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A Fast Multipole Boundary Element Method for the Thin Plate Bending Problem

Huang, Shuo
http://rave.ohiolink.edu/etdc/view?acc_num=ucin1368026582

Abstract Details

2013, MS, University of Cincinnati, Engineering and Applied Science: Mechanical Engineering.
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
Yijun Liu, Ph.D. (Committee Chair)
Guirong Liu, Ph.D. (Committee Member)
Kumar Vemaganti, Ph.D. (Committee Member)
57 p.
Mechanics
Boundary element method; Fast multipole method; Thin plate bending problems;

Recommended Citations

Citations

  • Huang, S. (2013). A Fast Multipole Boundary Element Method for the Thin Plate Bending Problem [Master's thesis, University of Cincinnati]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1368026582

    APA Style (7th edition)

  • Huang, Shuo. A Fast Multipole Boundary Element Method for the Thin Plate Bending Problem. 2013. University of Cincinnati, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=ucin1368026582.

    MLA Style (8th edition)

  • Huang, Shuo. "A Fast Multipole Boundary Element Method for the Thin Plate Bending Problem." Master's thesis, University of Cincinnati, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1368026582

    Chicago Manual of Style (17th edition)

ucin1368026582
561
© 2013, all rights reserved.
This open access ETD is published by University of Cincinnati and OhioLINK.