Computational Methods for Shape Prediction for steel plate with stiffener subjected to explosive loads

Almost all the structural elements are designed against static and dynamic loading. But, by increasing the terrorist attacks, they should strengthen against explosive loads. There are several limited studies in this field, but more comprehensive studies are required in order to provide a simple method for engineers and industry design. In this study, a comprehensive study is conducted to assess the behavior of steel plates 1x1, 1x2, and 1x3 m2, which are strengthened with stiffeners of a width of 4, 6, or 10 cm and a stiffener distance of 10, 20, or 30 cm subjected to various five blast loads. These five explosive loadings include an explosion effect of 19 kg TNT with a standoff distance of 50cm, 16 kg TNT with a standoff distance of 100cm, 35 kg TNT with a standoff distance of 100cm, 25 kg TNT with a standoff distance of 150cm, and 60 kg TNT with a standoff distance of 150cm on the steel plates. The steel plate 1x1 m2 represents a steel plate with a height of 1 m and a length of 1 m, and the steel plate 1x2 m2 refers to a steel plate with a length of 1 m and a height of 2m. Also, the steel plate 1x3 m2 refers to a steel plate with a length of 1 m and a height of 3m. The thickness of the steel plate and stiffener is considered as 8mm, 10 mm, 15mm, or 20 mm. On the other hand, four design parameters, including height, thickness, stiffener width, and stiffener distance, three levels for height, stiffener distance, and stiffener width, as well as four levels for thickness, are considered. Moreover, five levels for loading conditions, as mentioned above, are considered. Regarding the levels of design parameters and loading parameters, 540 samples are designed. The results of two numerical and experimental studies are used to validate a finite element (FE) model. Based on the validated finite element FE model, 540 samples are simulated and analyzed, and their behavior is evaluated. The deflection in the center, height, and length of the steel plate is compared and assessed. Furthermore, the deformation of steel plates is compared and evaluated. Four white box artificial intelligence (AI) methods, including Gene Expression Programming (GEP), High Correlated Creator Machine (HCVCM), Multi-Ln-Equation Regression (MLnR), the combination of HCVCM and MLnR as the first ensemble model, the combination of HCVCM, MLnR, and GEP as the second ensemble model, and Dynamic Selecting Machine (DSM), are used to simulate the deflection of steel plates in height and length of the steel plates as well as their deformation. The results show that the loading condition has the maximum effect on the deflection in the center of the steel plate. The maximum deflection in the center points of the steel plate occurs when the steel plate is subjected to 19 kg TNT with a standoff distance of 50 cm, but the maximum deflection of the points at 10%-30% of the height of the steel plate 1x2 and 1x3 happened when the steel plates are subjected to 60 kg TNT with a standoff distance of 150cm. The results demonstrate that a lower effect of the explosion of 19 kg TNT reaches the round points of steel plates 1x2 and 1x3 m. The maximum deflection decreases 15.6-75.2% by increasing the stiffener width from 4 cm to 6 cm, as well as from 6 cm to 10 cm. The distance of stiffeners can increase the deflection by 9.9-62.7% if they are changed from 10 cm to 20 cm or from 20 cm to 30 cm. Moreover, by increasing the distance stiffener, the deflection is reduced by 36.6-96.6%. The results show that among the design parameters, the thickness can have the maximum effect on the deflection of steel plates. The deformation is related to explosive loads, the height of the steel plate, and finally, the distance of the stiffeners. Most of the deformation shape of the steel plates in length and height was pointed curved parabola or curved parabola, but according to the results of the steel plates 1x3 m2, the deformation can be changed into a wave curve parabola or a wave curve parabola with an inverse curve at the base. The wave curve parabola occurs in the steel plate with strength stiffeners, such as the stiffener width of 6 cm or 10 cm, which stiffeners can control and reduce deflection highly in their place. Furthermore, the results show that the points that are close to the explosion have more deflection, and in these points, the changes in shape deformation occur, as well, and the possibility of plasticity is higher. The results of AI methods show that among the single models, only MLnR is reliable in predicting the deflection in the length and height of the steel plate. Furthermore, the results show that the ensemble models, including the combination of HCVCM and MLnR and the combination of HCVCM, MLnR, and GEP, have better performance in comparison to MLnR with respect to statistical parameters and error terms. Also, the results indicate that the second ensemble model, which is the combination of the three models, is more accurate than the first ensemble model. On the other hand, by increasing the complexity of surrogate models, the accuracy of the model will be better. The maximum positive error for both ensemble models in predicting the height and length of the steel plate was less than 75% and 54%; therefore, the presented formulas by both ensemble models can be used with a safety factor between 1.75 and 1.54. DSM is a strong surrogate model that can predict an appropriate model for deflection in the height and length of the steel plate. Regarding the results, sometimes, the single models can predict better than the ensemble models. Overall, DSM can reduce the maximum positive and negative error, Root Mean Square Error (RSME), Normalized Mean Square Error (NMSE), and Mean Absolute Percentage Error (MAPE) by selecting the best model dynamically in the whole dataset. As a result, it improves the accuracy of the model. The coefficient of determination, RMSE, and NMSE of DSM are determined as 0.952, 0.006, and 0.040, as well as 0.874, 0.006, and 0.081 for training and testing datasets for the prediction of the deflection in the height of the steel plate. Also, the coefficient of determination, RMSE, and NMSE of DSM to determine the deflection in the length of the steel plate for both training datasets are 0.965, 0.005, and 0.032, as well as for the testing datasets are 0.965, 0.003, and 0.036, respectively. MAPE of the DSM model is determined at 12.836% and 8.251% for estimation of the deflection in the height and length of the steel plate. This model can predict the height and length of the steel plate with a maximum positive error of 44.138% and 47.707%, respectively. Thus, the results of this model must be used with a safety factor of 1.45 and 1.48 to predict the deflection in the height and length of the steel plate, respectively. The formula of the present research can be used by engineers to design steel plates subjected to explosive loads; therefore, the outputs of this research, especially the formulas, can be used in design books.