Stress analysis of two-dimensional perforated plates using boundary element alternating method

Abstract

In this paper, the boundary element alternating method (BEAM) is developed to study the stress concentration of a two-dimensional (2D) perforated plate. This method involves the iterative superposition between the boundary element solution of a bounded plate without holes and the analytical solution of an infinite 2D plate with a circular hole subjected to arbitrary normal and sheer loading until the required boundary conditions of the original problem are satisfied. Excellent agreements between the solutions of the present simplified procedure and the numerical methods (conventional finite element and boundary element techniques) are observed and show the advantages of the proposed method. (C) 2000 Elsevier Science Ltd. All rights reserved

Stress Calculations on Multiply Connected Domains

“…An advantage with (49), over Sherman's original equation [38], is that (49) is based on the potentials¨´Þµ and ©´Þµ, simply related to stress via (3,4), while Sherman's original equation is based on the potentials ´Þµ and ´Þµ, related to stress via differentiation.…”

“…The value for Ã Ø of the setup in Figure 3a has also been computed for the case Ê Û ¼ ½ and Û ½, by Leung, Zavareh, and Beskos [26] and for the case Ê Û ¼ and Û ½¼ by Chen, Ting, and Yang [4]. Leung, Zavareh, and Beskos [26] use a variety of methods, including a combined finite element/boundary element scheme, and the commercial software BEASY and NASTRAN.…”

“…Chen, Ting, and Yang [4] use a combination of a boundary element method and a spectral method and arrive at a value of Ã Ø ¿¾ for their choice of parameters. A number of ¿¾ to quadratic boundary elements on an adaptive mesh and ½¾ Fourier modes were used.…”

“…One setup studied by Chen, Ting, and Yang [4] involves two equisized holes of radius Ê Û ¼ separated a distance È Û ½ in a rectangle with Û ½¼, see Figure 5a. A number of ¿¼ to ¼ quadratic elements and a number of ½¾ to ¾ Fourier modes on each hole were used.…”

“…Later work focus more on specialized numerical techniques. See Refs [3,4,5,6,18,27,43] for recent examples. Parallel to this development there has been a steady improvement of general purpose finite element packages which, among other things, can solve for stress on multiply connected domains.…”