Nonlinear Mechanics of Elastic Rods Constrained to Deform on Rigid Tubular Surfaces PDF Download
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Author: Rehan Shah
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
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.
Author: Rehan Shah
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
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.
Author: Oliver M. O'Reilly
Publisher: Springer
ISBN: 9783319844374
Category : Mathematics
Languages : en
Pages : 0
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Book Description
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: Irna Lyublinskaya
Publisher:
ISBN: 9781938168932
Category : Physics
Languages : en
Pages : 1665
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Book Description
"This introductory, algebra-based, two-semester college physics book is grounded with real-world examples, illustrations, and explanations to help students grasp key, fundamental physics concepts. ... This online, fully editable and customizable title includes learning objectives, concept questions, links to labs and simulations, and ample practice opportunities to solve traditional physics application problems."--Website of book.
Author: Alain Goriely
Publisher: Springer
ISBN: 038787710X
Category : Mathematics
Languages : en
Pages : 651
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Book Description
This monograph presents a general mathematical theory for biological growth. It provides both a conceptual and a technical foundation for the understanding and analysis of problems arising in biology and physiology. The theory and methods are illustrated on a wide range of examples and applications. A process of extreme complexity, growth plays a fundamental role in many biological processes and is considered to be the hallmark of life itself. Its description has been one of the fundamental problems of life sciences, but until recently, it has not attracted much attention from mathematicians, physicists, and engineers. The author herein presents the first major technical monograph on the problem of growth since D’Arcy Wentworth Thompson’s 1917 book On Growth and Form. The emphasis of the book is on the proper mathematical formulation of growth kinematics and mechanics. Accordingly, the discussion proceeds in order of complexity and the book is divided into five parts. First, a general introduction on the problem of growth from a historical perspective is given. Then, basic concepts are introduced within the context of growth in filamentary structures. These ideas are then generalized to surfaces and membranes and eventually to the general case of volumetric growth. The book concludes with a discussion of open problems and outstanding challenges. Thoughtfully written and richly illustrated to be accessible to readers of varying interests and background, the text will appeal to life scientists, biophysicists, biomedical engineers, and applied mathematicians alike.
Author: T. W. Clyne
Publisher: Cambridge University Press
ISBN: 1108837891
Category : Science
Languages : en
Pages : 297
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Book Description
Discover a novel approach to the subject, providing detailed information about established and innovative mechanical testing procedures.
Author:
Publisher:
ISBN:
Category : Mechanics, Applied
Languages : en
Pages : 348
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Book Description
Author: Martin H. Sadd
Publisher: Elsevier
ISBN: 008047747X
Category : Technology & Engineering
Languages : en
Pages : 474
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Book Description
Although there are several books in print dealing with elasticity, many focus on specialized topics such as mathematical foundations, anisotropic materials, two-dimensional problems, thermoelasticity, non-linear theory, etc. As such they are not appropriate candidates for a general textbook. This book provides a concise and organized presentation and development of general theory of elasticity. This text is an excellent book teaching guide. - Contains exercises for student engagement as well as the integration and use of MATLAB Software - Provides development of common solution methodologies and a systematic review of analytical solutions useful in applications of
Author: Anthony C. Fischer-Cripps
Publisher: Springer Science & Business Media
ISBN: 1475759436
Category : Technology & Engineering
Languages : en
Pages : 283
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Book Description
This new edition of Nanoindentation includes a dedicated chapter on thin films, new material on dynamic analysis and creep, accounts of recent research, and three new appendices on nonlinear least squares fitting, frequently asked questions, and specifications for a nanoindentation instrument. Nanoindentation Second Edition is intended for those who are entering the field for the first time and to act as a reference for those already conversant with the technique.
Author: Vladislav A. Yastrebov
Publisher: John Wiley & Sons
ISBN: 1118648056
Category : Mathematics
Languages : en
Pages : 303
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Book Description
Computational contact mechanics is a broad topic which brings together algorithmic, geometrical, optimization and numerical aspects for a robust, fast and accurate treatment of contact problems. This book covers all the basic ingredients of contact and computational contact mechanics: from efficient contact detection algorithms and classical optimization methods to new developments in contact kinematics and resolution schemes for both sequential and parallel computer architectures. The book is self-contained and intended for people working on the implementation and improvement of contact algorithms in a finite element software. Using a new tensor algebra, the authors introduce some original notions in contact kinematics and extend the classical formulation of contact elements. Some classical and new resolution methods for contact problems and associated ready-to-implement expressions are provided. Contents: 1. Introduction to Computational Contact. 2. Geometry in Contact Mechanics. 3. Contact Detection. 4. Formulation of Contact Problems. 5. Numerical Procedures. 6. Numerical Examples. About the Authors Vladislav A. Yastrebov is a postdoctoral-fellow in Computational Solid Mechanics at MINES ParisTech in France. His work in computational contact mechanics was recognized by the CSMA award and by the Prix Paul Caseau of the French Academy of Technology and Electricité de France.
Author: Morton E. Gurtin
Publisher: SIAM
ISBN: 0898711681
Category : Technology & Engineering
Languages : en
Pages : 58
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Book Description
This monograph presents a derivation of the basic equations of the theory of finite elasticity.
