Prediction of large deflection of chromium nanobeams using a hybrid meta-heuristic algorithm

In this paper, the prediction of large deflection of the chromium nanobeams has been studied using hybrid meta-heuristic methods. At first, using the full factorial design of experiment method, 100 experiments were designed in which the length and force applied to the nanobeams were considered as input variables at 25 and 4 levels, respectively. Also, the deflection of the nanobeam was considered as the output. The nanobeam’s deflection was estimated through the regression models by first, second, and third-order equations, respectively. The preliminary results demonstrated that the third-order regression model predicts the deflection with high accuracy and its error is less than the other models. In the following, to reduce the number of required experiments, two levels of the applied force (8 and 11 nN) were used to predict the deflection. Accordingly, the new equations were used for interpolation and extrapolation of the deflection in other levels of forces i.e., 9.5 and 12.5 nN. Finally, the coefficients of both third-order equations obtained by 4 and 2 levels of forces were optimized using the meta-heuristic algorithms i.e., Big Bang-Big Crunch (BBBC) and Ray Optimization algorithm (ROA). Comparing the results showed that by using the BBBC and RAO methods, the error value decreases by 10% and 20%, respectively. The results of this paper showed that the deflections of the chromium nanobeam can be estimated by algebraic formulas with high accuracy and fewer experiments, time, and cost.