Abstract
In this study, an attempt was made to introduce the optimal values of effective parameters on the stress distribution around a circular/elliptical/quasi-square cutout in the perforated orthotropic plate under in-plane loadings. To achieve this goal, Lekhnitskii’s complex variable approach and Particle Swarm Optimization (PSO) method were used. This analytical method is based on using the complex variable method in the analysis of two-dimensional problems. The Tsai–Hill criterion and Stress Concentration Factor (SCF) are taken as objective functions and the fiber angle, bluntness, aspect ratio of cutout, the rotation angle of cutout, load angle, and material properties are considered as design variables. The results show that the PSO algorithm is able to predict the optimal value of each effective parameter. In addition, these parameters have significant effects on stress distribution around the cutouts and the load-bearing capacity of structures can be increased by appropriate selection of the effective design variables. The main innovation of this study is the use of PSO algorithm to determine the optimal design variables to increase the strength of the perforated plates. Finite element method (FEM) was employed to examine the results of the present analytical solution. The results obtained by the present solution are in accordance with numerical results.
Highlights
Nowadays, the design of metal and composite plates with cutouts is of a great importance due to their extensive application in different industries [1,2]
Moussavian and Jafari [49] calculated the optimal values of effective parameters on the stress distribution around a quasi-square cutout using different optimization algorithms such as Particle Swarm Optimization (PSO), genetic algorithm (GA), and Ant Colony Optimization (ACO) [50]
Tsai–Wu criterion are considered as a cost function for the PSO algorithm
Summary
The design of metal and composite plates with cutouts is of a great importance due to their extensive application in different industries [1,2]. The analysis of this phenomenon, called stress concentration, has a significant importance for designers of engineering structures. The fracture strength of these structures depends strongly on the stress concentration caused by cutouts. Stress concentration and fracture criterions are very important in evaluating the reliability of engineering structures [4]. In this study, according to the extensive usage of different types of cutouts and considering a long process of trial and error to find their optimum design, particle swarm optimization (PSO) algorithm (see, e.g., [5]) is employed for the Mathematics 2020, 8, 569; doi:10.3390/math8040569 www.mdpi.com/journal/mathematics. The main innovation of this paper is the use of PSO algorithm to determine the optimal design variables to increase the strength of the perforated plates
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