Modeling of large deflection of the chromium nanobeams using design of experiments method

علوم کاربردی و محاسباتی در مکانیک

Article 8, Volume 35, Issue 4 - Serial Number 34, December 2023, Pages 107-120   

Document Type: Original Article

DOI: 10.22067/jacsm.2023.83862.1198

Authors

Vahid Modanloo^* ; Yasser Taghipour Lahijani; Ahmad Mashayekhi; Behnam Akhoundi

Mechanical Engineering Department, Sirjan University of Technology, Sirjan, Iran

Abstract

This paper investigates the deflection of chromium nanobeams using the design of experiments method. Using the full factorial method, a number of 100 experiments were designed in which the length and the force on the nanobeam were considered input variables at 25 and 4 levels, respectively and the deflection of the nanobeam was considered output. First, all 4 force levels (8, 9.5, 11, and 12.5 nN) were used for the analysis, and closed-form equations were obtained to estimate the deflection of the nanobeam. The results showed that the effect of the length is more than the force, by increasing the length so that the deflection changes with third degree. The third-order regression model predicts the deflection with high accuracy, and its error value is lower than the first and second-order regression models. Afterward, two levels of force (8 and 11 nN) were used for analysis, and new equations were obtained to estimate the deflection of the nanobeam. The new equations were used for interpolation and extrapolation of the nanobeam's deflection in forces of 9.5 and 12.5 nN, respectively. The results demonstrated that the regression model using two force levels accurately predicts the deflections of nanobeams as well. The results of this research demonstrated that it is possible to estimate the nanobeam's deflection without the need to perform more experiments and spend cost, perform complex calculations, and solve differential equations; the nanobeam's deflection can be accurately estimated with algebraic formulas.

Keywords

Nanobeam; Large Deflection; Regression Model; Design of Experiment

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