This paper reviews and compares existing theories for the analysis of perforated plates with holes arranged in equilateral triangular patterns. A search of recent literature reveals that three methods are available for the solution of flat perforated steel plates. All three methods are based on the assumption that a set of equivalent elastic constants can be determined, and that such constants when used in conjunction with the classical solid plate theory will completely describe its deflection and stress patterns. This paper also presents a modification which applies to two of the three existing theories. This modification improves the agreement between theory and available test results.
The three solutions which are found in the literature are: I. Malkin's bending analysis, G. Horvay's bending analysis and G. Horvay's plane stress analysis which can be modified to take into account plate bending. Each of these analyses is presented herein for purposes of comparison.
Differences have been found in the bending theories of Horvay and Malkin. While there is nothing in the separate developments which indicates that both theories should yield the same solution or that a limiting process could yield a common, recognizable limit for both theories, or that one is more correct than the other a priori, both solutions arc very good approximations and give results which are very close to each other (Figs 4, 12 and 13).
The modification proposed in this paper for the Horvay-Malkin theories is to include the shape factor and the effect of constrained warping on the St. Venant torsion of the ligament beams.
This modification improves the existing agreement between theory and experiment.
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| Number of Pages : | 33 |
| Published : | 1959 |
