Stress sensitivity analysis and optimization of automobile body frame consisting of rectangular tubes

At conceptual design stage, beam element is extensively used to create the frame structure of automobile body, which can not only archive the accurate stiffness but also reduce much computational cost. However, the stress definition of beam element is very complex so that the stress sensitivity and optimization are difficult to analytically derive and numerically program. This paper presents an solution to this problem and an application in the lightweight optimization design of automobile frame. Firstly, maximal Von Mises stress of rectangular tube is calculated by using the superposition of stress, which is together induced by the axial force, bending moments, torsional moment and shear force. Secondly, the sensitivity of Von Mises Stress with respect to size design variables: breadth, height and thickness are derived, respectively. Thirdly, an optimal criterion is constructed by Lagrangian multiplier method to solve the frame optimization with stress constraints. Lastly, numerical example of car frame proves that the proposed method can guarantee the stress of each beam element almost fully reaches at the yielding stress.