Determination of Optimal Parameters for Finite Plates with a Quasi-Square Hole

Subject Areas : Engineering

M  Jafari ¹ (Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran)
M.H  Bayati Chaleshtari ² (Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran)
E  Ardalani ³ (Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran)

Received: 2018-02-16 Accepted : 2018-04-07 Published : 2018-06-30

Keywords: Metaheuristic Algorithms, Analytical solution, Isotropic finite plate, Complex variable method,

Abstract :

This paper aims at optimizing the parameters involved in stress analysis of perforated plates, in order to achieve the least amount of stress around the square-shaped holes located in a finite isotropic plate using metaheuristic optimization algorithms. Metaheuristics may be classified into three main classes: evolutionary, physics-based, and swarm intelligence algorithms. This research uses Genetic Algorithm (GA) from evolutionary algorithm category, Gravitational Search Algorithm (GSA) from physics-based algorithm category and Bat Algorithm (BA) from Swarm Intelligence (SI) algorithm category. The results obtained from the present study necessitate the determination of the actual boundary between finite and infinite plate for the plates with square-shaped holes. The design variables such as bluntness, hole orientation, and plate dimension ratio as effective parameters on stress distribution are investigated. The results obtained from comparing BA, GA and GSA indicate that BA as SI algorithm category competitive results, proper convergence to global optimal solution and more optimal stress level than the two mentioned algorithms. The obtained results showed that the aforementioned parameters have a significant impact on stress distribution around a square-shaped holes and that the structure’s load-bearing capability can be increased by proper selection of these parameters without needing any change in material properties.

References:

[1] Muskhelishvili N., 1954, Some Basic Problems of the Mathematical Theory of Elasticity, Dordrecht, Springer, Netherlands.
[2] Savin G.N., 1961, Stress Concentration Around Holes, Pregamon Press.
[3] Lekhnitskiy S.G., 1969, Anperforated Plates, New York, Gordon-Breach Science.
[4] Theocaris P.S, Petrou L., 1986, Stress distributions and intensities at corners of equilateral triangular holes, International Journal of Fracture 31(1): 271-289.
[5] Daoust J., Hoa S.V., 1991, An analytical solution for anperforated plates containing triangular holes, Composite Structures 19(1): 107-130.
[6] Abuelfoutouh N.M., 1993, Preliminary design of unstiffened composite shells, Symposium of 7th Technical Conference of ASC.
[7] Rezaeepazhand J., Jafari M., 2005, Stress analysis of perforated composite plates, Composite Structures 71(1): 463-468.
[8] Rezaeepazhand J., Jafari M., 2010, Stress concentration in metallic plates with special shaped cutout, International Journal of Mechanical Sciences 52(1): 96-102.
[9] Odishelidze N., Criado F., 2016, Stress concentration in an elastic square plate with a full-strength hole, Mathematics and Mechanics of Solids 21: 552-561.
[10] Sharma D.S., 2011, Stress concentration around circular / elliptical / triangular cutouts in infinite composite plate, Proceedings of the World Congress on Engineering.
[11] Kradinov V., Madenci E., Ambur D.R., 2007, Application of genetic algorithm for optimum design of bolted composite lap joints, Composite Structures 77: 148-159.
[12] Yun K., 2009, Optimal bound on high stresses occurring between stiff fibers with arbitrary shaped cross-sections, Journal of Mathematical Analysis and Applications 350: 306-312.
[13] Fuschi P., Pisano A.A., Domenico D. De., 2015, Plane stress problems in nonlocal elasticity : finite element solutions with a strain-difference-based formulation, Journal of Mathematical Analysis and Applications 1: 1-23.
[14] Bazehhour B.G., Rezaeepazhand J., 2014, Torsion of tubes with quasi-polygonal holes using complex variable method, Mathematics and Mechanics of Solids 19: 260-276.
[15] Ghugal Y.M., Sayyad A.S., 2010, A static flexure of thick perforated plates using trigonometric shear deformation theory, Journal of Solid Mechanics 2: 79-90.
[16] Pan Z., Cheng Y., Liu J., 2013, Stress analysis of a finite plate with a rectangular hole subjected to uniaxial tension using modified stress functions, International Journal of Mechanical Sciences 75: 265-277.
[17] Jafari M., Ardalani E., 2016, Stress concentration in finite metallic plates with regular holes, International Journal of Mechanical Sciences 106: 220-230.
[18] Liu Y., Jin F., Li Q., 2006, A strength-based multiple cutout optimization in composite plates using fixed grid finite element method, Composite Structures 73: 403-412.
[19] Sivakumara K., Iyengar N.G.R., Deb K., 1998, Optimum design of laminated composite plates with cutouts using a genetic algorithm, Composite Structures 42: 265-279.
[20] Almeida F.S., Awruch A.M., 2009, Design optimization of composite laminated structures using genetic algorithms and finite element analysis, Composite Structures 88: 443-454.
[21] Jianqiao C., Yuanfu T., Rui G., Qunli A., 2013, Reliability design optimization of composite structures based on PSO together with FEA, Chinese Journal of Aeronautics 26: 343-349.
[22] Holdorf R., Lemosse D., Eduardo J., Cursi S.D., Rojas J., 2011, An approach for the reliability based design optimization, Optimization and Engineering 43: 1079-1094.
[23] Vosoughi A.R., Gerist S., 2014, New hybrid FE-PSO-CGAs sensitivity base technique for damage detection of laminated composite beams, Composite Structures 118: 68-73.
[24] Sharma D.S., Patel N.P., Trivedi R.R., 2014, Optimum design of laminates containing an elliptical hole, International Journal of Mechanical Sciences 85: 76-87.
[25] Jafari M., Rohani A., 2016, Optimization of perforated composite plates under tensile stress using genetic algorithm, Journal of Composite Materials 50: 2773-2781.
[26] Suresh S., Sujit P.B., Rao A.K., 2007, Particle swarm optimization approach for multi-objective composite box-beam design, Composite Structures 81: 598-605.
[27] Vigdergauz S., 2012, Stress-smoothing holes in an elastic plate: From the square lattice to the checkerboard, Mathematics and Mechanics of Solids 17: 289-299.
[28] Zhu X., He R., Lu X., Ling X., Zhu L., Liu B., 2015, A optimization technique for the composite strut using genetic algorithms, Materials and Design 65: 482-488.
[29] Izquierdo J., Campbell E., Montalvo I., Pérez-García R., 2016, Injecting problem-dependent knowledge to improve evolutionary optimization search ability, Journal of Computational and Applied Mathematics 291: 281-292.
[30] Yang W., Yue Z., Li L., Wang P., 2015, Aircraft wing structural design optimization based on automated finite element modelling and ground structure approach, Optimization and Engineering 273: 1-21.
[31] Rezaeipouralmasi A., Fariba F., Rasoli S., 2015, Modifying stress-strain curves using optimization and finite elements simulation methods, Journal of Solid Mechanics 7: 71-82.
[32] Gen M., Cheng R., 2000, Genetic Algorithms and Engineering Optimization, New York, John Wiley & Sons.
[33] Sivanandam S.N., Deepa S.N., 2008, Genetic Algorithm Optimization Problems, In Introduction to Genetic Algorithms, Springer Berlin Heidelberg, New York.
[34] Sun Z.L., Zhao M.Y., Luo L.L., 2013, Reinforcement design for composite laminate with large Cutout by a genetic algorithm method, Advanced Materials Research 631: 754-758.
[35] Toledo C.F.M., Oliveira L., França P.M., 2014, Global optimization using a genetic algorithm with hierarchically structured population, Journal of Computational and Applied Mathematics 261: 341-351.
[36] Rashedi E., Nezamabadipour H., Saryazdi S., 2009, GSA: A gravitational search algorithm, Information Science 179: 2232-2248.
[37] Sabri N.M., Puteh M., Mahmood M.R., 2013, A review of gravitational search algorithm, International Journal of Advances in Soft Computing and its Applications 5: 1-39.
[38] Yang X.S., 2010, A new metaheuristic bat-inspired algorithm, Inspired Cooperative Strategies for Optimization 284: 65-74.
[39] Yang X., Gandomi A.H., 2012, Bat algorithm: a novel approach for global engineering optimization, Engineering Computations 29: 464-483.