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An informative look at the theory, computer implementation, and application of the scaled boundary finite element method This reliable resource, complete with MATLAB, is an easy-to-understand introduction to the fundamental principles of the scaled boundary finite element method. It establishes the theory of the scaled boundary finite element method systematically as a general numerical procedure, providing the reader with a sound knowledge to expand the applications of this method to a broader scope. The book also presents the applications of the scaled boundary finite element to illustrate its salient features and potentials. The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation covers the static and dynamic stress analysis of solids in two and three dimensions. The relevant concepts, theory and modelling issues of the scaled boundary finite element method are discussed and the unique features of the method are highlighted. The applications in computational fracture mechanics are detailed with numerical examples. A unified mesh generation procedure based on quadtree/octree algorithm is described. It also presents examples of fully automatic stress analysis of geometric models in NURBS, STL and digital images. Written in lucid and easy to understand language by the co-inventor of the scaled boundary element method Provides MATLAB as an integral part of the book with the code cross-referenced in the text and the use of the code illustrated by examples Presents new developments in the scaled boundary finite element method with illustrative examples so that readers can appreciate the significant features and potentials of this novel method—especially in emerging technologies such as 3D printing, virtual reality, and digital image-based analysis The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation is an ideal book for researchers, software developers, numerical analysts, and postgraduate students in many fields of engineering and science.
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.
This volume not only covers the fundamental concepts of fracture mechanics, but also the computational methodologies necessary for practical engineering designs aimed at fracture control. It gives a concise summary of various fracture theories: linear elastic, elastic-plastic, and dynamic fracture mechanics of metals and composites. Novel numerical methods (finite element and boundary element) that enable the treatment of complicated engineering problems are emphasized. Examined are problems of linear elastic fracture of metallic and non-metallic composite materials, three-dimensional problems of surface flaws, elastic-plastic fracture, stable crack growth, and dynamic crack propagation. A comprehensive outline of the energetic approach and energy integrals on fracture mechanics is also given. Contents: Preface. Parts: I. Chapters: 1. Fracture: Mechanics or Art? (F. Erdogan). II. 2. Linear Elastic Fracture Mechanics (A.S. Kobayashi). 3. Elastic-Plastic Fracture (Quasi-Static) (S.N. Atluri and A.S. Kobayashi). 4. Dynamic Crack Propagation in Solids (L.B. Freund). 5. Energetic Approaches and Path-Independent Integrals in Fracture Mechanics (S.N. Atluri). III. 6.
The so-called boundary element methods BEM, i.e. finite element approxima tions of boundary integral equations have been improved recently even more vividly then ever before and found some remarkable support by the German Research Foundation DFG in the just finished Priority Research Program "boundary element methods" . When this program began, we could start from several already existing particular activities which then during the six years initiated many new re sults and decisive new developments in theory and algorithms. The program was started due to encouragement by E. Stein, when most of the later par ticipants met in Stuttgart at a Boundary Element Conference 1987. Then W. Hackbusch, G. Kuhn, S. Wagner and W. Wendland were entrusted with writing the proposal which was 1988 presented at the German Research Foun dation and started in 1989 with 14 projects at 11 different universities. After German unification, the program was heavily extended by six more projects, four of which located in Eastern Germany. When we started, we were longing for the following goals: 1. Mathematicians and engineers should do joint research. 2. Methods and computational algorithms should be streamlined with re spect to the new computer architectures of vector and parallel computers. 3. The asymptotic error analysis of boundary element methods should be further developed. 4. Non-linear material laws should be taken care of by boundary element methods for crack-mechanics. 5. The coupling of finite boundary elements should be improved.
This text provides a three dimensional Boundary Element Method for the analysis of fatigue crack problems in both linear and nonlinear fracture mechanics. Special attention is devoted to the use of singular and near-singular integrals.
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.
The Boundary Element Method, as well as other meshless techniques continue to evolve and grow in importance, with new applications developed every year. The proceedings of the Wessex Institute of Technology 's conferences on the Boundary Element Method, first convened in 1978 and now held annually, are recognised internationally as the record of the latest advances on the Method and other meshless techniques and their applications. The papers presented at the 35th conference cover topics such as Advanced meshless and mesh reduction methods; Advanced formulations; Computational methods; Stochastic modelling; Emerging applications; Solid mechanics applications; Dynamics and vibrations; Damage mechanics and fracture; Material characterisation; Fluid flow modelling; Electrical engineering and electromagnetics; Heat and mass transfer.
to Boundary Elements Theory and Applications With 194 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo Hong Kong Dr.-Ing. Friedel Hartmann University of Dortmund Department of Civil Engineering 4600 Dortmund 50 FRG ISBN-13: 978-3-642-48875-7 e-ISBN-13: 978-3-642-48873-3 001: 10.1007/978-3-642-48873-3 Library of Congress Cataloging-in-Publication Data Hartmann, F. (Friedel) Introduction to boundary elements: theory and applications/Friedel Hartmann. ISBN-13: 978-3-642-48875-7 1. Boundary value problems. I. Title. TA347.B69H371989 515.3'5--dc19 89-4160 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provision of the German Copyright Law of September 9,1965, in its version of June 24,1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1989 Softcover reprint of the hardcover 1 st edition 1989 The use of registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.