| Owing to the puzzle of nearly singular integrals in boundary element methods(BEMs), it is difficult to use BEMs for the analysis of thin and narrow domains. A regularization algorithm is introduced to evaluate the nearly singular integrals. In the algorithm, the parameter, which causes nearly singular integrals, is removed out of the integral signs, so that the nearly strongly singular and hypersingular integrals are transformed to non-singular integrals. Therefore the problems of nearly singular integrals are successfully solved. In this thesis, the regularization algorithm is applied to the analysis of thin- walled structures in tow-dimensional elasticity problems. First, linear or quadratic isoparametric elements are used. The results of several examples show that this algorithm is more effective compared with the standard Gaussian quadrature in BEMs. Next, two improvements of the regularization algorithm in the application are proposed. One improvement is about the use of quadratic isoparametric elements. The elements are subdivided into some linear elements only when the nearly singular integrals on the elements need to be determined, and the algorithm is used on every linear element respectively. Another improvement is that the regularization algorithm is used with non-isoparametric elements, a large number of corresponding formulas are given. Therefore the nearly singular integrals can be evaluated more accurately than before. It also show that BEMs are suitable to deal with thin-walled structures. Finally, by analyzing the characteristics of every application project mentioned above, the application range of every project is given. |
