Vehicle crashworthiness

The crash safety design problem has three objectives, which need to be minimized. Objectives are \((f_1)\) the mass of the vehicle, \((f_2)\) acceleration-induced biomechanical damage of occupants and \((f_3)\) the toe board intrusion in the ‘offset-frontal crash’. More details about the problem can be found in [1].

Definition

\[\begin{split}\min f_1(x) = & \; 1640.2823 + 2.3573285x_1 + 2.3220035x_2 \\[2mm] & + 4.5688768x_3 + 7.7213633x_4 + 4.4559504x_5 \\[2mm] \min f_2(x) = & \; 6.5856 + 1.15x_1 - 1.0427x_2 + 0.9738x_3 \\[2mm] & + 0.8364x_4 - 0.3695x_1x_4 + 0.0861x_1x_5 + 0.3628x_2x_4 \\[2mm] & - 0.1106x_1^2 - 0.3437x_3^2 + 0.1764x_4^2 \\[2mm] \min f_3(x) = & -0.0551 + 0.0181x_1 + 0.1024x_2 \\[2mm] & + 0.0421x_3 - 0.0073x_1x_2 + 0.024x_2x_3 - 0.0118x_2x_4 \\[2mm] & - 0.0204x_3x_4 - 0.008x_3x_5 - 0.0241x_2^2 + 0.0109x_4^2 \\[2mm] \\ & s.t. \; 1mm \leq x \leq 3mm\end{split}\]

The design variables represent the thickness of the five reinforced members around the frontal structure, which could significantly affect crash safety.

[1]

Liao, X., Li, Q., Yang, X., Zhang, W. & Li, W. (2007). Multiobjective optimization for crash safety design of vehicles using stepwise regression model. Structural and multidisciplinary optimization, 35(6), 561-569. https://doi.org/10.1007/s00158-007-0163-x