Presenting an explicit relation for analyzing stress of plates with quasi-square holes and under tension by using multiple linear regression

Stress concentration on the geometric discontinuities is one of the factors of structure failure. Nowadays, plates with holes are inseparable parts of designs and pieces, therefore studying the stress concentration caused by these holes is necessary to prevent structure failure. So the designer for presenting a design must be aware of the stress concentration in the hole and according to it design the basis. In this research, by using the regression method and on the basis of the mechanical properties of the materials and the radius of curvature in the corner of the hole, we try to present an explicit relation for estimating stress concentration in the orthotropic plates with quasi-square hole. This relation, in addition to easing the use and bypassing the hard and complex process of analytical solution, provides designer with the opportunity to calculate stress of perforated viscoelastic plates by using the effective module method or Boltzmann's superposition principle. At first, with analytical solution based on the Lekhnitskii method the stress values are calculated in many composite plates with quasi-square hole. Then, by using multiple linear regression and on the grounds of mechanical properties, is given an explicit relation for the stress concentration coefficient. The results show that the multiple regression model is able to predict the circumferential stress with a maximum error of 2%.