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Open AccessArticle

Optimum Design of Infinite Perforated Orthotropic and Isotropic Plates

Faculty of Mechanical and Mechatronics Engineering, Shahrood University of Technology, P.O. box 3619995161 Shahrood, Iran
Lehrstuhl für Technische Mechanik, Institut für Mechanik, Fakultät für Maschinenbau, Otto-von-Guericke-Universität Magdeburg, 39106 Magdeburg, Germany
Faculty of Mechanical, Industrial and Maritime Engineering, Ovidius University of Constanta, 900527 Constanta, Romania
Author to whom correspondence should be addressed.
Mathematics 2020, 8(4), 569;
Received: 6 March 2020 / Revised: 30 March 2020 / Accepted: 7 April 2020 / Published: 11 April 2020
(This article belongs to the Special Issue Applied Mathematics and Solid Mechanics)
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. View Full-Text
Keywords: infinite orthotropic plates; quasi-square cutout; particle swarm algorithm; analytical solution; complex variable method infinite orthotropic plates; quasi-square cutout; particle swarm algorithm; analytical solution; complex variable method
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Jafari, M.; Hoseyni, S.A.M.; Altenbach, H.; Craciun, E.-M. Optimum Design of Infinite Perforated Orthotropic and Isotropic Plates. Mathematics 2020, 8, 569.

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