A New Boundary Element Formulation In Engineering

Author : Tania G.B. DeFigueiredo
Publisher : Springer Science & Business Media
Page : 210 pages
File Size : 54,9 Mb
Release : 2013-03-12
Category : Science
ISBN : 9783642845048

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A New Boundary Element Formulation in Engineering by Tania G.B. DeFigueiredo Pdf

1. 1 The Hybrid Displacement Boundary Element Model This work is concerned with the derivation of a numerical model for the solution of boundary-value problems in potential theory and linear elasticity. It is considered a boundary element model because the final integral equation involves some boundary integrals, whose evaluation requires a boundary discretization. Furthermore, all the unknowns are boundary vari ables. The model is completely new; it differs from the classical boundary element formulation ·in the way it is generated and consequently in the fi nal equations. A generalized variational principle is used as a basis for its derivation, whereas the conventional boundary element formulation is based on Green's formula (potential problems) and on Somigliana's identity (elas ticity), or alternatively through the weighted residual technique. 2 The multi-field variational principle which generates the formulation in volves three independent variables. For potential problems, these are the potential in the domain and the potential and its normal derivative on the boundary. In the case of elasticity, these variables are displacements in the domain and displacements and tractions on the boundary. For this reason, by analogy with the assumed displacement hybrid finite element model, ini tially proposed by Tong [1] in 1970, it can be called a hybrid displacement model. The final system of equations to be solved is similar to that found in a stiffness formulation. The stiffness matrix for this model is symmetric and can be evaluated by only performing integrations along the boundary.

Author : Adib A. Becker
Publisher : McGraw-Hill Companies
Page : 360 pages
File Size : 45,7 Mb
Release : 1992
Category : Business & Economics
ISBN : PSU:000033784328

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The Boundary Element Method in Engineering by Adib A. Becker Pdf

Author : Youssef F. Rashed
Publisher : Computational Mechanics
Page : 184 pages
File Size : 44,8 Mb
Release : 2000
Category : Mathematics
ISBN : UOM:39015052466045

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Boundary Element Formulations for Thick Plates by Youssef F. Rashed Pdf

Plate bending problems have many applications in civil and mechanical engineering. The analysis of plates using the Boundary Element Method (BEM), however, has received little attention in existing research and literature. This book presents new Boundary Element formulations for plate bending problems in which the Reissner plate bending theory is used to model the bending behaviour of the plate. The author applies several integral equations to solve engineering problems relating to a building slab, beam, footing, and simple raft and the results are compared against analytical solutions such as a finite difference method, a finite element method and a three-dimensional boundary element method. These confirm that the Boundary Element formulations presented are a competitive alternative to existing numerical methods.

Author : C. A. Brebbia,J. Dominguez
Publisher : WIT Press
Page : 327 pages
File Size : 47,6 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,J. C. F. Telles,L. C. Wrobel
Publisher : Springer Science & Business Media
Page : 479 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783642488603

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Boundary Element Techniques by C. A. Brebbia,J. C. F. Telles,L. C. Wrobel Pdf

VI SOCRATES: I think that we ought to stress that we will write only about things that we have first hand experience in, in a coherent way that will be useful to engineers and other scientists and stressing the formulation without being too mathematical. We should write with integrity and honesty, giving reference to other authors where reference is due, but avoiding mentioning everybody just to be certain that our book is widely advertised. Above all, the book should be clear and useful. PLATO: I think we should include a good discussion of fundamental ideas, of how integral equations are formed, pointing out that they are like two dimensional shadows of three dimensional objects, ... SOCRATES: Stop there! Remember you are not 'the' Plato! PLATO: Sorry, I was carried away. ARISTOTLE: I think that the book should have many applications so that the reader can learn by looking at them how to use the method. SOCRATES: I agree. But we should be careful. It is easy to include many illustra tions and examples in a book in order to disguise its meagre contents. All examples should be relevant. ARISTOTLE: And we should also include a full computer program to give the reader if so he wishes, a working experience of the technique.

Author : John T. Katsikadelis
Publisher : Academic Press
Page : 464 pages
File Size : 53,9 Mb
Release : 2016-10-10
Category : Technology & Engineering
ISBN : 9780128020104

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The Boundary Element Method for Engineers and Scientists by John T. Katsikadelis Pdf

The Boundary Element Method for Engineers and Scientists: Theory and Applications is a detailed introduction to the principles and use of boundary element method (BEM), enabling this versatile and powerful computational tool to be employed for engineering analysis and design. In this book, Dr. Katsikadelis presents the underlying principles and explains how the BEM equations are formed and numerically solved using only the mathematics and mechanics to which readers will have been exposed during undergraduate studies. All concepts are illustrated with worked examples and problems, helping to put theory into practice and to familiarize the reader with BEM programming through the use of code and programs listed in the book and also available in electronic form on the book’s companion website. Offers an accessible guide to BEM principles and numerical implementation, with worked examples and detailed discussion of practical applications This second edition features three new chapters, including coverage of the dual reciprocity method (DRM) and analog equation method (AEM), with their application to complicated problems, including time dependent and non-linear problems, as well as problems described by fractional differential equations Companion website includes source code of all computer programs developed in the book for the solution of a broad range of real-life engineering problems

Author : J. Dominguez
Publisher : WIT Press
Page : 724 pages
File Size : 53,8 Mb
Release : 1993
Category : Technology & Engineering
ISBN : 9781853122583

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Boundary Elements in Dynamics by J. Dominguez Pdf

A reference for those who need to acquire detailed knowledge of the formulation, implementation, and practical applications of BEM in dynamics. The author presents research on BEM in dynamics of continua. The main emphasis is on the development of the different boundary element formulations.

Author : C. A. Brebbia,S. Walker
Publisher : Elsevier
Page : 221 pages
File Size : 40,6 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 : J.C.F. Telles
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 53,7 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783642455629

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The Boundary Element Method Applied to Inelastic Problems by J.C.F. Telles Pdf

Author : C. A. Brebbia,Jerome J. Connor
Publisher : Unknown
Page : 472 pages
File Size : 54,5 Mb
Release : 1989
Category : Boundary element methods
ISBN : 185312026X

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Advances in Boundary Elements by C. A. Brebbia,Jerome J. Connor Pdf

Author : Dragan Poljak,C. A. Brebbia
Publisher : WIT Press
Page : 209 pages
File Size : 55,7 Mb
Release : 2005
Category : Technology & Engineering
ISBN : 9781845640330

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Boundary Element Methods for Electrical Engineers by Dragan Poljak,C. A. Brebbia Pdf

Presents Boundary Element Method (BEM) in a simple fashion in order to help the beginner to understand the very basic principles of the method. This book initially derives BEM for the simplest potential problems, and subsequently builds on these to formulate BEM for a wide range of applications in electromagnetics.

Author : Carlos A. Brebbia
Publisher : Springer
Page : 200 pages
File Size : 48,8 Mb
Release : 1987-09-08
Category : Mathematics
ISBN : 3540174974

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Applications in Geomechanics by Carlos A. Brebbia Pdf

The first volume of this series dealt with the Basic Principles of Boundary Elements, while the second concentrated on time dependent problems and Volume three on the Computational Aspects of the method. This volume studies the applications of the method to a wide variety of geomechanics problems, most of which are ideally suited for boundary elements demonstrating the potentiality of the technique. Chapter 1 deals with the application of BEM to three dimensional elastody namics soil-structure interaction problems. It presents detailed formulations for rigid, massless foundations of arbitrary shape both in the frequency and time domains. The foundations are assumed to be resting on a linearly elastic, homogeneous, isotropic half-space and be subjected to externally applied loads on obliquely incident body. The chapter reviews the major advances in soil foundation interaction presents a series of numerical results and stresses the practical application of BEM, pointing out the high accuracy and efficiency of the technique, even when using coarse mesh discretizations.

Author : M. H. Aliabadi
Publisher : John Wiley & Sons
Page : 614 pages
File Size : 55,6 Mb
Release : 2002-04-29
Category : Technology & Engineering
ISBN : 0470842989

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The Boundary Element Method, Volume 2 by M. H. Aliabadi Pdf

The boundary element method (BEM) is a modern numerical technique, which has enjoyed increasing popularity over the last two decades, and 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 modelling effort. This two-volume book set is designed to provide the readers with a comprehensive and up-to-date account of the boundary element method and its application to solving engineering problems. Each volume is a self-contained book including a substantial amount of material not previously covered by other text books on the subject. Volume 1 covers applications to heat transfer, acoustics, electrochemistry and fluid mechanics problems, while volume 2 concentrates on solids and structures, describing applications to elasticity, plasticity, elastodynamics, fracture mechanics and contact analysis. The early chapters are designed as a teaching text for final year undergraduate courses. Both volumes reflect the experience of the authors over a period of more than twenty years of boundary element research. This volume, Applications in Solids and Structures, provides a comprehensive presentation of the BEM from fundamentals to advanced engineering applications and encompasses: Elasticity for 2D, 3D and Plates and Shells Non-linear, Transient and Thermal Stress Analysis Crack Growth and Multi-body Contact Mechanics Sensitivity Analysis and Optimisation Analysis of Assembled Structures. An important feature of this book is the in-depth presentation of BEM formulations in all the above fields, including detailed discussions of the basic theory, numerical algorithms and where possible simple examples are included, as well as test results for practical engineering applications of the method. Although most of the methods presented are the latest developments in the field, the author has included some simple techniques, which are helpful in understanding the computer implementation of BEM. Another notable feature is the comprehensive presentation of a new generation of boundary elements known as the Dual Boundary Element Method. Written by an internationally recognised authority in the field, this is essential reading for postgraduates, researchers and practitioners in Aerospace, Mechanical and Civil Engineering and Applied Mathematics.

Author : W.S. Venturini
Publisher : Springer Science & Business Media
Page : 255 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783642820991

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Boundary Element Method in Geomechanics by W.S. Venturini Pdf

Numerical techniques for solving many problems in continuum mechanics have experienced a tremendous growth in the last twenty years due to the development of large high speed computers. In particular, geomechanical stress analysis can now be modelled within a more realistic context. In spite of the fact that many applications in geomechanics are still being carried out applying linear theories, soil and rock materials have been demonstrated experimentally to be physically nonlinear. Soils do not recover their initial state after removal of temporary loads and rock does not deform in proportion to the loads applied. The search for a unified theory to model the real response of these materials is impossible due to the complexities involved in each case. Realistic solutions in geomechanical analysis must be provided by considering that material properties vary from point to point, in addition to other significant features such as non-homogeneous media, in situ stress condition, type of loading, time effects and discontinuities. A possible alternative to tackle such a problem is to inttoduce some simplified assumptions which at least can provide an approximate solution in each case. The validity or accuracy of the final solution obtained is always dependent upon the approach adopted. As a consequence, the choice of a reliable theory for each particular problem is another difficult decision which should be 2 taken by the analyst in geomechanical stress analysis.

Author : Ghodratollah Karami
Publisher : Springer Science & Business Media
Page : 256 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9783642838972

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Lecture Notes in Engineering by Ghodratollah Karami Pdf

The Boundary Element Method (BEM) has been established as a powerful numerical tool for the analysis of continua in recent years. The method is based on an attempt to transfer the governing differential equations into integral equations over the boundary. Thus, the discretization scheme or the intro duction of any approximations must be done over the boundary. This book presents a BEM for two-dimensional elastic, thermo -elastic and body-force contact problems. The formulation is implemented for the general case of contact with various fric tional conditions. The analysis is limited to linear elasto statics and small strain theory. Following a review of the basic nature of contact problems, the analytical basis of the direct formulation of the BEM method is described. The numerical implementation employs three-noded isoparametric line elements for the representa tion of the boundary of the bodies in contact. Opposite nodal points in equi-Iength element-pairs are defined on the two surfaces in the area which is expected to come into contact under an increasing load. The use of appropriate contact IV conditions enables the integral equations for the two bodies to be coupled together. To find the proper contact dimensions and the contact load a combined incremental and iterative approach is utilised. With this approach, the loads are applied progressively, and the sliding and adhering portion of the contact region is established for each load increment using an iterative procedure. A coulomb type of friction law is assumed.