Boundary Integral Equation Analyses Of Singular Potential And Biharmonic Problems
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Boundary Integral Equation Analyses Of Singular Potential And Biharmonic Problems
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Author : D. B. Ingham
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Boundary Integral Equation Analyses Of Singular Potential And Biharmonic Problems written by D. B. Ingham and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Technology & Engineering categories.
Harmonic and biharmonic boundary value problems (BVP) arising in physical situations in fluid mechanics are, in general, intractable by analytic techniques. In the last decade there has been a rapid increase in the application of integral equation techniques for the numerical solution of such problems [1,2,3]. One such method is the boundary integral equation method (BIE) which is based on Green's Formula [4] and enables one to reformulate certain BVP as integral equations. The reformulation has the effect of reducing the dimension of the problem by one. Because discretisation occurs only on the boundary in the BIE the system of equations generated by a BIE is considerably smaller than that generated by an equivalent finite difference (FD) or finite element (FE) approximation [5]. Application of the BIE in the field of fluid mechanics has in the past been limited almost entirely to the solution of harmonic problems concerning potential flows around selected geometries [3,6,7]. Little work seems to have been done on direct integral equation solution of viscous flow problems. Coleman [8] solves the biharmonic equation describing slow flow between two semi infinite parallel plates using a complex variable approach but does not consider the effects of singularities arising in the solution domain. Since the vorticity at any singularity becomes unbounded then the methods presented in [8] cannot achieve accurate results throughout the entire flow field.
Boundary Integral Equation Analyses Of Singular Potential And Biharmonic Problems
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Author : D. B Ingham
language : en
Publisher:
Release Date : 1984-08-01
Boundary Integral Equation Analyses Of Singular Potential And Biharmonic Problems written by D. B Ingham and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-08-01 with categories.
Boundary Integral Equation Analysis Of Singular Potential And Biharmonic Problems
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Author : Derek B. Ingham
language : en
Publisher:
Release Date : 1984
Boundary Integral Equation Analysis Of Singular Potential And Biharmonic Problems written by Derek B. Ingham and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Boundary value problems categories.
Boundary Integral And Singularity Methods For Linearized Viscous Flow
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Author : C. Pozrikidis
language : en
Publisher: Cambridge University Press
Release Date : 1992-02-28
Boundary Integral And Singularity Methods For Linearized Viscous Flow written by C. Pozrikidis and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-02-28 with Mathematics categories.
In addition to theory, this study focuses on practical application and computer implementation in a coherent introduction to boundary integrals, boundary element and singularity methods for steady and unsteady flow at zero Reynolds numbers.
The Numerical Solution Of Integral Equations Of The Second Kind
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Author : Kendall E. Atkinson
language : en
Publisher: Cambridge University Press
Release Date : 1997-06-28
The Numerical Solution Of Integral Equations Of The Second Kind written by Kendall E. Atkinson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-28 with Mathematics categories.
This book provides an extensive introduction to the numerical solution of a large class of integral equations.
Numerical Solution Of Integral Equations
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Author : Michael A. Golberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Numerical Solution Of Integral Equations written by Michael A. Golberg and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
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.
Boundary Element Analysis Of Nonhomogeneous Biharmonic Phenomena
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Author : Charles V. Camp
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Boundary Element Analysis Of Nonhomogeneous Biharmonic Phenomena written by Charles V. Camp and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Technology & Engineering categories.
At the date of this writing, there is no question that the boundary element method has emerged as one of the major revolutions on the engineering science of computational mechanics. The emergence of the technique from relative obscurity to a cutting edge engineering analysis tool in the short space of basically a ten to fifteen year time span is unparalleled since the advent of the finite element method. At the recent international conference BEM XI, well over one hundred papers were presented and many were pub lished in three hard-bound volumes. The exponential increase in interest in the subject is comparable to that shown in the early days of finite elements. The diversity of appli cations of BEM, the broad base of interested parties, and the ever-increasing presence of the computer as an engineering tool are probably the reasons for the upsurge in pop ularity of BEM among researchers and industrial practitioners. Only in the past few years has the BEM audience become large enough that we have seen the development of specialty books on specific applications of the boundary element method. The present text is one such book. In this work, we have attempted to present a self-contained treatment of the analysis of physical phenomena governed by equations containing biharmonic operators. The biharmonic operator defines a very important class of fourth-order PDE problems which includes deflections of beams and thin plates, and creeping flow of viscous fluids.
The Boundary Integral Equatio Method In Axisymmetric Stress Analysis Problems
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Author : Adib A. Bakr
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-12
The Boundary Integral Equatio Method In Axisymmetric Stress Analysis Problems written by Adib A. Bakr and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-12 with Science categories.
The Boundary Integral Equation (BIE) or the Boundary Element Method is now well established as an efficient and accurate numerical technique for engineering problems. This book presents the application of this technique to axisymmetric engineering problems, where the geometry and applied loads are symmetrical about an axis of rotation. Emphasis is placed on using isoparametric quadratic elements which exhibit excellent modelling capabilities. Efficient numerical integration schemes are also presented in detail. Unlike the Finite Element Method (FEM), the BIE adaptation to axisymmetric problems is not a straightforward modification of the two or three-dimensional formulations. Two approaches can be used; either a purely axisymmetric approach based on assuming a ring of load, or, alternatively, integrating the three-dimensional fundamental solution of a point load around the axis of rotational symmetry. Throughout this ~ook, both approaches are used and are shown to arrive at identi cal solutions. The book starts with axisymmetric potential problems and extends the formulation to elasticity, thermoelasticity, centrifugal and fracture mechanics problems. The accuracy of the formulation is demonstrated by solving several practical engineering problems and comparing the BIE solution to analytical or other numerical methods such as the FEM. This book provides a foundation for further research into axisymmetric prob lems, such as elastoplasticity, contact, time-dependent and creep prob lems.
Slope Analysis Using Boundary Elements
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Author : Yansheng Jiang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Slope Analysis Using Boundary Elements written by Yansheng Jiang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Science categories.
The aim of this book is to provide a new angle on the analysis of slope stability with the Boundary Element Method. The main advantages of BEM are the reduction of the dimensionality of the problem to be solved and accurate selective calculation of internal stresses. This makes it possible, as shown in the book, to develop the algorithms of slip surface analysis of slope more accurate, more rigorous and more easy to be used than in the conventional limit equilibrium methods. The full elastoplastic analysis of slope is also investigated. Besides, the interested reader can find a detailed study of Melan's fundamental solution such as its displacements, its corresponding Galerkin tensor and the treatment of body forces in the half-plan. The basic theory of BEM is outlined in the book so that undergraduate and graduate students of civil engineering, mining engineering and engineering geology can read it without difficulty.
Boundary Element Analysis Of Viscous Flow
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Author : Koichi Kitagawa
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-08
Boundary Element Analysis Of Viscous Flow written by Koichi Kitagawa and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-08 with Science categories.
In recent years, the performance of digital computers has been improved by the rapid development of electronics at remarkable speed. In addition, substantial research has been carried out in developing numerical analysis techniques. Nowadays, a variety of problems in the engineering and scientific fields can be solved by using not only super computers but also personal computers. After the first book titled "Boundary Element" was published by Brebbia in 1978, the boundary element method (BEM) has been recognized as a powerful numerical technique which has some advantages over the finite difference method (FDM) and finite element method (FEM). A great amount of research has been carried out on the applications of BEM to various problems. The numerical analysis of fluid mechanics and heat transfer problems plays a key role in analysing some phenomena and it has become recognized as a new research field called "Computational Fluid Dynamics". In partic ular, the analysis of viscous flow including thermal convection phenomena is one of the most important problems in engineering fields. The FDM and FEM have been generally .applied to solve these problems because of non singularities of governing equations.