Singular Integrals In Boundary Element Methods
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Singular Integrals In Boundary Element Methods
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Author : Vladimír Sládek
language : en
Publisher: Computational Mechanics
Release Date : 1998
Singular Integrals In Boundary Element Methods written by Vladimír Sládek and has been published by Computational Mechanics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.
A text in singular integrals in boundary element methods. Topics covered include: treatment in crack problems; regularization of boundary integral equations by the derivative transfer method; regularization and evaluation of singular domain integrals in boundary element methods and others.
Advanced Formulations In Boundary Element Methods
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Author : M. H. Aliabadi
language : en
Publisher:
Release Date : 1993
Advanced Formulations In Boundary Element Methods written by M. H. Aliabadi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
A Projection Transformation Method For Nearly Singular Surface Boundary Element Integrals
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Author : Ken Hayami
language : en
Publisher: Springer
Release Date : 2012-04-07
A Projection Transformation Method For Nearly Singular Surface Boundary Element Integrals written by Ken Hayami and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-07 with Mathematics categories.
In three dimensional boundary element analysis, computation of integrals is an important aspect since it governs the accuracy of the analysis and also because it usually takes the major part of the CPU time. The integrals which determine the influence matrices, the internal field and its gradients contain (nearly) singular kernels of order lIr a (0:= 1,2,3,4,.··) where r is the distance between the source point and the integration point on the boundary element. For planar elements, analytical integration may be possible 1,2,6. However, it is becoming increasingly important in practical boundary element codes to use curved elements, such as the isoparametric elements, to model general curved surfaces. Since analytical integration is not possible for general isoparametric curved elements, one has to rely on numerical integration. When the distance d between the source point and the element over which the integration is performed is sufficiently large compared to the element size (d> 1), the standard Gauss-Legendre quadrature formula 1,3 works efficiently. However, when the source is actually on the element (d=O), the kernel 1I~ becomes singular and the straight forward application of the Gauss-Legendre quadrature formula breaks down. These integrals will be called singular integrals. Singular integrals occur when calculating the diagonals of the influence matrices.
Singular Integral Equations
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Author : E.G. Ladopoulos
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Singular Integral Equations written by E.G. Ladopoulos 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 Computers categories.
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.
Symmetric Galerkin Boundary Element Method
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Author : Alok Sutradhar
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-26
Symmetric Galerkin Boundary Element Method written by Alok Sutradhar 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 2008-09-26 with Technology & Engineering categories.
Symmetric Galerkin Boundary Element Method presents an introduction as well as recent developments of this accurate, powerful, and versatile method. The formulation possesses the attractive feature of producing a symmetric coefficient matrix. In addition, the Galerkin approximation allows standard continuous elements to be used for evaluation of hypersingular integrals. FEATURES • Written in a form suitable for a graduate level textbook as well as a self-learning tutorial in the field. • Covers applications in two-dimensional and three-dimensional problems of potential theory and elasticity. Additional basic topics involve axisymmetry, multi-zone and interface formulations. More advanced topics include fluid flow (wave breaking over a sloping beach), non-homogeneous media, functionally graded materials (FGMs), anisotropic elasticity, error estimation, adaptivity, and fracture mechanics. • Presents integral equations as a basis for the formulation of general symmetric Galerkin boundary element methods and their corresponding numerical implementation. • Designed to convey effective unified procedures for the treatment of singular and hypersingular integrals that naturally arise in the method. Symbolic codes using Maple® for singular-type integrations are provided and discussed in detail. • The user-friendly adaptive computer code BEAN (Boundary Element ANalysis), fully written in Matlab®, is available as a companion to the text. The complete source code, including the graphical user-interface (GUI), can be downloaded from the web site http://www.ghpaulino.com/SGBEM_book. The source code can be used as the basis for building new applications, and should also function as an effective teaching tool. To facilitate the use of BEAN, a video tutorial and a library of practical examples are provided.
Numerical Techniques For Boundary Element Methods
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Author : Wolfgang Hackbusch
language : de
Publisher: Springer-Verlag
Release Date : 2013-09-03
Numerical Techniques For Boundary Element Methods written by Wolfgang Hackbusch and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-03 with Technology & Engineering categories.
Error Analysis Of Nearly Singular Integrals In The Boundary Element Method
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Author : Kristy Lee Evangelista
language : en
Publisher:
Release Date : 2003
Error Analysis Of Nearly Singular Integrals In The Boundary Element Method written by Kristy Lee Evangelista and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Boundary value problems categories.
The Scaled Boundary Finite Element Method
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Author : John P. Wolf
language : en
Publisher: John Wiley & Sons
Release Date : 2003-03-14
The Scaled Boundary Finite Element Method written by John P. Wolf and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-14 with Technology & Engineering categories.
A novel computational procedure called the scaled boundary finite-element method is described which combines the advantages of the finite-element and boundary-element methods : Of the finite-element method that no fundamental solution is required and thus expanding the scope of application, for instance to anisotropic material without an increase in complexity and that singular integrals are avoided and that symmetry of the results is automatically satisfied. Of the boundary-element method that the spatial dimension is reduced by one as only the boundary is discretized with surface finite elements, reducing the data preparation and computational efforts, that the boundary conditions at infinity are satisfied exactly and that no approximation other than that of the surface finite elements on the boundary is introduced. In addition, the scaled boundary finite-element method presents appealing features of its own : an analytical solution inside the domain is achieved, permitting for instance accurate stress intensity factors to be determined directly and no spatial discretization of certain free and fixed boundaries and interfaces between different materials is required. In addition, the scaled boundary finite-element method combines the advantages of the analytical and numerical approaches. In the directions parallel to the boundary, where the behaviour is, in general, smooth, the weighted-residual approximation of finite elements applies, leading to convergence in the finite-element sense. In the third (radial) direction, the procedure is analytical, permitting e.g. stress-intensity factors to be determined directly based on their definition or the boundary conditions at infinity to be satisfied exactly. In a nutshell, the scaled boundary finite-element method is a semi-analytical fundamental-solution-less boundary-element method based on finite elements. The best of both worlds is achieved in two ways: with respect to the analytical and numerical methods and with respect to the finite-element and boundary-element methods within the numerical procedures. The book serves two goals: Part I is an elementary text, without any prerequisites, a primer, but which using a simple model problem still covers all aspects of the method and Part II presents a detailed derivation of the general case of statics, elastodynamics and diffusion.
Boundary Elements And Other Mesh Reduction Methods Xxxvi
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Author : X. W. Gao
language : en
Publisher: WIT Press
Release Date : 2013-12-11
Boundary Elements And Other Mesh Reduction Methods Xxxvi written by X. W. Gao and has been published by WIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-11 with Mathematics categories.
The Conference on Boundary Elements and Mesh Reduction Methods (BEM/MRM) is recognised as the international forum for the latest advances in these techniques and their applications in science and engineering. Launched in 1978 the Conference continues to attract original contributions and has become the forum for their rapid dissemination throughout the international scientific community. Practically all new boundary element ideas have first appeared in the proceedings of these meetings.
Boundary Element Techniques In Geomechanics
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Author : George D. Manolis
language : en
Publisher:
Release Date : 1993
Boundary Element Techniques In Geomechanics written by George D. Manolis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.