基于双层规划的白车身结构优化

在单次优化中，具有高维设计空间、多形态变量的优化易求解困难。因此将其分解成低维、单一形态变量的多层次优化。若优化分为双层次，上、下级相互依赖、相互作用、共同决定响应，即为双层规划问题。但是，双层规划令下级在上级的决策环境中寻求最优解，本质上求解困难。为此，通过上、下级间的迭代进行求解。为提高白车身性能并实现轻量化，应同时优化截面形状和板件尺寸。复杂截面形状的参数化引用网格变形技术，易引起板件穿透和单元质量差，进而导致单次优化的重分析失效而终止迭代。因此基于近似模型优化截面形状。然而，尺寸优化为实现轻量化而增加设计变量，随设计空间维数的提高响应面模型的采样点成倍增加、拟合精度急剧下降。因此采用Nastran Sol200优化的方法。根据截面形状和板件尺寸优化的特点，将双层规划法引入白车身结构优化，解决了优化求解困难的问题，同时有效提升其静态刚度、模态频率和实现轻量化。

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.