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In this paper, by expanding Muskhelishvili’s stress functions and with use of Schwarz’s alternating method, the stress distribution in a plate with two quasi-rectangular cut outs has been studied. Muskhelishvili represented the mentioned stress functions for studying the stress distribution in an isotropic plate with a circular or an elliptical cut out. In order to expand the Muskhelishvili’s analytical solution for deriving the stress functions related to quasi-rectangular cut outs, a conformal mapping function has been used. This conformal mapping transformed the area external of the quasi-rectangular cut out into the area outside the unit circle. Considering Schwarz’s alternating method, for calculating the stress distribution around two cut outs, complex series with unknown coefficients have been used. In this study, the effect of different parameters such as the location of the cut outs relative to each other, bluntness and aspect ratio of cut out sides on stress concentration factor can be investigated. The finite element method has been used to verify the accuracy of semi-analytical results. Comparison of two methods demonstrates the precision of obtained semi-analytical solution and indicates that it can be used for computing stress distribution in plates with two rectangular cut outs. Analysis of the proposed solution shows that the mentioned parameters have a significant effect on stress distribution and stress concentration factor decreases noticeably with selection of appropriate values of these parameters.

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One of the designers concerns is structural failure as a result of stress concentration in the geometrical discontinuities. Stress concentration factor in the presence of cutout, is a key parameter in reducing the structural load-bearing capacity. In the analysis of perforated isotropic plates, the effective parameters on stress distribution around cutouts are the cutout geometry, curvature radius of cutout corner, rotation angle of cutout and load angle. In this study, using PSO method it has been tried to introduce the optimum parameters to achieve the minimum amount of stress around the n-sided cutouts in isotropic plates under uniaxial tension. In this paper, an analytical method has been used to calculate the stress around cutouts with different shapes. According to this method, by using the conformal mapping, Muskhelishvili’s complex variable method which is only for circular and elliptical cutouts, has been developed for the other cutouts. The results presented in this case shows that by choosing the appropriate shape of cutout and the optimal effective parameters, stress concentration factor can be significantly reduced and lowest stress concentration factor rather than amount of stress concentration corresponding to circular hole can be achieved.