The Complex Variable Boundary Element Method In Engineering Analysis

Author : Theodore V. Hromadka,Chintu Lai
Publisher : Springer Science & Business Media
Page : 397 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Medical
ISBN : 9781461246602

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The Complex Variable Boundary Element Method in Engineering Analysis by Theodore V. Hromadka,Chintu Lai Pdf

The Complex Variable Boundary Element Method (CVBEM) has emerged as a new and effective modeling method in the field of computational mechanics and hydraulics. The CVBEM is a generalization of the Cauchy integral formula into a boundary integral equation method. The model ing approach by boundary integration, the use of complex variables for two-dimensional potential problems, and the adaptability to now-popular microcomputers are among the factors that make this technique easy to learn, simple to operate, practical for modeling, and efficient in simulating various physical processes. Many of the CVBEM concepts and notions may be derived from the Analytic Function Method (AFM) presented in van der Veer (1978). The AFM served as the starting point for the generalization of the CVBEM theory which was developed during the first author's research engagement (1979 through 1981) at the University of California, Irvine. The growth and expansion of the CVBEM were subsequently nurtured at the U. S. Geological Survey, where keen interest and much activity in numerical modeling and computational mechanics-and-hydraulics are prevalent. Inclusion of the CVBEM research program in Survey's computational-hydraulics projects, brings the modeling researcher more uniform aspects of numerical mathematics in engineering and scientific problems, not to mention its (CVBEM) practicality and usefulness in the hydrologic investigations. This book is intended to introduce the CVBEM to engineers and scientists with its basic theory, underlying mathematics, computer algorithm, error analysis schemes, model adjustment procedures, and application examples.

Author : T. V. Hromadka
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 43,5 Mb
Release : 2013-03-12
Category : Mathematics
ISBN : 9783642823619

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The Complex Variable Boundary Element Method by T. V. Hromadka Pdf

The Complex Variable Boundary Element Method or CVBEM is a generalization of the Cauchy integral formula into a boundary integral equation method or BIEM. This generalization allows an immediate and extremely valuable transfer of the modeling techniques used in real variable boundary integral equation methods (or boundary element methods) to the CVBEM. Consequently, modeling techniques for dissimilar materials, anisotropic materials, and time advancement, can be directly applied without modification to the CVBEM. An extremely useful feature offered by the CVBEM is that the pro duced approximation functions are analytic within the domain enclosed by the problem boundary and, therefore, exactly satisfy the two-dimensional Laplace equation throughout the problem domain. Another feature of the CVBEM is the integrations of the boundary integrals along each boundary element are solved exactly without the need for numerical integration. Additionally, the error analysis of the CVBEM approximation functions is workable by the easy-to-understand concept of relative error. A sophistication of the relative error analysis is the generation of an approximative boundary upon which the CVBEM approximation function exactly solves the boundary conditions of the boundary value problem' (of the Laplace equation), and the goodness of approximation is easily seen as a closeness-of-fit between the approximative and true problem boundaries.

Author : Theodore V. Hromadka,Robert J. Whitley
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 44,5 Mb
Release : 2013-03-14
Category : Technology & Engineering
ISBN : 9781447136118

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Advances in the Complex Variable Boundary Element Method by Theodore V. Hromadka,Robert J. Whitley Pdf

As well as describing the extremely useful applications of the CVBEM, the authors explain its mathematical background -- vital to understanding the subject as a whole. This is the most comprehensive book on the subject, bringing together ten years of work and can boast the latest news in CVBEM technology. It is thus of particular interest to those concerned with solving technical engineering problems -- while scientists, graduate students, computer programmers and those working in industry will all find the book helpful.

Author : D. E. Beskos
Publisher : Unknown
Page : 360 pages
File Size : 43,7 Mb
Release : 1989
Category : Mathematics
ISBN : UOM:39015013848265

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Boundary Element Methods in Structural Analysis by D. E. Beskos Pdf

Author : B. D. Wilkins,T. V. Hromadka II
Publisher : WIT Press
Page : 290 pages
File Size : 54,5 Mb
Release : 2021-09-22
Category : Mathematics
ISBN : 9781784664510

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Excel in Complex Variables with the Complex Variable Boundary Element Method by B. D. Wilkins,T. V. Hromadka II Pdf

Using the familiar software Microsoft ® Excel, this book examines the applications of complex variables. Implementation of the included problems in Excel eliminates the “black box” nature of more advanced computer software and programming languages and therefore the reader has the chance to become more familiar with the underlying mathematics of the complex variable problems. This book consists of two parts. In Part I, several topics are covered that one would expect to find in an introductory text on complex variables. These topics include an overview of complex numbers, functions of a complex variable, and the Cauchy integral formula. In particular, attention is given to the study of analytic complex variable functions. This attention is warranted because of the property that the real and imaginary parts of an analytic complex variable function can be used to solve the Laplace partial differential equation (PDE). Laplace's equation is ubiquitous throughout science and engineering as it can be used to model the steady-state conditions of several important transport processes including heat transfer, soil-water flow, electrostatics, and ideal fluid flow, among others. In Part II, a specialty application of complex variables known as the Complex Variable Boundary Element Method (CVBEM) is examined. CVBEM is a numerical method used for solving boundary value problems governed by Laplace's equation. This part contains a detailed description of the CVBEM and a guide through each step of constructing two CVBEM programs in Excel. The writing of these programs is the culminating event of the book. Students of complex variables and anyone with an interest in a novel method for approximating potential functions using the principles of complex variables are the intended audience for this book. The Microsoft Excel applications (including simple programs as well as the CVBEM program) covered will also be of interest in the industry, as these programs are accessible to anybody with Microsoft Office.

Author : Levon G. Petrosian,Vladimir A. Ambartsumian
Publisher : John Wiley & Sons
Page : 528 pages
File Size : 55,9 Mb
Release : 2020-05-11
Category : Technology & Engineering
ISBN : 9781119592839

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Static and Dynamic Analysis of Engineering Structures by Levon G. Petrosian,Vladimir A. Ambartsumian Pdf

An authoritative guide to the theory and practice of static and dynamic structures analysis Static and Dynamic Analysis of Engineering Structures examines static and dynamic analysis of engineering structures for methodological and practical purposes. In one volume, the authors – noted engineering experts – provide an overview of the topic and review the applications of modern as well as classic methods of calculation of various structure mechanics problems. They clearly show the analytical and mechanical relationships between classical and modern methods of solving boundary value problems. The first chapter offers solutions to problems using traditional techniques followed by the introduction of the boundary element methods. The book discusses various discrete and continuous systems of analysis. In addition, it offers solutions for more complex systems, such as elastic waves in inhomogeneous media, frequency-dependent damping and membranes of arbitrary shape, among others. Static and Dynamic Analysis of Engineering Structures is filled with illustrative examples to aid in comprehension of the presented material. The book: Illustrates the modern methods of static and dynamic analysis of structures; Provides methods for solving boundary value problems of structural mechanics and soil mechanics; Offers a wide spectrum of applications of modern techniques and methods of calculation of static, dynamic and seismic problems of engineering design; Presents a new foundation model. Written for researchers, design engineers and specialists in the field of structural mechanics, Static and Dynamic Analysis of Engineering Structures provides a guide to analyzing static and dynamic structures, using traditional and advanced approaches with real-world, practical examples.

Author : M H Aliabadi,P H Wen
Publisher : World Scientific
Page : 412 pages
File Size : 48,8 Mb
Release : 2010-11-25
Category : Technology & Engineering
ISBN : 9781908977977

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Boundary Element Methods in Engineering and Sciences by M H Aliabadi,P H Wen Pdf

The boundary element method (BEM), also known as the boundary integral equation method (BIEM), is a modern numerical technique which has enjoyed increasing popularity over the past two decades. It is now an established alternative to traditional computational methods of engineering analysis. The main advantage of the BEM is its unique ability to provide a complete solution in terms of boundary values only, with substantial savings in modeling effort. This book is designed to provide readers with a comprehensive and up-to-date account of the method and its application to problems in engineering and science. Each chapter provides a brief description of historical development, followed by basic theory, derivation and examples. Contents:The Boundary Element Method for Geometrically Nonlinear Analyses of Plates and Shells (P H Wen et al.)Time-Domain BEM Techniques (W J Mansur et al.)The Boundary Element Method for the Fracture Analysis of the General Piezoelectric Solids (M Denda)Boundary Integral Analysis for Three-Dimensional Exponentially Graded Elasticity (J E Ortiz et al.)Fast Hierarchical Boundary Element Method for Large Scale 3-D Elastic Problems (I Benedetti et al.)Modelling of Plates and Shallow Shells by Meshless Local Integral Equation Method (J Sladek et al.)Boundary Element Technique for Slow Viscous Flows About Particles (A Sellier)BIT for Free Surface Flows (G Baker)Simulation of Cavitating and Free Surface Flows using BEM (S A Kinnas)Condition Numbers and Local Errors in the Boundary Element Method (W Dijkstra et al.) Readership: Graduate students, academics and researchers in engineering mechanics, materials engineering, mechanical engineering, and software engineering/programming. Keywords:Boundary Element Method (BEM);Boundary Equation Method (BIEM)Key Features:The book will provide a comprehensive presentation of the BEM from fundamentals to advanced engineering applications and encompasses: solids and structures; heat transfer; fluid dynamics; and acousticsIt will also include chapters dealing specifically with mathematical and computational aspects of the method

Author : C.A. Brebbia,M.S. Ingber
Publisher : Springer Science & Business Media
Page : 911 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9789401128728

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Boundary Element Technology VII by C.A. Brebbia,M.S. Ingber Pdf

Seventh International Conference on Boundary Element Technology 'Betech 92', held at the University of New Mexico in Albuquerque, June 1992

Author : M. H. Aliabadi,P. H. Wen
Publisher : World Scientific
Page : 412 pages
File Size : 53,5 Mb
Release : 2011
Category : Technology & Engineering
ISBN : 9781848165793

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Boundary Element Methods in Engineering and Sciences by M. H. Aliabadi,P. H. Wen Pdf

The boundary element method (BEM), also known as the boundary integral equation method (BIEM), is a modern numerical technique. It is an established alternative to traditional computational methods of engineering analysis. This book provides a comprehensive account of the method and its application to problems in engineering and science.

Author : P. K. Banerjee,Prasanta Kumar Banerjee,Roy Butterfield
Publisher : McGraw-Hill (UK)
Page : 476 pages
File Size : 47,8 Mb
Release : 1981
Category : Mathematics
ISBN : UOM:39015003730762

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Boundary Element Methods in Engineering Science by P. K. Banerjee,Prasanta Kumar Banerjee,Roy Butterfield Pdf

Author : C.A. Brebbia,G.S. Gipson
Publisher : Springer Science & Business Media
Page : 1005 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9789401136969

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Boundary Elements XIII by C.A. Brebbia,G.S. Gipson Pdf

Since its origin in 1978, the International Conference on Boundary Element Methods has provided the recognized and established forum for innovations in boundary element research. Practically all new ideas on boundary ele ments have been presented at these conferences and the resulting papers can be found in the published books. The conference brings together the most renowned scientists and engineers working on boundary element research throughout the world. A unique feature of these meetings is that the participation of younger researchers is actively encouraged by the organizers in an effort to .bring forward to the attention of the international community an ever expanding range of new ideas. This book contains the edited version of the papers presented at the XIIIth BEM Conference held in Tulsa, Oklahoma in August of 1991. The meeting attracted a large number of participants and many excellent contributions which have been divided into nineteen different sections, i.e. Potential Prob lems; Diffusion and Convection Problems; Fluid Mechanics; Fluid Flow; Wave Propagation; Groundwater Flow; Heat Transfer; Electrical Problems; Geomechanics; Plates and Shells; Inelastic Problems; Damage Tolerance; Contact Mechanics; Industrial Applications; Design Sensitivity and Opti mization; Inverse Problems; Special Techniques; Numerical Aspects and Computational Aspects.

Author : Abhijit Chandra,Subrata Mukherjee
Publisher : Oxford University Press
Page : 525 pages
File Size : 54,6 Mb
Release : 1997-04-10
Category : Technology & Engineering
ISBN : 9780195359978

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Boundary Element Methods in Manufacturing by Abhijit Chandra,Subrata Mukherjee Pdf

This book focuses on the analysis of manufacturing processes and the integration of this analysis into the design cycle. Uniquely, the boundary element method (BEM) is the computational model of choice. This versatile and powerful method has undergone extensive development during the past two decades and has been applied to virtually all areas of engineering mechanics as well as to other fields. Among topics covered are BEM infrastructure, design sensitivity analysis, and detailed discussions of a broad range of manufacturing processes including forming, solidification, machining, and ceramic grinding.

Author : C. A. Brebbia,J. Dominguez
Publisher : WIT Press
Page : 327 pages
File Size : 52,8 Mb
Release : 1994-05-31
Category : Mathematics
ISBN : 9781853123498

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Boundary Elements by C. A. Brebbia,J. Dominguez Pdf

This best-selling text provides a simple introduction to the Boundary Element Method. Based on the authors' long teaching experience it is designed to convey in the most effective manner the fundamentals of the method. The book is presented in a way which makes it accessible to both undergraduate and graduate students as well as to practising engineers who want to learn the foundations of the technique. Of particular interest is the way in which Boundary Element concepts are introduced and immediately applied in simple, but useful, computer codes to facilitate understanding. A CD with the complete listing of program codes in Fortran is also included.

Author : C. A. Brebbia,S. Walker
Publisher : Elsevier
Page : 221 pages
File Size : 53,9 Mb
Release : 2016-01-29
Category : Technology & Engineering
ISBN : 9781483102566

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Boundary Element Techniques in Engineering by C. A. Brebbia,S. Walker Pdf

Boundary Element Techniques in Engineering deals with solutions of two- and three-dimensional problems in elasticity and the potential theory where finite elements are inefficient. The book discusses approximate methods, higher-order elements, elastostatics, time-dependent problems, non-linear problems, and combination of regions. Approximate methods include weighted residual techniques, weak formulations, the inverse formulation, and boundary methods. The text also explains Laplace's equation, indirect formulation, matrix formulation, Poisson's equation, and the Helmholtz equation. It describes how elements with linear variations of u and q (i.e. linear elements) can be developed for two dimensional problems, as well as for quadratic and higher order elements for two-dimensional problems. The text investigates the Dirac delta function as a sum of Eigen functions, including some methods to determine the explicit form of fundamental solutions for recurrent problems. The book also tackles the application of boundary elements to problems with both material and certain types of geometric non-linearities, and also the applications of boundary elements to plasticity problems. The text is ideal for mathematicians, students, and professor of calculus or advanced mathematics.

Author : O.P. Gupta
Publisher : Routledge
Page : 496 pages
File Size : 50,8 Mb
Release : 2022-03-23
Category : Technology & Engineering
ISBN : 9781351448642

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Finite and Boundary Element Methods in Engineering by O.P. Gupta Pdf

The interest in finite element method as a solution technique of the computer age is reflected in the availability of many general and special purpose software based on this technique. This work aims to provide a complete and detailed explanation of the basics of the application areas.