Author: A.A. Ivanov
Publisher: Springer Science & Business Media
ISBN: 9789028600362
Category : Mathematics
Languages : en
Pages : 358

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Book Description

Author: A.A. Ivanov
Publisher: Springer
ISBN: 9789048184620
Category : Mathematics
Languages : en
Pages : 330

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Author: R.S. Anderssen
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 280

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Book Description
This publication reports the proceedings of a one-day seminar on The Application and Numerical Solution of Integral Equations held at the Australian National University on Wednesday, November 29, 1978. It was organized by the Computing Research Group, Australian National University and the Division of Mathematics and Statistics, CSIRO. Due to unforeseen circumstances, Dr M.L. Dow was unable to participate. At short notice, Professor D. Elliott reviewed Cauchy singular integral equations, but a paper on same is not included in these proceedings. The interested reader is referred to the recent translation of V.V. Ivanov, The Theory of Approximate Methods and their Application to the Numerical Solution of Singular Integral Equations, Noordhoff International Publishers, Leyden, 1976. An attempt was made to structure the program to the extent that the emphasis was on the numerical solution of integral equations for which known applications exist along with explanations of how and why integral equation formalisms arise. In addition, the programme reflected the broad classification of most integral equations as either singular or non singular, as either Fredholm or Volterra and as either first or second kind.

Author: M. A. Goldberg
Publisher: Springer Science & Business Media
ISBN: 1475714661
Category : Science
Languages : en
Pages : 351

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Author: E.G. Ladopoulos
Publisher: Springer Science & Business Media
ISBN: 3662042916
Category : Technology & Engineering
Languages : en
Pages : 569

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Book Description
The present book deals with the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are currently used in many fields of engineering mechanics with applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, fluid mechanics, aerodynamics and elastodynamics. These types of singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new technology of the twentieth-one century. Chapter 1 is devoted with a historical report and an extended outline of References, for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations. Chapter 2 provides a finite-part singular integral representation analysis in Lp spaces and in general Hilbert spaces. In the same Chapter are investigated all possible approximation methods for the numerical evaluation of the finite-part singular integral equations, as closed form solutions for the above type of integral equations are available only in simple cases. Also, Chapter 2 provides further a generalization of the well known Sokhotski-Plemelj formulae and the Nother theorems, for the case of a finite-part singular integral equation.

Author: Kendall E. Atkinson
Publisher: Cambridge University Press
ISBN: 0521583918
Category : Mathematics
Languages : en
Pages : 572

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Book Description
This book provides an extensive introduction to the numerical solution of a large class of integral equations.

Author: Michael A. Golberg
Publisher: Springer Science & Business Media
ISBN: 1489925937
Category : Mathematics
Languages : en
Pages : 428

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Book Description
In 1979, I edited Volume 18 in this series: Solution Methods for Integral Equations: Theory and Applications. Since that time, there has been an explosive growth in all aspects of the numerical solution of integral equations. By my estimate over 2000 papers on this subject have been published in the last decade, and more than 60 books on theory and applications have appeared. In particular, as can be seen in many of the chapters in this book, integral equation techniques are playing an increas ingly important role in the solution of many scientific and engineering problems. For instance, the boundary element method discussed by Atkinson in Chapter 1 is becoming an equal partner with finite element and finite difference techniques for solving many types of partial differential equations. Obviously, in one volume it would be impossible to present a complete picture of what has taken place in this area during the past ten years. Consequently, we have chosen a number of subjects in which significant advances have been made that we feel have not been covered in depth in other books. For instance, ten years ago the theory of the numerical solution of Cauchy singular equations was in its infancy. Today, as shown by Golberg and Elliott in Chapters 5 and 6, the theory of polynomial approximations is essentially complete, although many details of practical implementation remain to be worked out.

Author: I. K. Lifanov
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110926040
Category : Mathematics
Languages : en
Pages : 488

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Book Description
This monograph is divided into five parts and opens with elements of the theory of singular integral equation solutions in the class of absolutely integrable and non-integrable functions. The second part deals with elements of potential theory for the Helmholtz equation, especially with the reduction of Dirichlet and Neumann problems for Laplace and Helmholtz equations to singular integral equations. Part three contains methods of calculation for different one-dimensional and two-dimensional singular integrals. In this part, quadrature formulas of discrete vortex pair type in the plane case and closed vortex frame type in the spatial case for singular integrals are described for the first time. These quadrature formulas are applied to numerical solutions of singular integral equations of the 1st and 2nd kind with constant and variable coefficients, in part four of the book. Finally, discrete mathematical models of some problems in aerodynamics, electrodynamics and elasticity theory are given.

Author: O.O. Ochoa
Publisher: Springer Science & Business Media
ISBN: 9401579954
Category : Science
Languages : en
Pages : 222

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Book Description
Composite materials are increasingly used in aerospace, underwater, and automotive structures. To take advantage of the full potential of composite materials, structural analysts and designers must have accurate mathematical models and design methods at their disposal. The objective of this monograph is to present the laminated plate theories and their finite element models to study the deformation, strength and failure of composite structures. Emphasis is placed on engineering aspects, such as the analytical descriptions, effective analysis tools, modeling of physical features, and evaluation of approaches used to formulate and predict the response of composite structures. The first chapter presents an overview of the text. Chapter 2 is devoted to the introduction of the definitions and terminology used in composite materials and structures. Anisotropic constitutive relations and Iaminate plate theories are also reviewed. Finite element models of laminated composite plates are presented in Chapter 3. Numerical evaluation of element coefficient matrices, post-computation of strains and stresses, and sample examples of laminated plates in bending and vibration are discussed. Chapter 4 introduces damage and failure criteria in composite laminates. Finally, Chapter 5 is dedicated to case studies involving various aspects and types of composite structures. Joints, cutouts, woven composites, environmental effects, postbuckling response and failure of composite laminates are discussed by considering specific examples.

Author: R. S. Azad
Publisher: Springer Science & Business Media
ISBN: 9401117853
Category : Technology & Engineering
Languages : en
Pages : 589

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Book Description
While I was participating in the IUTAM Symposium on Structure of Turbulence and Drag Reduction in Zurich, Switzerland, in 1989, I was approached by Prof. Dr. Themistocles Dracos to give a course oflectures on the Atmospheric Boundary Layer during my sabbatical leave at Eidgenossische Technische Hochschule (ETH) Zurich - Hoenggerberg in 1991. His reason for the suggestion was the growing interest in the environment and its dynamics created by flow in the Atmospheric Boundary Layer. I have been teaching boundary layer to undergraduate and graduate students for more than twenty five years, so I agreed to give a series of lectures on boundary layer of the atmosphere. From the start I thought very seriously about the problem and consulted all the published works in English on the Atmospheric Boundary Layer (ABL). First consider the topography of the Earth which has oceans calm and turbulent, mountain ranges of height up to 9 km, lands of variable height with forests, food growing vegetable and deserts. The shape of the Earth is nearly spherical except at the north and south poles. Sun supplies the energy to drive circulation of air around the Earth's atmosphere which for all practical purposes occupies the region up to about 10 to 11 km. This brief scenerio of Earth's topography reveals the complexity of flow very close to the Earth's surface that is hardly flat except at the oceans' surface which consists of about 70% of the total Earth's surface.