Singular Perturbations in Elasticity Theory PDF Download

Author: Leonid S. Frank
Publisher:
ISBN:
Category : Science
Languages : en
Pages : 382

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Author: W. Eckhaus
Publisher: Springer
ISBN: 3540393323
Category : Mathematics
Languages : en
Pages : 371

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Book Description

Author: L.S. Frank
Publisher: Elsevier
ISBN: 0080875440
Category : Mathematics
Languages : en
Pages : 581

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Book Description
Singular perturbations, one of the central topics in asymptotic analysis, also play a special role in describing physical phenomena such as the propagation of waves in media in the presence of small energy dissipations or dispersions, the appearance of boundary or interior layers in fluid and gas dynamics, as well as in elasticity theory, semi-classical asymptotic approximations in quantum mechanics etc. Elliptic and coercive singular perturbations are of special interest for the asymptotic solution of problems which are characterized by boundary layer phenomena, e.g. the theory of thin buckling plates, elastic rods and beams. This first volume deals with linear singular perturbations (on smooth manifolds without boundary) considered as equicontinuous linear mappings between corresponding families of Sobolev-Slobodetski's type spaces of vectorial order.

Author: Donald R. Smith
Publisher: Cambridge University Press
ISBN: 9780521300421
Category : Mathematics
Languages : en
Pages : 532

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Book Description
Introduction to singular perturbation problems. Since the nature of the nonuniformity can vary from case to case, the author considers and solves a variety of problems, mostly for ordinary differential equations.

Author: Robert E. O'Malley
Publisher: Springer
ISBN: 3319119249
Category : Mathematics
Languages : en
Pages : 263

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Book Description
This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A particularly valuable bonus are the historical remarks. These remarks are found throughout the manuscript. They demonstrate the growth of mathematical thinking on this topic by engineers and mathematicians. The book focuses on detailing how the various methods are to be applied. These are illustrated by a number and variety of examples. Readers are expected to have a working knowledge of elementary ordinary differential equations, including some familiarity with power series techniques, and of some advanced calculus. Dr. O'Malley has written a number of books on singular perturbations. This book has developed from many of his works in the field of perturbation theory.

Author: S. A. Lomov
Publisher: American Mathematical Soc.
ISBN: 9780821897416
Category : Mathematics
Languages : en
Pages : 402

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Book Description
This book is aimed at researchers and students in physics, mathematics, and engineering. It contains the first systematic presentation of a general approach to the integration of singularly perturbed differential equations describing nonuniform transitions, such as the occurrence of a boundary layer, discontinuities, boundary effects and so on. The method of regularization of singular perturbations presented here can be applied to the asymptotic integration of systems of ordinary and partial differential equations.

Author: J.K. Kevorkian
Publisher: Springer Science & Business Media
ISBN: 1461239680
Category : Mathematics
Languages : en
Pages : 642

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Book Description
This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter.

Author: Tosio Kato
Publisher: Springer Science & Business Media
ISBN: 3662126788
Category : Mathematics
Languages : en
Pages : 610

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Author:
Publisher: UM Libraries
ISBN:
Category : Education, Higher
Languages : en
Pages : 1400

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Book Description

Author: Oleksandra Datsyshyn
Publisher: Springer
ISBN: 3030230694
Category : Science
Languages : en
Pages : 325

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Book Description
This book focuses on surface layers fracture of cyclical contacting bodies (machine parts). Calculation models and calculating procedures of stress-strain states of cyclically contacting solids with cracks, are included. Recommendations for the optimization of operating parameters of joints (contact stresses magnitude, friction/lubrication conditions, materials crack resistance etc) for elements of rolling pairs (wheel–rail systems, backup roll – working roll of rolling mills etc.) and some fretting pairs are formulated.