[PDF] Numerical Methods For Elliptic Problems With Singularities Boundary Mtds And Nonconforming Combinatn eBook

Author : Zi-cai Li
Publisher : World Scientific
Page : 280 pages
File Size : 27,47 MB
Release : 1990-12-27
Category : Mathematics
ISBN : 981450680X

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This book presents two kinds of numerical methods for solving elliptic boundary value problems with singularities. Part I gives the boundary methods which use analytic and singular expansions, and Part II the nonconforming methods combining finite element methods (FEM) (or finite difference methods (FDM)) and singular (or analytic) expansions. The advantage of these methods over the standard FEM and FDM is that they can cope with complicated geometrical boundaries and boundary conditions as well as singularity. Therefore, accurate numerical solutions near singularities can be obtained. The description of methods, error bounds, stability analysis and numerical experiments are provided for the typical problems with angular, interface and infinity singularities. However, the approximate techniques and coupling strategy given can be applied to solving other PDE and engineering problems with singularities as well. This book is derived from the author's Ph. D. thesis which won the 1987 best doctoral dissertation award given by the Canadian Applied Mathematics Society.

Author : Zi Cai Li
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 21,34 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1461333385

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In this book the author sets out to answer two important questions: 1. Which numerical methods may be combined together? 2. How can different numerical methods be matched together? In doing so the author presents a number of useful combinations, for instance, the combination of various FEMs, the combinations of FEM-FDM, REM-FEM, RGM-FDM, etc. The combined methods have many advantages over single methods: high accuracy of solutions, less CPU time, less computer storage, easy coupling with singularities as well as the complicated boundary conditions. Since coupling techniques are essential to combinations, various matching strategies among different methods are carefully discussed. The author provides the matching rules so that optimal convergence, even superconvergence, and optimal stability can be achieved, and also warns of the matching pitfalls to avoid. Audience: The book is intended for both mathematicians and engineers and may be used as text for advanced students.

Author : Zohar Yosibash
Publisher : Springer Science & Business Media
Page : 473 pages
File Size : 18,72 MB
Release : 2011-12-02
Category : Mathematics
ISBN : 146141508X

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This introductory and self-contained book gathers as much explicit mathematical results on the linear-elastic and heat-conduction solutions in the neighborhood of singular points in two-dimensional domains, and singular edges and vertices in three-dimensional domains. These are presented in an engineering terminology for practical usage. The author treats the mathematical formulations from an engineering viewpoint and presents high-order finite-element methods for the computation of singular solutions in isotropic and anisotropic materials, and multi-material interfaces. The proper interpretation of the results in engineering practice is advocated, so that the computed data can be correlated to experimental observations. The book is divided into fourteen chapters, each containing several sections. Most of it (the first nine Chapters) addresses two-dimensional domains, where only singular points exist. The solution in a vicinity of these points admits an asymptotic expansion composed of eigenpairs and associated generalized flux/stress intensity factors (GFIFs/GSIFs), which are being computed analytically when possible or by finite element methods otherwise. Singular points associated with weakly coupled thermoelasticity in the vicinity of singularities are also addressed and thermal GSIFs are computed. The computed data is important in engineering practice for predicting failure initiation in brittle material on a daily basis. Several failure laws for two-dimensional domains with V-notches are presented and their validity is examined by comparison to experimental observations. A sufficient simple and reliable condition for predicting failure initiation (crack formation) in micron level electronic devices, involving singular points, is still a topic of active research and interest, and is addressed herein. Explicit singular solutions in the vicinity of vertices and edges in three-dimensional domains are provided in the remaining five chapters. New methods for the computation of generalized edge flux/stress intensity functions along singular edges are presented and demonstrated by several example problems from the field of fracture mechanics; including anisotropic domains and bimaterial interfaces. Circular edges are also presented and the author concludes with some remarks on open questions. This well illustrated book will appeal to both applied mathematicians and engineers working in the field of fracture mechanics and singularities.

Author : Garrett Birkhoff
Publisher : SIAM
Page : 330 pages
File Size : 21,21 MB
Release : 1984-01-01
Category : Mathematics
ISBN : 9781611970869

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A study of the art and science of solving elliptic problems numerically, with an emphasis on problems that have important scientific and engineering applications, and that are solvable at moderate cost on computing machines.

Author : Andreas Pomp
Publisher : Springer Science & Business Media
Page : 188 pages
File Size : 37,67 MB
Release : 1998-03-18
Category : Mathematics
ISBN : 9783540641636

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This monograph gives a description of all algorithmic steps and a mathematical foundation for a special numerical method, namely the boundary-domain integral method (BDIM). This method is a generalization of the well-known boundary element method, but it is also applicable to linear elliptic systems with variable coefficients, especially to shell equations. The text should be understandable at the beginning graduate-level. It is addressed to researchers in the fields of numerical analysis and computational mechanics, and will be of interest to everyone looking at serious alternatives to the well-established finite element methods.

Author : D. Leguillon
Publisher : John Wiley & Sons
Page : 208 pages
File Size : 48,78 MB
Release : 1987
Category : Mathematics
ISBN :

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The stress field in composite elastic media often contains singularities, in particular at the intersections of interfaces with boundaries. This book describes two new methods of computing the eigenvalues and eigenvectors of singularities, leading to a full description of their structure.

Author : Mark T. DeMeuse
Publisher : Elsevier
Page : 295 pages
File Size : 32,7 MB
Release : 2011-07-18
Category : Technology & Engineering
ISBN : 0857092952

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Biaxial (having two axes) stretching of film is used for a range of applications and is the primary manufacturing process by which products are produced for the food packaging industry. Biaxial stretching of film: principles and applications provides an overview of the manufacturing processes and range of applications for biaxially stretched films.Part one reviews the fundamental principles of biaxial stretching. After an introductory chapter which defines terms, chapters discuss equipment design and requirements, laboratory evaluations, biaxial film structures and typical industrial processes for the biaxial orientation of films. Additional topics include post production processing of biaxially stretched films, the stress-strain behaviour of poly(ethylene terephthalate) and academic investigations of biaxially stretched films. Part two investigates the applications of biaxial films including fresh cut produce, snack packaging and product labelling. A final chapter investigates potential future trends for biaxially oriented films and orienting lines.Biaxial stretching of film: principles and applications is a valuable reference tool for a broad spectrum of readers, ranging from polymer and fibre engineers to electrical engineers. It will also be suitable for professionals in the food packaging and paper industries. A valuable reference tool for polymer and fibre engineers, electrical engineers and professionals in the food packaging and paper industries Provides a comprehensive overview of the manufacturing processes of biaxially stretched films and includes a discussion of their future applications Places emphasis on the technology as well as the different types of polymers used