Keywords: axial crushing, thin-walled tubes, impact, optimization, neural networks, genetic algorithm.

Ever-increasing application of thin-walled members as a shock absorber under impact load is because of the remarkable capability of these structures in absorbing kinetic energy in crush situations. Over the last years, a great number of experimental and theoretical studies have been carried out on the crushing of cylindrical thin-walled tubes as shock absorbers. Most of this researche deals with studying the influence of different geometrical or physical parameters such as tube dimensions [1] on the collapse behaviour of the structure or finding design methods such as cutting circumferential grooves in the tube to improve the collapse shape [2], whereas, nowadays finding the optimum value of the effective parameters on collapsing behaviour seems to become a necessary part of the design procedure.

The optimization procedure requires repetitive and iterative validation of the selected objective function (that can be any of the crashworthiness parameters) for various values of design variables, when finding these values by using experimental tests it is almost impossible and using numerical simulation for each iteration is so time consuming. To avoid the calculation of the objective function in continual iterations by computationally costly numerical simulations, approximated functions may be used to simulate the crush behaviour of the structure. Artificial neural network systems [3] use the results of a limited number of numerical crush behaviour simulations for some selected points in design variables space as input and after training can be replaced with numerical simulation for evaluating the objective function for arbitrary points in design variables space.

In this paper, the collapse of thin-walled tubes under axial impact load is taken into consideration. A system of parallel neural networks is developed to reproduce the structural behaviour during the crush phenomenon. The most important crashworthiness parameters of structure (specific absorbed energy, the crush force efficiency and the maximum axial deflection) are set as the objective function and the tube dimensions are the design variables. A limited number of finite element simulations are performed to train and test the neural network systems. Some experimental tests under quasi-static situation are carried out for evaluating the results of the finite element simulation and the acceptable accuracy of the finite element simulation for predicting the collapse shape and calculation of crashworthiness parameters is shown. After training the neural network systems and testing their accuracy, the genetic algorithm is implemented to find the optimal configuration and the dimensions of the tube for both single objective and multi objective optimizations.

1

S.R. Guillow, G. Lu, R.H. Grzebieta, "Quasi-static axial compression of thin-walled circular aluminum tubes", Int J Mech Sci, 43: 2103-2123, 2001. doi:10.1016/S0020-7403(01)00031-5

2

M. Shakeri, R. Mirzaeifar, A. Alibeiglou, "Plastic buckling modes contribution to the modification of collapsing behaviour of circular tubes under axial impact load", Fourth international conference on Mechanical Engineering Advanced Technology for Industrial Production (MEATIP4), Assiut univ., Egypt, December 12-14, 2006.

3

L. Lanzi, C. Bisagni, S. Ricci, "Neural network systems to reproduce crash behaviour of structural components", Computers and Structures, 82: 93-108, 2004. doi:10.1016/j.compstruc.2003.06.001

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