Structural optimization of body-in-white based on bi-level programming

An optimization with a high-dimensional design space and multi-form variables processed within an all-in-one optimization is sometimes unsolvable. Therefore, it is decomposed into a multi-level optimization with a low dimension and variables of single form. An optimization decomposed into a bi-level problem in which the upper-level and the lower-level interdepend, interact and codetermine the responses, is a bi-level programming problem. However, due to the optima of the lower-level are searched within the decision environment of the upper-level, a bi-level programming is intrinsically hard. So iterations between the upper-level and the lower-level are performed. To enhance the body-in-white performance and achieve lightweight, both section shape and shell thickness optimization should be executed. The complex section shape parameterized by mesh morphing technology is accompanied with problems of shell penetration and poor element quality, which result in the failure of reanalysis within all-in-one optimization and in turn terminate the iteration. Therefore, the section shape optimization is applied based on response surface model. While to achieve lightweight, the design variable size of the size optimization should be increased. With the improvement of the design space dimension, sample points multiply accordingly and the fitting accuracy declines radically. So the size optimization is applied in Nastran Sol200. Considering the traits of section shape and shell thickness optimization, a bi-level programming is introduced into the structural optimization of body-in-white, so that the unsolvable optimization is settled, meanwhile the static stiffness and modal frequency are enhanced greatly and lightweight is achieved.