Optimization of functionally graded plates under Thermo-elastic free vibration using nature-based algorithms

Abstract

This article presents the parametric optimization of the free vibration characteristics of a functionally graded material (FGM) plate exposed to nonlinear thermal loading using the finite element method and nature-based algorithms. The one-dimensional (1D) Fourier heat conduction equation is used to calculate temperature distributions over the thickness of the plate. Using Lagrange’s equation, we get the dynamic equation of motion for the plate. An eight-noded iso-parametric plate element with five degrees of freedom per node is used in the finite element formulation based on first-order shear deformation theory. Rectangular plates have temperature-dependent material characteristics; the thickness of the plates is scaled using a straightforward power law distribution. Here, the investigation of the FGM plate is conducted with two different boundary conditions, such as simple support and fully clamped. Additionally, new hybrid optimization approaches, namely RSM-Composite Desirability Optimization (RSM-CDO), Whale Optimization Algorithm (WOA), Corrected Moth Search Optimization (CMSO), Lichtenberg Algorithm Optimization (LAO), Sunflower Optimization Algorithm (SFO), and Forensic-Based Investigation Algorithm (FBI), are utilised to determine the best optimal solution, and the obtained findings are validated using confirmatory tests.

Keywords

FGM finite element method metaheuristic optimization plate thermal environment

Get full access to this article

View all access options for this article.

References

Shinno

Hirai

Watanabe

. Tilting functional materials: Aiming for ultra-heat-resistant materials for spacecraft. J. Jpn. Soc. Compos. Mater 1987; 13(6): 257–264, DOI: 10.6089/jscm.13.257.

Reddy

. Mechanics of laminated composite plates and shells: theory and analysis. Boca Raton, Florida: CRC press, 2003, https://www.google.co.in/books/edition/Mechanics_of_Laminated_Composite_Plates/eeUr_AJiGRcC?hl=en&gbpv=1&dq=Mechanics+of+laminated+composite+plates+and+shells:+theory+and+analysis&printsec=frontcover.

Zhao

Liew

. Free vibration analysis of functionally graded conical shell panels by a meshless method. Composite Structures 2011; 93(2): 649–664, DOI: 10.1016/j.compstruct.2010.08.014.

Nejati

Asanjarani

Dimitri

, et al. Static and free vibration analysis of functionally graded conical shells reinforced by carbon nanotubes. International Journal of Mechanical Sciences 2017; 130: 383–398, DOI: 10.1016/j.ijmecsci.2017.06.024.

Alipour

Shariyat

Shaban

. Free vibration analysis of bidirectional functionally graded conical/cylindrical shells and annular plates on nonlinear elastic foundations, based on a unified differential transform analytical formulation. Journal of Solid Mechanics 2020; 12(2): 385–400, DOI: 10.22034/jsm.2019.1869981.1450.

Rezaiee-Pajand

Sobhani

Masoodi

. Free vibration analysis of functionally graded hybrid matrix/fiber nanocomposite conical shells using multiscale method. Aerospace Science and Technology 2020; 105: 105998, DOI: 10.1016/j.ast.2020.105998.

Hao

Chen

Zhang

, et al. Nonlinear oscillations, bifurcations and chaos of functionally graded materials plate. Journal of Sound and Vibration 2008; 312(4–5): 862–892, DOI: 10.1016/j.jsv.2007.11.033.

Zhang

Yang

Hao

. Chaotic vibrations of an orthotropic FGM rectangular plate based on third-order shear deformation theory. Nonlinear Dyn 2010; 59(4): 619–660, DOI: 10.1007/s11071-009-9568-y.

Hao

Zhang

Yang

. Nonlinear oscillation of a cantilever FGM rectangular plate based on third-order plate theory and asymptotic perturbation method. Composites Part B: Engineering 2011; 42(3): 402–413, DOI: 10.1016/j.compositesb.2010.12.010.

10.

Klaus-Jurgen

Bathe

(2014) Finite element procedures: PHI Learning Private Limited, Delhi https://books.google.co.in/books?hl=en&lr=&id=rWvefGICfO8C&oi=fnd&pg=PR13&dq=%5B10%5D%09Bathe+Klaus-Jurgen,+Finite+Element+Procedures,+PHI+Learning+Private+Limited&ots=gHHGCOuoG-&sig=GmyY8HSrSqwMs2Ij_HGJOTduJg8&redir_esc=y#v=onepage&q&f=false

11.

Choudhury

Chandrasekaran

. Gas Tungsten arc welding of inconel 825 sheet: study on weld bead geometry and GA optimization. In: Advances in Materials and Manufacturing Engineering. Lecture Notes in Mechanical Engineering. Singapore: Springer, 2020, pp. 413–420, DOI: 10.1007/978-981-15-1307-7_46.

12.

Senthil

Parameshwaran

Ragu Nathan

, et al. A multi-objective optimization of the friction stir welding process using RSM-based-desirability function approach for joining aluminum alloy 6063-T6 pipes. Struct Multidiscipl Optim 2020; 62(3): 1117–1133, DOI: 10.1007/s00158-020-02542-2.

13.

Das

Karmakar

. Free vibration characteristics of functionally graded pre-twisted conical shells under rotation. J Inst Eng India Ser C 2018; 99(6): 681–692, DOI: 10.1007/s40032-017-0378-6.

14.

Maji

Rout

Karmakar

. Free vibration response of carbon nanotube reinforced pretwisted conical shell under thermal environment. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 2020; 234(3): 770–783, DOI: 10.1177/0954406219886325.

15.

Derringer

Suich

. Simultaneous optimization of several response variables. Journal of Quality Technology 2018; 12(4): 214–219, DOI: 10.1080/00224065.1980.11980968.

16.

Myers

Montgomery

Anderson-Cook

. Response surface methodology: process and product optimization using designed experiments: John Wiley and Sons, 2016, https://www.wiley.com/en-us/Response+Surface+Methodology%3A+Process+and+Product+Optimization+Using+Designed+Experiments%2C+4th+Edition-p-9781118916018

17.

Zhai

Huang

, et al. Whale optimization algorithm for multi-constraint second-order stochastic dominance portfolio optimization. Comput Intell Neurosci 2020; 2020: 8834162–8834219, DOI: 10.1155/2020/8834162.