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This is the first and only monograph on this subject, and provides a systematic presentation of theoretical fundamentals of the mechanics of rods as well as numerical methods used for practical purposes. Includes problems and solutions for self-study.
The volume is devoted to mechanics of rods, which is a branch of mechanics of deformable bodies. The main goal of the book is to present systematically theoretical fundamentals of mechanics of rods as well as numerical methods used for practical purposes. The monograph is concerned with the most general statements of the problems in mechanics of rods. Various types of external loads that a rod may be subject to are discussed. Advanced technique that includes vector is used in the derivation of linear analysis, linear algebra, and distributions and nonlinear equilibrium equations. The use of this technique helps us to make transformations and rearrangement of equations more transparent and compact. Theoretical basics of rods interacting with external and internal flows of fluid and the derivation of the formulas for the hydrodynamic and aerody namic forces are presented. The book consists of six chapters and appendices and may be convention ally divided into two parts. That is, Chapters 1 to 3 contain, in the main, theoretical material, whereas Chapters 4 to6 illustrate the application of the theoretical results to problems of practical interest. Problems for self-study are found in Chapters 1, 3, 4, and 5. The solutions to most of the problems are given in Appendix B. The monograph is addressed to scientists, institutional and industrial re searchers, lecturers, and graduate students.
Modeling Nonlinear Problems in the Mechanics of Strings and Rods by Oliver M. O'Reilly Pdf
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.
A Primer on the Kinematics of Discrete Elastic Rods by M. Khalid Jawed,Alyssa Novelia,Oliver M. O'Reilly Pdf
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 : Alan R Champneys,G W Hunt,J Michael T Thompson Publisher : World Scientific Page : 398 pages File Size : 45,8 Mb Release : 1999-11-30 Category : Science ISBN : 9789814494625
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Structure-preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics by Peter Betsch Pdf
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Structure And Dynamics Of Materials In The Mesoscopic Domain - Proceedings Of The Fourth Royal Society-unilever Indo-uk Forum In Materials Science And Engineering by B D Kulkarni,Moti Lal,Ragunath A Mashelkar,V M Naik Pdf
The mesoscopic domain encompasses structures that are best described in terms of the time and length scales which lie between the two extremes of the molecular and the phenomenological description of materials. Important examples of such structures are self-assemblies, emulsions, gels, colloids aggregates and macromolecules networks. Discussing the key advances made in recent years in our understanding of both equilibrium and dynamic aspects of mesoscopic structures, most talks at the conference were given by world class researchers in the field, who included, among others, Prof J S Higgins, CBE, FRS (Imperial College, London), Prof D Frenkel (FOM, Amsterdam), Prof M E Cates (Edinburgh), Prof R C Ball (Warwick), Prof S Ramaswamy (Indian Institute of Science, Bangalore), Prof R Pandit (Bangalore), Dr J A Yeomans (Oxford), Prof S Puri (JNU, New Delhi), Dr D Langevin (CRPP, Bordeaux), and Prof W G M Agterof (Unilever Research, Vlaardingen).
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Stability Theory of Elastic Rods by Teodor M. Atanackovic Pdf
This book treats stability problems of equilibrium states of elastic rods. Euler energy and dynamical methods of stability analysis are introduced and stability criteria for each method is developed. Stability analysis is accompanied by a number of classical conservative and non-conservative, two- and three-dimensional problems. Some problems are treated by all three methods. Many generalized versions of known problems are presented (heavy vertical rod, rotating rod, Greenhill's problem, Beck's column, Pflger's rod, strongest column, etc.). The generalizations consist in using either a generalized form of constitutive equations or a more general form of loading, or both. Special attention is paid to the influence of shear stresses and axis compressibility on the value of the critical load. Variational methods are applied to obtain estimates of the critical load and maximal deflection in the post-critical state, in a selected number of examples.
Stability Theory Of Elastic Rods by Teodor Atanackovic Pdf
This book treats stability problems of equilibrium states of elastic rods. Euler energy and dynamical methods of stability analysis are introduced and stability criteria for each method is developed. Stability analysis is accompanied by a number of classical conservative and non-conservative, two- and three-dimensional problems. Some problems are treated by all three methods. Many generalized versions of known problems are presented (heavy vertical rod, rotating rod, Greenhill's problem, Beck's column, Pflüger's rod, strongest column, etc.). The generalizations consist in using either a generalized form of constitutive equations or a more general form of loading, or both. Special attention is paid to the influence of shear stresses and axis compressibility on the value of the critical load. Variational methods are applied to obtain estimates of the critical load and maximal deflection in the post-critical state, in a selected number of examples.
Multiscale Modeling in Biomechanics and Mechanobiology by Suvranu De,Wonmuk Hwang,Ellen Kuhl Pdf
Presenting a state-of-the-art overview of theoretical and computational models that link characteristic biomechanical phenomena, this book provides guidelines and examples for creating multiscale models in representative systems and organisms. It develops the reader's understanding of and intuition for multiscale phenomena in biomechanics and mechanobiology, and introduces a mathematical framework and computational techniques paramount to creating predictive multiscale models. Biomechanics involves the study of the interactions of physical forces with biological systems at all scales – including molecular, cellular, tissue and organ scales. The emerging field of mechanobiology focuses on the way that cells produce and respond to mechanical forces – bridging the science of mechanics with the disciplines of genetics and molecular biology. Linking disparate spatial and temporal scales using computational techniques is emerging as a key concept in investigating some of the complex problems underlying these disciplines. Providing an invaluable field manual for graduate students and researchers of theoretical and computational modelling in biology, this book is also intended for readers interested in biomedical engineering, applied mechanics and mathematical biology.
