Abstract
In this paper, the optimization of the volume fraction of functionally graded (FG) beams for maximizing the first natural frequency is investigated. Distribution laws using three, four and five parameters are used to describe volume fraction. Navier-type solutions based on various shear deformation theories are developed to compute the natural frequencies. A new metaheuristic algorithm called Social Group Optimization (SGO) is employed for the first time to solve the functionally graded beam optimization problem. Optimal volume fractions for beams with different material properties are then obtained. It is found that the five-parameter distributions give the highest first natural frequency for all cases. Moreover, the results show the consistency of the optimal volume fractions obtained by different shear deformation theories. It is also confirmed that SGO is an efficient tool for this complicated optimization problem.
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References
Miyamoto Y, Kaysser WA, Rabin BH, Kawasaki A, Ford RG (1999) Functionally graded materials: design, processing and applications. Chapman & Hall, London
Save WPM, Warner WH (eds) (1990) Structural optimization. Springer
Goupee AJ, Vel SS (2006) Optimization of natural frequencies of bidirectional functionally graded beams. Struct Multidiscip Optim 32(6):473–484
Yas MH, Kamarian S, Eskandari J, Pourasghar A (2011) Optimization of functionally graded beams resting on elastic foundations. J Solid Mech 3(4):365–378
Yas MH, Kamarian S, Pourasghar A (2014) Application of imperialist competitive algorithm and neural networks to optimise the volume fraction of three-parameter functionally graded beams. J Exp Theor Artif Intell 26(1):1–12
Kamarian S, Yas M, Pourasghar A, Daghagh M (2014) Application of firefly algorithm and anfis for optimisation of functionally graded beams. J Exp Theor Artif Intell 26(2):197–209
Roque CMC, Martins PALS (2015) Differential evolution for optimization of functionally graded beams. Compos Struct 133:1191–1197
Roque CMC, Martins PALS, Ferreira AJM, Jorge RMN (2016) Differential evolution for free vibration optimization of functionally graded nano beams. Compos Struct 156:29–34
Alshabatat NT, Naghshineh K (2014) Optimization of natural frequencies and sound power of beams using functionally graded material. Adv Acoust Vib 2014
Tsiatas GC, Charalampakis AE (2017) Optimizing the natural frequencies of axially functionally graded beams and arches. Compos Struct 160:256–266
Aydogdu M, Taskin V (2007) Free vibration analysis of functionally graded beams with simply supported edges. Mater Des 28(5):1651–1656
Şimşek M (2010) Fundamental frequency analysis of functionally graded beams by using different higher-order beam theories. Nucl Eng Des 240(4):697–705
Thai HT, VO TP (2012) Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories. Int J Mech Sci 62(1):57–66
Mashat DS, Carrera E, Zenkour AM, Al Khateeb SA, Filippi M (2014) Free vibration of FGM layered beams by various theories and finite elements. Compos Part B: Eng 59(2014) 269–278
Hadji L, Khelifa Z, Daouadji TH, Bedia EA (2015) Static bending and free vibration of FGM beam using an exponential shear deformation theory. Coupled Syst Mech 4(1):99–114
Bao G, Wang L (1995) Multiple cracking in functionally graded ceramic/metal coatings. Int J Solids Struct 32(19):2853–2871
Chi S-H, Chung Y-L (2006) Mechanical behavior of functionally graded material plates under transverse loadpart I: analysis. Int J Solids Struct 43(13):3657–3674
Ait Atmane H, Tounsi A, Meftah SA, Belhadj HA (2011) Free vibration behavior of exponential functionally graded beams with varying crosssection. J Vib Control 17(2):311–318
Viola E, Tornabene F (2009) Free vibrations of three parameter functionally graded parabolic panels of revolution. Mech Res Commun 36(5):587–594
Karama M, Afaq KS, Mistou S (2003) Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity. Int J Solids Struct 40(6):1525–1546
Soldatos KP (1992) A transverse shear deformation theory for homogeneous monoclinic plates. Acta Mech 94(3):195–220
Touratier M (1991) An efficient standard plate theory. Int J Eng Sci 29(8):901–916
Reddy JN (1984) A simple higher-order theory for laminated composite plates. J Appl Mech 51(4):745–752
Satapathy S, Naik A (2016) Social group optimization (SGO): a new population evolutionary optimization technique. Complex Intell Syst 2(3):173–203
Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2):311–338
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Pham, A.H., Vu, T.V., Tran, T.M. (2018). Optimal Volume Fraction of Functionally Graded Beams with Various Shear Deformation Theories Using Social Group Optimization. In: Nguyen-Xuan, H., Phung-Van, P., Rabczuk, T. (eds) Proceedings of the International Conference on Advances in Computational Mechanics 2017. ACOME 2017. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-10-7149-2_27
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DOI: https://doi.org/10.1007/978-981-10-7149-2_27
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