Fast multipole boundary element method for the analysis of plates with many holes

A three-node quadratic element version of the fast multipole boundary element method (FMBEM) for two-dimensional elastostatic problems is presented. The method is applied to the analysis of perforated plates. A comparison of convergence and accuracy of the present method using quadratic elements with the method using constant elements, presented by other authors, is given. Stress results for a square plate with a circular hole are investigated. Effective material properties of plates with many holes are estimated and compared to analytical results. Implementation of quadratic-element version of the FMBEM resulted in a lower number of degrees of freedom and expansion terms, and similar accuracy to constant-element version of the method, for the same structures. Influence of boundary conditions on the convergence of the iterative solver is investigated. The effectiveness of the FMBEM in relation to the conventional BEM is presented.