Optimal Stochastic Distribution of CNTS in a Cantilever Polymer Microbeam Using Artificial Neural Networks
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OPTIMAL STOCHASTIC DISTRIBUTION OF CNTS IN A CANTILEVER POLYMER MICROBEAM USING ARTIFICIAL NEURAL NETWORKS
M. Nahas,1 M. Alzahrani1,2
Keywords: artificial neural network, carbon nanotubes, optimization, microbeam The optimal stochastic distribution of carbon nanotubes (CNTs) in nanoreinforced polymer composite of a cantilevered microbeam is investigated. Finite-element simulations of the CNT-reinforced microbeams were conducted to obtain data for training an artificial neural network to construct a surrogate model. This model was then used in an optimization routine to determine the optimal CNT distribution in the microbeam with inclusion of an uncertainty in the dispersion of CNTs across the microbeam. The results obtained within the framework of this model showed an improvement compared with those reported in the literature.
1. Introduction Carbon-nanotube (CNT)-reinforced composites are an attractive choice for designers when the weight, strength, and toughness are important factors [1]. Because of the ultrahigh elastic modulus and tensile strength of CNTs, they provide a high-strength reinforcement for composites. Such composites are also used in atomic transportation, nanosensors, and Micro Electro Mechanical Systems (MEMS) [2, 3]. An important factor concerning CNT-reinforced composites is the uncertainties associated with CNTs such as their dispersion, diameter, length, and the interfacial boding between them and the matrix [4, 5]. In [6, 7], a multiscale model that incorporates various uncertainties at different levels of CNT-reinforced composites is developed. The model was implemented on the basis of a 3-point bending sample and a thick cylinder with a radial load and showed that the deterministic approach may Mechanical Engineering Department, King Abdulaziz University, Jeddah, 80204, Saudi Arabia G. W. Woodruff School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, 30332, USA * Corresponding author; e-mail: [email protected] 1 2
Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 56, No. 5, pp. 967-976, SeptemberOctober, 2020. Original article submitted May 28, 2019; revision submitted February 3, 2020. 0191-5665/20/5605-0665 © 2020 Springer Science+Business Media, LLC
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1
l = 4000 m
2 t = 40 m w = 400 m
Fig. 1. Cantilever microbeam. underestimate the mechanical properties of the composites, which can lead to an overconservative design, or may overestimate them, which can lead to a catastrophic failure. In this paper, CNT-reinforced polymer microbeams are considered. Microbeams are widely used in various MEMS [8] — sensors, microscopes, and actuating devices [9-12]. In [13], the optimal CNT distribution in a microbeam made of an LY-5052 polyester epoxy/amine resin is investigated to increase its first five natural frequencies. The beam was divided into 10 segments with a total of 10 wt.%. CNTs. But the optimization algorithm in the work evaluated all possible permutations of CNT distributions in 10 segments of the microbeam. Each of the
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