A Fast Multipole Boundary Element Method for Solving Two-dimensional Thermoelasticity Problems

by Yuxiang Li

Institution: University of Cincinnati
Department: Engineering and Applied Science: Mechanical Engineering
Degree: MS
Year: 2014
Keywords: Mechanics; fast multipole method; boundary element method; thermoelasticity
Record ID: 2043186
Full text PDF: http://rave.ohiolink.edu/etdc/view?acc_num=ucin1397477834


A fast multipole boundary element method (BEM) for solving general uncoupled two-dimensional (2-D) steady-state thermoelasticity problems is presented in this thesis. Though the computer technology develops very fast, the conventional BEM is still not efficient to solve large-scale thermoelasticity problems due to the O(N2) increase of the CPU time and memory consumption with N (N is the degrees of freedom of the model). The fast multipole BEM is developed to reduce the computational complexity. In this thesis, the direct BIEs and the conventional BEM formulations for 2-D steady-state thermoelasticity are reviewed first. Then, fast multipole expansions, local expansions and related translations for the thermal term are derived using complex variables. Finally, several numerical examples are presented to show the accuracy and effectiveness of the developed fast multipole BEM in calculating the displacement and stress fields for 2-D elastic bodies under various thermal loads, including thin structure domains that are difficult to mesh using the finite element method (FEM). The BEM results using constant elements are found to be accurate compared with the analytical solutions, and the accuracy of the BEM results is found to be comparable to that of the FEM with linear elements. In addition, the BEM mesh is easier to be generated for a thin structure domain or a domain with complicated geometry, such as a perforated plate with randomly distributed holes for which the FEM fails to provide an adequate mesh. These results clearly show the advantages of the developed fast multipole BEM for solving 2-D thermoelasticity problems. Some discussions are provided to conclude this thesis.