphere) are considered. Methods introduced in the book can also be applied in fracture mechanics, hydrodynamics, electrostatics, thermodynamics and diffusion theory, continuum mechanics, and mathematical physics, as well as by engineers and students in mathematics, mechanics, and physics.
| Author | : J.J. Kalker |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 352 |
| Release | : 1990-10-31 |
| Genre | : Science |
| ISBN | : 9780792307129 |
This book is intended for mechanicians, engineering mathematicians, and, generally for theoretically inclined mechanical engineers. It has its origin in my Master's Thesis (J 957), which I wrote under the supervision of Professor Dr. R. Timman of the Delft TH and Dr. Ir. A. D. de Pater of Netherlands Railways. I did not think that the surface of the problem had even been scratched, so I joined de Pater, who had by then become Professor in the Engineering Mechanics Lab. of the Delft TH, to write my Ph. D. Thesis on it. This thesis (1967) was weil received in railway circles, which is due more to de Pater's untiring promotion than to its merits. Still not satisfied, I feit that I needed more mathe matics, and I joined Professor Timman's group as an Associate Professor. This led to the present work. Many thanks are due to G. M. L. Gladwell, who thoroughly polished style and contents of the manuscript. Thanks are also due to my wife, herself an engineering mathematician, who read the manuscript through critically, and made many helpful comments, to G. F. M. Braat, who also read an criticised, and, in addition, drew the figures together with J. Schonewille, to Ms. A. V. M. de Wit, Ms. M. den Boef, and Ms. P. c. Wilting, who typed the manuscript, and to the Publishers, who waited patiently. Delft-Rotterdam, 17 July 1990. J. J.
| Author | : A.I. Lurie |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 1036 |
| Release | : 2010-05-30 |
| Genre | : Technology & Engineering |
| ISBN | : 3540264558 |
The classical theory of elasticity maintains a place of honour in the science ofthe behaviour ofsolids. Its basic definitions are general for all branches of this science, whilst the methods forstating and solving these problems serve as examples of its application. The theories of plasticity, creep, viscoelas ticity, and failure of solids do not adequately encompass the significance of the methods of the theory of elasticity for substantiating approaches for the calculation of stresses in structures and machines. These approaches constitute essential contributions in the sciences of material resistance and structural mechanics. The first two chapters form Part I of this book and are devoted to the basic definitions ofcontinuum mechanics; namely stress tensors (Chapter 1) and strain tensors (Chapter 2). The necessity to distinguish between initial and actual states in the nonlinear theory does not allow one to be content with considering a single strain measure. For this reason, it is expedient to introduce more rigorous tensors to describe the stress-strain state. These are considered in Section 1.3 for which the study of Sections 2.3-2.5 should precede. The mastering of the content of these sections can be postponed until the nonlinear theory is studied in Chapters 8 and 9.
| Author | : Valentin L. Popov |
| Publisher | : Springer |
| Total Pages | : 268 |
| Release | : 2014-08-19 |
| Genre | : Science |
| ISBN | : 3642538762 |
This book describes for the first time a simulation method for the fast calculation of contact properties and friction between rough surfaces in a complete form. In contrast to existing simulation methods, the method of dimensionality reduction (MDR) is based on the exact mapping of various types of three-dimensional contact problems onto contacts of one-dimensional foundations. Within the confines of MDR, not only are three dimensional systems reduced to one-dimensional, but also the resulting degrees of freedom are independent from another. Therefore, MDR results in an enormous reduction of the development time for the numerical implementation of contact problems as well as the direct computation time and can ultimately assume a similar role in tribology as FEM has in structure mechanics or CFD methods, in hydrodynamics. Furthermore, it substantially simplifies analytical calculation and presents a sort of “pocket book edition” of the entirety contact mechanics. Measurements of the rheology of bodies in contact as well as their surface topography and adhesive properties are the inputs of the calculations. In particular, it is possible to capture the entire dynamics of a system – beginning with the macroscopic, dynamic contact calculation all the way down to the influence of roughness – in a single numerical simulation model. Accordingly, MDR allows for the unification of the methods of solving contact problems on different scales. The goals of this book are on the one hand, to prove the applicability and reliability of the method and on the other hand, to explain its extremely simple application to those interested.
| Author | : Valentin L. Popov |
| Publisher | : Springer |
| Total Pages | : 357 |
| Release | : 2019-04-26 |
| Genre | : Science |
| ISBN | : 3662587092 |
This open access book contains a structured collection of the complete solutions of all essential axisymmetric contact problems. Based on a systematic distinction regarding the type of contact, the regime of friction and the contact geometry, a multitude of technically relevant contact problems from mechanical engineering, the automotive industry and medical engineering are discussed. In addition to contact problems between isotropic elastic and viscoelastic media, contact problems between transversal-isotropic elastic materials and functionally graded materials are addressed, too. The optimization of the latter is a focus of current research especially in the fields of actuator technology and biomechanics. The book takes into account adhesive effects which allow access to contact-mechanical questions about micro- and nano-electromechanical systems. Solutions of the contact problems include both the relationships between the macroscopic force, displacement and contact length, as well as the stress and displacement fields at the surface and, if appropriate, within the half-space medium. Solutions are always obtained with the simplest available method - usually with the method of dimensionality reduction (MDR) or approaches which use the solution of the non-adhesive normal contact problem to solve the respective contact problem.
| Author | : |
| Publisher | : Elsevier |
| Total Pages | : 495 |
| Release | : 1988-04-01 |
| Genre | : Technology & Engineering |
| ISBN | : 0080875416 |
This volume is a thorough introduction to contemporary research in elasticity, and may be used as a working textbook at the graduate level for courses in pure or applied mathematics or in continuum mechanics. It provides a thorough description (with emphasis on the nonlinear aspects) of the two competing mathematical models of three-dimensional elasticity, together with a mathematical analysis of these models. The book is as self-contained as possible.
| Author | : Yukio Nakajima |
| Publisher | : Springer |
| Total Pages | : 1284 |
| Release | : 2019-04-03 |
| Genre | : Science |
| ISBN | : 9811357994 |
This book highlights the mechanics of tire performance, offering detailed explanations of deriving basic equations for the fundamental properties of tires, and discussing ways to improve tire performance using these equations. It also compares the theory with practical measurements. The book commences with composite mechanics, which is the fundamental theory for belt and carcass tires, and covers classical, modified and discrete lamination theory. It then addresses the theory of tire shape and spring properties and the mechanics of tread pattern contact properties, as was well as the performance of various tires. This comprehensive book is a valuable resource for engineers involved in tire design and offers unique insights and examples of improvement of tire performances.
| Author | : Alistair R. Brown |
| Publisher | : AAPG |
| Total Pages | : 664 |
| Release | : 2011-08-20 |
| Genre | : Science |
| ISBN | : 0891813748 |
| Author | : Guido Dhondt |
| Publisher | : John Wiley & Sons |
| Total Pages | : 362 |
| Release | : 2004-11-19 |
| Genre | : Science |
| ISBN | : 0470857625 |
Though many 'finite element' books exist, this book provides a unique focus on developing the method for three-dimensional, industrial problems. This is significant as many methods which work well for small applications fail for large scale problems, which generally: are not so well posed introduce stringent computer time conditions require robust solution techniques. Starting from sound continuum mechanics principles, derivation in this book focuses only on proven methods. Coverage of all different aspects of linear and nonlinear thermal mechanical problems in solids are described, thereby avoiding distracting the reader with extraneous solutions paths. Emphasis is put on consistent representation and includes the examination of topics which are not frequently found in other texts, such as cyclic symmetry, rigid body motion and nonlinear multiple point constraints. Advanced material formulations include anisotropic hyperelasticity, large strain multiplicative viscoplasticity and single crystal viscoplasticity. Finally, the methods described in the book are implemented in the finite element software CalculiX, which is freely available (www.calculix.de; the GNU General Public License applies). Suited to industry practitioners and academic researchers alike, The Finite Element Method for Three-Dimensional Thermomechanical Applications expertly bridges the gap between continuum mechanics and the finite element method.
| Author | : Olivier Faugeras |
| Publisher | : MIT Press |
| Total Pages | : 712 |
| Release | : 1993 |
| Genre | : Computers |
| ISBN | : 9780262061582 |
This monograph by one of the world's leading vision researchers provides a thorough, mathematically rigorous exposition of a broad and vital area in computer vision: the problems and techniques related to three-dimensional (stereo) vision and motion. The emphasis is on using geometry to solve problems in stereo and motion, with examples from navigation and object recognition. Faugeras takes up such important problems in computer vision as projective geometry, camera calibration, edge detection, stereo vision (with many examples on real images), different kinds of representations and transformations (especially 3-D rotations), uncertainty and methods of addressing it, and object representation and recognition. His theoretical account is illustrated with the results of actual working programs.Three-Dimensional Computer Vision proposes solutions to problems arising from a specific robotics scenario in which a system must perceive and act. Moving about an unknown environment, the system has to avoid static and mobile obstacles, build models of objects and places in order to be able to recognize and locate them, and characterize its own motion and that of moving objects, by providing descriptions of the corresponding three-dimensional motions. The ideas generated, however, can be used indifferent settings, resulting in a general book on computer vision that reveals the fascinating relationship of three-dimensional geometry and the imaging process.
