Bi-level optimization for the cross-sectional shape of a thin-walled car body frame with static stiffness and dynamic frequency stiffness constraints

In usual automobile practice, the structural optimization of a car body is based on changes in the topology, the shape, the cross-sectional shape and finally the thickness size successively depending on the development stages. However, design engineers mostly rely on their experience, intuition and data accumulation when making decisions on the cross-sectional shape of a car body frame. Therefore, a bi-level structural optimization model is proposed to determine the optimal cross-sectional shapes of each thin-walled beam and to achieve a lightweight car body frame with a high stiffness. Intermediate box sections are introduced to bridge the relationships between the two levels. At level 1, the car body frame with static stiffness and dynamic frequency stiffness constraints is optimized to obtain the optimal sizes of the box section, using a sequential approximate optimization method. At level 2, arbitrarily shaped cross-sections constrained with cross-sectional properties are optimized using a genetic algorithm. Component sensitivity analysis and manufacturing constraints promote this model to be closer to actual automobile practice. Finally, a numerical example, solved by the developed software Vehicle Body - Forward Design and Optimization, verifies that the presented method is effective in guiding the conceptual design of the car body frame.