Evaluation of optimal parameters affecting of isotropic plates with polygonal cutout under shear load using particle swarm algorithm

Authors

Abstract

In this paper the optimal values of effective parameters on the stress distribution around polygonal cutouts in isotropic plates are calculated. To achieve this goal, the complex variable method and PSO algorithm have been used. The expansion of the Muskhelishvili’s method are used to analyze the stress distribution in infinite isotropic plates containing various cutouts. By using conformal mapping, the area outside the non-circular cutout is mapped to the area outside of unit circle. The effective parameters on stress distribution around the cutout as design variables include: cutout shape, cutout orientatin and bluntness. The proper selection of these parameters leads to achieve minimum stress around the cutout and result in the load-bearing capacity of structures increases. The goal function in this problem is the maximum stress created around the cutout calculated by the analytical solution method. The results presented in this study shows that by choosing the appropriate shape of cutout and the optimal effective parameters, stress concentration factor can be significantly reduced and lowest stress concentration factor rather than the value of stress concentration corresponding to circular hole can be achieved.

Keywords

Main Subjects

References

[1] Muskhelishvili NI (1962) Some basic problems of the mathematical theory of elasticity. 2ed edn. Noordhooff , Netherlands.
[2] Savin GN (1961) Stress concentration around holes. Pergamon Press, New York.
[3] Lekhnitskii SG (1968) Anisotropic plates. 2ed edn. Gordon and Breach Science, New York.
[4] Rezaeepazhand J, Jafari M (2010) Stress concentration in metallic plates with special shaped cutout. Int J Mech Sci 52: 96-102.
[5] Rao DKN, Babu MR, Reddy KRN, Sunil D (2010)  Stress around square and rectangular cutouts in symmetric laminates. Compos Struct 92(12): 2845-2859.
[6] Jafari M, Rahimi-petroudi A (2015) A study of the effect of various parameters on the stress analysis of isotropic and anisotropic plates containing a central quadrilateral cutout subjected to shear stress. Journal of Solid and Fluid Mechanics 5(1): 101-114. (in persion)
[7] Jafari M, Ardalani E (2015) Analytical solution to calculate the stress distribution around triangular hole in finite isotropic plates under in-plane loading. Modares Mech Eng 15(5):165-175. (in persion)
[8] Batista M (2011) On the stress concentration around a hole in an infinite plate subject to uniform load at infinity. Int J Mech Sci 53(4): 254-261.
[9] Banerjee M, Jain NK, Sanyal S (2013) Stress concentration in isotropic and orthotropic composite plates with center circular hole subjected to transverse static loading. Int J Mech Ind Eng 3(1):109-113.
[10] Kathiravan R, Ganguli R (2007) Strength design of composite beam using gradient and particle swarm optimization. Compos Struct 81: 471-479.
[11] Sivakumar K, Iyengar NGR, Deb K (1998) Optimum design of laminated composite plates with cutout using a genetic algorithm. Compos Struct 42: 265-279.
[12] Cho HK, Rowlands RE (2007) Reducing tensile stress concentration in perforated hybrid laminate by genetic algorithm. Com Sci and Tech 67:2877-2883.
[13] Hemmatian H, Fereidoon F, Rajabpour M (2010) Optimization of prismatic core based on particle swarm algorithm. Modeling in Engineering 8(20):  17-26.
[14] Omkar SN, Khandelwal R, Ananth TVS, NarayanaNaik G, Gopalakrishnan S (2009) Quantum behaved particle swarm optimization (QPSO) for multi-objective design optimization of composite structures. Expert Syst Appl 36: 11312-11322.
[15] Martin H Sadd (2009) Elasticity theory, applications and numerics. 2ed edn. Elsevier Inc., Burlington.
[16] Yang X, Yuan J, Mao H (2007) A modified particle swarm optimizer with dynamic adaptation. Appl Math Comput 189: 1205-1213.
[17] El-ghazali T (2009) Metaheuristics: from design to implementation. Wiley & sons, New Jersey.
[18] Ratnaweera A, Halgamuge SK, C.Watson H (2004) Self-Organizing hierarchical particle swarm optimizer with time-varying acceleration coefficients. IEEE T Evolut Comput 8(3): 240-255.
Journal of Solid and Fluid Mechanics
Volume 6, Issue 2
July and August 2016
Pages 29-40

Files

Share

How to cite

Statistics