Coupled PIEM/FEM Algorithm Based on Mindlin-Reissner Plate Theory for Bending Analysis of Plates with Through-Thickness Hole
De-Shin Liu, Chin-Yi Tu, and Cho-Liang Chung

doi:10.3970/cmes.2013.092.573
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 92, No. 6, pp. 573-594, 2013
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Keywords IEM, FEM, Mindlin-Reissner plate theory, Four-point bending test, through-thickness hole.
Abstract

The Infinite Element Method (IEM) is widely used for the analysis of elastostatic structures containing singularities. In the IEM method, the problem domain is partitioned into multiple element layers, where the stiffness matrix of each layer is similar to that of the other layers in the discretized domain. However, in Mindlin-Reissner plate theory, the stiffness matrix varies through the layers of the plate, and thus the conventional IEM algorithm cannot be applied. Accordingly, the present study proposes a Plate Infinite Element Method (PIEM) in which the element stiffness matrix is separated into two sub-matrices; each being similar to the equivalent sub-matrix of the element layers above and below it. The validity of the proposed algorithm is demonstrated by comparing the results obtained for the deflection contour of a plate under four-point bending with those obtained using conventional ABAQUS Finite Element Method (FEM) software. The PIEM algorithm is then coupled with an FEM algorithm and used to investigate the effects of the hole size, hole position and hole profile / area on the bending strength (Sb) of plates containing through-thickness holes. In general, the results show that the combined PIEM/FEM algorithm provides an accurate and computationally efficient means of analyzing the bending behavior of plates containing through-thickness holes.

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