Optimization of finite plates with polygonal cutout under in-plane loading by gray wolf optimizer

Abstract

This article investigates the optimum design of isotropic finite plates with different polygonal cutouts under in-plane loading (uniaxial tensile, biaxial, and pure shear load). This purpose is pursued by a gray wolf optimization algorithm. The important features of this algorithm include flexibility, simplicity, short solution time, and the ability to avoid local optimums. The objective function used for this algorithm seeks to minimize the value of stress concentration factor around different cutouts. The method used for the calculation of stress concentration is based on analytical solution of Muskhelishvili complex variable and conformal mapping with plane stress assumption. The plate is assumed to be isotropic, linear elastic, and finite (the ratio of cutout side to plate's longest side in the square and triangular cutouts and the ratio of diameter of circle circumscribing other n-gonals to the plate's longest side are greater than 0.2). Results show that by selecting the aforementioned parameters properly, less amounts of stress could be achieved around the polygonal cutout leading to an increase in load-bearing capacity of the structure.

Effect of various discontinuities present in a plate on stress concentration: a review

“…Muskhelishvili's complex variable method [1] Finite element analysis [13, 46, 52] Least square boundary collocation method [1] Genetic algorithm [6, 21] Modified mapping collocation method [51] Gravitational search algorithm [53] Swarm intelligence algorithm [34] Experimental method Differential evolution algorithm [54] MTS hydraulic testing machine [55] Harmony search algorithm [54] universal testing machine [49] Big bang-big crunch algorithm [54] Two-dimensional photoelasticity test (Plane Polariscope) [50] Grey wolf optimizer algorithm [56] Particle swarm optimization [29] Bat algorithm [53] Abdullah Alshaya has evaluated individual stresses and displacements in vertically-loaded notched finite graphite/epoxy laminated composite anisotropic plate with an airy stress function in complex variables and hydraulic testing machine with image correlation as shown in figure 4. These results were compared with FEA results [55].…”

“…He had optimized the various parameters in the finite isotropic plates having the hexagonal cutout under in-plane loading with the help of DE (Differential evolution algorithm) and HSA (Harmony search algorithm), BB-BC (Big bang-big crunch algorithm), GWO (Grey wolf optimizer algorithm), and PSO. Results of those algorithms were compared with one another, which indicated that the grey wolf optimizer has the entire performance, very small resolution time, and the having good ability to avoid local optimums [54,56]. M. Dehghani had obtained a general analytical answer to find stress distribution during a finite elastic plate having a circular or square hole with help of Muskhelishvili's complex variable technique.…”

Effect of cutout geometry on the failure strength of symmetric laminates under uniform heat flux

“…= Á q i ¼ 0 (11) By substituting Fourier's law into equation ( 11), the governing thermal equation for the homogeneous anisotropic material is expressed as equation ( 12)…”

“…10 The complex variable technique along with the conformal mapping function was employed by the authors for the stress functions estimation. The optimum design of isotropic finite plates considering various polygonal cutouts was studied by Bayati and Jafari 11 who focused on the plate dimension ratios impacts to reduce stress concentration surrounding polygonal cutouts. The complex variable method was also applied by Ukadgaonker and Rao 12 in identifying the distribution of the mechanical stress around different cutouts in symmetric laminates.…”

Optimum Design of Infinite Perforated Orthotropic and Isotropic Plates

“…Complex potential method established by G.V. Kolosov and N.I Muskhelishvili (see, e.g., [6][7][8]) has been applied for anisotropic plates by Green and Zerna [7], Lekhniskii [9], Sih et al [10], Lekhniskii [11], Bigoni and Movchan [12], Radi et al [13], Craciun and Soós [14], Craciun and Barbu [15], and Chaleshtari and Jafari [16]. Tsutsumi et al [17] investigated the solution of a semi-infinite plane with one circular hole.…”