Download or read book Uniqueness Theorems in Linear Elasticity by R J Knops and L E Payne written by Robin John Knops and published by . This book was released on 1971 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Uniqueness Theorems in Linear Elasticity written by Robin J. Knops and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical result for uniqueness in elasticity theory is due to Kirchhoff. It states that the standard mixed boundary value problem for a homogeneous isotropic linear elastic material in equilibrium and occupying a bounded three-dimensional region of space possesses at most one solution in the classical sense, provided the Lame and shear moduli, A and J1 respectively, obey the inequalities (3 A + 2 J1) > 0 and J1>O. In linear elastodynamics the analogous result, due to Neumann, is that the initial-mixed boundary value problem possesses at most one solution provided the elastic moduli satisfy the same set of inequalities as in Kirchhoffs theorem. Most standard textbooks on the linear theory of elasticity mention only these two classical criteria for uniqueness and neglect altogether the abundant literature which has appeared since the original publications of Kirchhoff. To remedy this deficiency it seems appropriate to attempt a coherent description ofthe various contributions made to the study of uniqueness in elasticity theory in the hope that such an exposition will provide a convenient access to the literature while at the same time indicating what progress has been made and what problems still await solution. Naturally, the continuing announcement of new results thwarts any attempt to provide a complete assessment. Apart from linear elasticity theory itself, there are several other areas where elastic uniqueness is significant.
Download or read book Canadian Mathematical Bulletin written by and published by . This book was released on 1975 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Theories of Elasticity and Thermoelasticity written by Clifford Truesdell and published by Springer. This book was released on 2013-12-17 with total page 755 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Elasticity and Geomechanics written by R. O. Davis and published by Cambridge University Press. This book was released on 1996-04-26 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: A concise examination of the use of elasticity in solving geotechnical engineering problems.
Download or read book A Primer in Elasticity written by P. Podio-Guidugli and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 114 pages. Available in PDF, EPUB and Kindle. Book excerpt: I want to thank R. L. Fosdick, M. E. Gurtin and W. O. Williams for their detailed criticism of the manuscript. I also thank F. Davi, M. Lembo, P. Nardinocchi and M. Vianello for valuable remarks prompted by their reading of one or another of the many previous drafts, from 1988 to date. Since it has taken me so long to bring this writing to its present form, many other colleagues and students have episodically offered useful comments and caught mistakes: a list would risk to be incomplete, but I am heartily grateful to them all. Finally, I thank V. Nicotra for skillfully transforming my hand sketches into book-quality figures. P. PODIO-GUIDUGLI Roma, April 2000 Journal of Elasticity 58: 1-104,2000. 1 P. Podio-Guidugli, A Primer in Elasticity. © 2000 Kluwer Academic Publishers. CHAPTER I Strain 1. Deformation. Displacement Let 8 be a 3-dimensional Euclidean space, and let V be the vector space associated with 8. We distinguish a point p E 8 both from its position vector p(p):= (p-o) E V with respect to a chosen origin 0 E 8 and from any triplet (~1, ~2, ~3) E R3 of coordinates that we may use to label p. Moreover, we endow V with the usual inner product structure, and orient it in one of the two possible manners. It then makes sense to consider the inner product a .
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.
Download or read book Elasticity in Engineering Mechanics written by Arthur P. Boresi and published by John Wiley & Sons. This book was released on 2010-12-01 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elasticity in Engineering Mechanics has been prized by many aspiring and practicing engineers as an easy-to-navigate guide to an area of engineering science that is fundamental to aeronautical, civil, and mechanical engineering, and to other branches of engineering. With its focus not only on elasticity theory, including nano- and biomechanics, but also on concrete applications in real engineering situations, this acclaimed work is a core text in a spectrum of courses at both the undergraduate and graduate levels, and a superior reference for engineering professionals.
Download or read book Partial Differential Equations in Mechanics 1 written by A.P.S. Selvadurai and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.
Download or read book Partial Differential Equations in Mechanics 2 written by A.P.S. Selvadurai and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.
Download or read book Multiscale Potential Theory written by Willi Freeden and published by Springer Science & Business Media. This book was released on 2004-09-21 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text/reference provides a basic foundation for practitioners, researchers, and students interested in any of the diverse areas of multiscale (geo)potential theory. New mathematical methods are developed enabling the gravitational potential of a planetary body to be modeled using a continuous flow of observations from land or satellite devices. Harmonic wavelets methods are introduced, as well as fast computational schemes and various numerical test examples. Presented are multiscale approaches for numerous geoscientific problems, including geoidal determination, magnetic field reconstruction, deformation analysis, and density variation modelling With exercises at the end of each chapter, the book may be used as a textbook for graduate-level courses in geomathematics, applied mathematics, and geophysics. The work is also an up-to-date reference text for geoscientists, applied mathematicians, and engineers.
Download or read book The Mechanics of Constitutive Modeling written by Niels Saabye Ottosen and published by Elsevier. This book was released on 2005-09-28 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: Constitutive modelling is the mathematical description of how materials respond to various loadings. This is the most intensely researched field within solid mechanics because of its complexity and the importance of accurate constitutive models for practical engineering problems. Topics covered include: Elasticity - Plasticity theory - Creep theory - The nonlinear finite element method - Solution of nonlinear equilibrium equations - Integration of elastoplastic constitutive equations - The thermodynamic framework for constitutive modelling – Thermoplasticity - Uniqueness and discontinuous bifurcations • More comprehensive in scope than competitive titles, with detailed discussion of thermodynamics and numerical methods. • Offers appropriate strategies for numerical solution, illustrated by discussion of specific models. • Demonstrates each topic in a complete and self-contained framework, with extensive referencing.
Download or read book Spherical Functions of Mathematical Geosciences written by Willi Freeden and published by Springer Science & Business Media. This book was released on 2008-12-14 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, the Geomathematics Group, TU Kaiserslautern, has worked to set up a theory of spherical functions of mathematical physics. This book is a collection of all the material that group generated during the process.
Download or read book Treatise on Classical Elasticity written by Petre P. Teodorescu and published by Springer Science & Business Media. This book was released on 2014-07-08 with total page 805 pages. Available in PDF, EPUB and Kindle. Book excerpt: Deformable solids have a particularly complex character; mathematical modeling is not always simple and often leads to inextricable difficulties of computation. One of the simplest mathematical models and, at the same time, the most used model, is that of the elastic body – especially the linear one. But, notwithstanding its simplicity, even this model of a real body may lead to great difficulties of computation. The practical importance of a work about the theory of elasticity, which is also an introduction to the mechanics of deformable solids, consists of the use of scientific methods of computation in a domain in which simplified methods are still used. This treatise takes into account the consideration made above, with special attention to the theoretical study of the state of strain and stress of a deformable solid. The book draws on the known specialized literature, as well as the original results of the author and his 50+ years experience as Professor of Mechanics and Elasticity at the University of Bucharest. The construction of mathematical models is made by treating geometry and kinematics of deformation, mechanics of stresses and constitutive laws. Elastic, plastic and viscous properties are thus put in evidence and the corresponding theories are developed. Space problems are treated and various particular cases are taken into consideration. New solutions for boundary value problems of finite and infinite domains are given and a general theory of concentrated loads is built. Anisotropic and non-homogeneous bodies are studied as well. Cosserat type bodies are also modeled. The connection with thermal and viscous phenomena will be considered too. Audience: researchers in applied mathematics, mechanical and civil engineering.
Download or read book Mathematical Foundations of Elasticity written by Jerrold E. Marsden and published by Courier Corporation. This book was released on 2012-10-25 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graduate-level study approaches mathematical foundations of three-dimensional elasticity using modern differential geometry and functional analysis. It presents a classical subject in a modern setting, with examples of newer mathematical contributions. 1983 edition.
Download or read book Weighted Energy Methods in Fluid Dynamics and Elasticity written by Giovanni P. Galdi and published by Springer. This book was released on 2006-11-14 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mathematical Aspects of Multi Porosity Continua written by Brian Straughan and published by Springer. This book was released on 2017-11-30 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to describing theories for porous media where such pores have an inbuilt macro structure and a micro structure. For example, a double porosity material has pores on a macro scale, but additionally there are cracks or fissures in the solid skeleton. The actual body is allowed to deform and thus the underlying theory is one of elasticity. Various different descriptions are reviewed. Chapter 1 introduces the classical linear theory of elastodynamics together with uniqueness and continuous dependence results. Chapters 2 and 3 review developments of theories for double and triple porosity using a pressure-displacement structure and also using voids-displacement. Chapter 4 compares various aspects of the pressure-displacement and voids-displacement theories via uniqueness studies and wave motion analysis. Mathematical analyses of double and triple porosity materials are included concentrating on uniqueness and stability studies in chapters 5 to 7. In chapters 8 and 9 the emphasis is on wave motion in double porosity materials with special attention paid to nonlinear waves. The final chapter embraces a novel area where an elastic body with a double porosity structure is analyzed, but the thermodynamics allows for heat to travel as a wave rather than simply by diffusion. This book will be of value to mathematicians, theoretical engineers and other practitioners who are interested in double or triple porosity elasticity and its relevance to many diverse applications.
