Two-level multiple cross-sectional shape optimization of automotive body frame with exact static and dynamic stiffness constraints

Automotive body frame comprises semi-rigid connected thin-walled beams (TWBs) that are fabricated from several stamped metal sheets. At conceptual design stage, cross-sectional shape design of the frame is a critical and intractable technique. In practice, design engineers mostly rely on empirical and intuitive trial-and-error approach to make decisions on the design of cross-sectional shape. This approach is laborious, time-consuming and unreliable, thus this article proposes a two-level multiple cross-sectional shape optimization approach. Our previously proposed transfer stiffness matrix method (TSMM) is adopted for the exact static and dynamic analyses of the frame. The dynamic stiffness matrix is refined by Love’s rod theory to take into account Poisson’s ratio effect. Moreover, scale vector method is introduced to remarkably reduce design variables. Then the shape optimization problem is formulated as a mass minimization problem, with exact static stiffness, dynamic frequency stiffness and four manufacturing constraints. Genetic algorithm (GA) is employed to solve the constrained nonlinear optimization problem. Afterwards, numerical examples with both of top-level and low-level shape optimization are carried out to demonstrate the validity of the proposed method. At last, parallel computing is introduced to notably speed up the optimization, and the shape optimization method is integrated into our object-oriented MATLAB toolbox to promote the conceptual development of auto-body.