Download or read book A Fast Multipole Boundary Element Method for the Thin Plate Bending Problem written by Shuo Huang and published by . This book was released on 2013 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: The boundary element method (BEM) has been applied to solve thin plate bending problems for more than four decades. From 1970s, many researchers have reported successful applications of the BEM in solving thin plate bending problems. Most of these researchers focused on the behaviors of plates of simple geometries due to the limitation of the computing power. With the fast development of the computer technology, large-scale thin plate bending problems are solvable now. However, compared to the finite element method (FEM), BEM is still not widely used in thin plate bending analysis. One reason is that the final coefficient matrix of linear equations is dense and non-symmetric so that all entries of the matrix will be calculated and stored. Thus, the CPU time and memory consumption of the BEM will increase as O(N^2) (here N is the degrees of freedom of the model). In order to avoid the drawbacks, the fast multipole BEM was developed in the mid of 1980s. With the help of the fast multipole algorithm, the used CPU time and memory storage in most cases can be O(NlogN) or O(N). In this thesis, the fast multipole BEM is employed to solve large-scale thin plate bending problems. First, the boundary integral equations based on Kirchhoff thin plate theory and steps of the conventional BEM are reviewed. Then the fast multipole BEM is introduced and the complex forms of kernel functions, expansions and translations are derived. Finally, some examples are given to show the accuracy and efficiency of the developed fast multipole BEM for thin plate bending problems. It is shown that the plate bending problems can be solved effectively and efficiently with the fast multipole BEM.
Download or read book Fast Multipole Boundary Element Method written by Yijun Liu and published by Cambridge University Press. This book was released on 2009-08-24 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fast multipole method is one of the most important algorithms in computing developed in the 20th century. Along with the fast multipole method, the boundary element method (BEM) has also emerged as a powerful method for modeling large-scale problems. BEM models with millions of unknowns on the boundary can now be solved on desktop computers using the fast multipole BEM. This is the first book on the fast multipole BEM, which brings together the classical theories in BEM formulations and the recent development of the fast multipole method. Two- and three-dimensional potential, elastostatic, Stokes flow, and acoustic wave problems are covered, supplemented with exercise problems and computer source codes. Applications in modeling nanocomposite materials, bio-materials, fuel cells, acoustic waves, and image-based simulations are demonstrated to show the potential of the fast multipole BEM. Enables students, researchers, and engineers to learn the BEM and fast multipole method from a single source.
Download or read book Plate Bending Analysis with Boundary Elements written by M. H. Aliabadi and published by Computational Mechanics. This book was released on 1998 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years the application of the boundary element to plate bending problems has gained much popularity. This book brings together leading researchers in the field of BEM and plate bending to provide a comprehensive and detailed report of these advances.
Download or read book A Fast Multipole Boundary Element Method and Its Application in Diffusion Problems written by Bo Wang and published by . This book was released on 2012 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Boundary Element Method for Plate Analysis written by John T. Katsikadelis and published by Elsevier. This book was released on 2014-07-16 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boundary Element Method for Plate Analysis offers one of the first systematic and detailed treatments of the application of BEM to plate analysis and design. Aiming to fill in the knowledge gaps left by contributed volumes on the topic and increase the accessibility of the extensive journal literature covering BEM applied to plates, author John T. Katsikadelis draws heavily on his pioneering work in the field to provide a complete introduction to theory and application. Beginning with a chapter of preliminary mathematical background to make the book a self-contained resource, Katsikadelis moves on to cover the application of BEM to basic thin plate problems and more advanced problems. Each chapter contains several examples described in detail and closes with problems to solve. Presenting the BEM as an efficient computational method for practical plate analysis and design, Boundary Element Method for Plate Analysis is a valuable reference for researchers, students and engineers working with BEM and plate challenges within mechanical, civil, aerospace and marine engineering. One of the first resources dedicated to boundary element analysis of plates, offering a systematic and accessible introductory to theory and application Authored by a leading figure in the field whose pioneering work has led to the development of BEM as an efficient computational method for practical plate analysis and design Includes mathematical background, examples and problems in one self-contained resource
Download or read book Fast Boundary Element Methods in Engineering and Industrial Applications written by Ulrich Langer and published by Springer Science & Business Media. This book was released on 2012-02-02 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains eight state of the art contributions on mathematical aspects and applications of fast boundary element methods in engineering and industry. This covers the analysis and numerics of boundary integral equations by using differential forms, preconditioning of hp boundary element methods, the application of fast boundary element methods for solving challenging problems in magnetostatics, the simulation of micro electro mechanical systems, and for contact problems in solid mechanics. Other contributions are on recent results on boundary element methods for the solution of transient problems. This book is addressed to researchers, graduate students and practitioners working on and using boundary element methods. All contributions also show the great achievements of interdisciplinary research between mathematicians and engineers, with direct applications in engineering and industry.
Download or read book Boundary Element Formulations for Thick Plates written by Youssef F. Rashed and published by Computational Mechanics. This book was released on 2000 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Boundary Element Method in Plate Bending written by Omar Mohammed Ben-Sasi and published by . This book was released on 1983 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Recent Advances in Boundary Element Methods written by George Manolis and published by Springer Science & Business Media. This book was released on 2009-05-12 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, dedicated to Professor Dimitri Beskos, contains contributions from leading researchers in Europe, the USA, Japan and elsewhere, and addresses the needs of the computational mechanics research community in terms of timely information on boundary integral equation-based methods and techniques applied to a variety of fields. The contributors are well-known scientists, who also happen to be friends, collaborators as past students of Dimitri Beskos. Dimitri is one the BEM pioneers who started his career at the University of Minnesota in Minneapolis, USA, in the 1970s and is now with the University of Patras in Patras, Greece. The book is essentially a collection of both original and review articles on contemporary Boundary Element Methods (BEM) as well as on the newer Mesh Reduction Methods (MRM), covering a variety of research topics. Close to forty contributions compose an over-500 page volume that is rich in detail and wide in terms of breadth of coverage of the subject of integral equation formulations and solutions in both solid and fluid mechanics.
Download or read book Application of Multipole Expansions to Boundary Element Method written by Kausik Mitra and published by . This book was released on 2002 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The Boundary Element Method (BEM) has long been considered to be a viable alternative to the Finite Element Method (FEM) for doing engineering analysis. The BEM reduces the dimensions of the problem by one and leads to smaller system of equations. One of the inherent limitations of the BEM has been the long time required for the solution of large problems. This makes the BEM prohibitively expensive to use while solving large problems involving crack propagation, elastodynamics, etc. This thesis is a successful attempt at reducing the solution time for the BEM. An iterative solver has been developed and the advantages it offers over the direct solver have been presented. The fast multipole method is a method used to reduce the number of computations while solving N body problems in astrophysics and molecular dynamics. A numerical formulation for accelerating the computation of boundary integrals based on the fast multipole method has been presented. An algorithm has been developed and it has been applied to the BEM for two-dimensional potential problems. It has been found that the use of this algorithm leads to savings in CPU time for large number of nodes. This method is very promising and future research can concentrate on improving the code so that more significant savings in time can be obtained.
Download or read book Analysis of Plate Bending Problems by the Direct Boundary Element Method written by David John Danson and published by . This book was released on 1980 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Boundary Elements and Other Mesh Reduction Methods XXXVIII written by A.H-D. Cheng and published by WIT Press. This book was released on 2015-11-16 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Containing the latest in a long line of conferences covering the most recent advances in Boundary Elements and Mesh Reduction Methods (BEM/MRM), this book contains an important chapter in the history of this important method used in science and engineering. The BEM/MRM conference has long been recognised as THE international forum on the technique. The proceedings of the conference therefore constitute a record of the development of the method, running from the initial successful development of boundary integral techniques into the BEM, a method that eliminates the need for an internal mesh, to the recent and most sophisticated Mesh Reduction and even Meshless Methods. Since the boundary elements, mesh reduction, and meshless methods are used in many engineering and scientific fields, the book will be of great interest to all engineers and scientists working within the areas of numerical analysis, boundary elements and meshless methods. Topics covered include: Advanced formulations; Advanced meshless and mesh reduction methods; Structural mechanics applications; Solid mechanics; Heat and mass transfer, Electrical engineering and electromagnetics; Computational methods; Fluid flow modelling; Damage mechanics and fracture; Dynamics and Vibrations Engineering applications.
Download or read book Computational Mechanics written by Zhenhan Yao and published by 清华大学出版社有限公司. This book was released on 2004 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book An Investigation of the Regular Direct Boundary Element Method for Plate Bending Problems written by O. Bettahar and published by . This book was released on 1993 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Adaptive Fast Multipole Boundary Element Methods for Three dimensional Potential and Acoustic Wave Problems written by Liang Shen and published by . This book was released on 2007 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a numerical method used in the simulations of many potential and acoustic problems, the boundary element method (BEM) has suffered from high solution cost for quite some time, although it has the advantage in the modeling or meshing stage. One way to improve the solution efficiency of the BEM is to use the fast multipole method (FMM). The reduction of the computing cost with the FMM is achieved by using multilevel clustering of the boundary elements, the use of multipole expansions of the fundamental solutions and adaptive fast multipole algorithms. In combination with iterative solvers, the fast multipole boundary element method (FMBEM) is capable of solving many large-scale 3-D problems on desktop PCs. In this dissertation, 3-D adaptive fast multipole boundary element methods for solving large-scale potential (e.g., thermal and electrostatic) and acoustic wave problems are developed. For large-scale potential problems, an adaptive fast multipole algorithm is developed in the FMBEM implementation. The conventional boundary integral equation (CBIE), hyper-singular boundary integral equation (HBIE) and their combination, dual boundary integral equation (CHBIE), are adopted and can be selectively chosen to solve different models. Both the conventional and the new fast multipole method with diagonal translations are implemented and their performances are compared. Implementation issues related to reusing the pre-conditioner and storing the coefficients to further improve the efficiency are addressed. Numerical examples, ranging from simple block models to heat sink and large-scale models of micro-electro-mechanical-systems are tested and presented. For large-scale acoustic problems, a modified version of adaptive fast multipole algorithm is developed for full-space problems first. The Burton-Miller formulation using a linear combination of the CBIE and HBIE is used to overcome the non-uniqueness difficulties in the BIEs for exterior problems. Several large-scale radiation and scattering problems, including scattering and radiating spheres and an engine model are tested. Then, the full-space algorithm is further modified and extended to solving half-space problems. Instead of using a tree structure that contains both real domain and its mirror image, the same tree structure that has been used in the full-space domain is used in the half-pace domain, which greatly simplifies the implementation of half-space FMBEM and reduces the memory storage size. Several examples including spheres sitting on the ground and sound barriers are tested. All the numerical examples of the potential and acoustic problems presented in this dissertation clearly demonstrate the effectiveness and efficiency of the developed adaptive fast multipole boundary element methods. The adaptive FMBEM code for potential problems and the adaptive FMEBM code for acoustic problems have been integrated in a single software package, which is well structured, modularized and extendable to handling other types of problems. Three journal papers have been published based on the work reported in this dissertation, and one journal paper on the half-space problem is in preparation. This dissertation research has significantly advanced the FMBEM for solving large-scale 3-D potential and acoustic problems. The developed adaptive fast multipole algorithms can be easily extended to the FMBEM for 3-D single-domain elasticity, Stokes flow, and multi-domain potential, acoustic, elasticity and Stokes problems for applications in large-scale modeling of composites, functionally-graded materials, micro-electro-mechanical-systems, and biological materials and fluids.
Download or read book The Boundary Element Method with Programming written by Gernot Beer and published by Springer Science & Business Media. This book was released on 2008-09-03 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thorough yet understandable introduction to the boundary element method presents an attractive alternative to the finite element method. It not only explains the theory but also presents the implementation of the theory into computer code, the code in FORTRAN 95 can be freely downloaded. The book also addresses the issue of efficiently using parallel processing hardware in order to considerably speed up the computations for large systems. The applications range from problems of heat and fluid flow to static and dynamic elasto-plastic problems in continuum mechanics.
Download or read book Development of a Computer Code Implementing a Direct Boundary Element Method for Plate Bending Problems written by Keh-Chang Yeh and published by . This book was released on 1985 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt:
