Neural Network Model and Finite Element Simulation of Spring back in Plane-Strain Metallic Beam Bending

Bending has significant importance in the sheet metal product industry. Moreover, the spring back of sheet metal should be taken into consideration in order to produce bent sheet metal parts within acceptable tolerance limits and to solve geometrical variation for the control of manufacturing process. Nowadays, the importance of this problem increases because of the use of sheet-metal parts with high mechanical characteristics. This research proposes a novel approach to predict springback in the air bending process. In this approach the finite element method is combined with metamodeling techniques to accurately predict the springback. Two metamodeling techniques namely the neural network and the response surface methodology are used and compared to approximate two multidimensional functions. The first function predicts the springback amount for a given material, geometrical parameters, and the bend angle before springback. The second function predicts the punch displacement for a given material, geometrical parameters, and the bend angle after springback. The training data required to train the two-metamodeling techniques were generated using a verified nonlinear finite element algorithm developed in the current research. The algorithm is based on the updated Lagrangian formulation, which takes into consideration geometrical, material nonlinearity, and contact. To validate the finite element model physical experiments were conducted. A neural network algorithm based on the backpropagation algorithm has been developed. This research utilizes computer generated D-optimal designs to select training examples for both metamodeling techniques so that a comparison between the two techniques can be considered as fair. Results from this research showed that finite element prediction of springback is in good agreement with the experimental results. The standard deviation is 1.213 degree. It has been found that the neural network metamodels give more accurate results than the response surface metamodels. The standard deviation between the finite element method and the neural network metamodels for the two functions are 0.635 degree and 0.985 mm respectively. The standard deviation between the finite element method and the response surface methodology are 1.758 degree and 1.878 mm for both functions, respectively.

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