Determination of Optimum Stress in Finite Metallic Plates with Polygonal Cutouts by Using Particle Swarm Algorithm

This paper investigates the influence parameters in optimum design of finite metallic plates with polygonal cutouts subjected to uniaxial loading. This objective is pursued by a particle swarm 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 in this algorithm seeks to minimize the value of stress concentration factor (optimum stress) around triangular, square, pentagonal and hexagonal cutouts. The novelty of this paper is determining of optimum stress around the polygonal cutouts in finite metallic plates under uniaxial loading. 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). Finite element numerical solution is employed to examine the results of present analytical solution. Numerical results are in good agreement with the results of the present analytical solution. Results show that by selecting the aforementioned parameters properly, less amounts of stress could be achieved around the polygonal cutouts leading to an increase in load-bearing capacity of the structure.