基于子结构的宏微结构协同优化方法

A Substructure-based Co-optimization Method for Macro-micro Structures

利用子结构自由度的缩减实现结构宏微观的一体化设计,需要预先建立不同子结构构型的样本。宏观结构优化时只能在预定的微观构型中插值,限制了结构宏微观的优化空间。结合子结构自由度缩减与反求理论,针对周期性结构的设计提出了结构的宏微观协同设计方法。利用固体各向同性材料惩罚(SIMP)方法和子结构方法,构建了基于子结构的周期性结构宏微观协同设计框架;分析了宏观结构与微观周期性单胞的材料体积变化关联关系,并给出了两个尺度上的惩罚因子、变量过滤半径等优化参数的匹配。在此基础上,结合传统的结构柔度最小优化模型,计算了设计变量在宏观结构、微观周期性结构的灵敏度值,实现了宏微结构的协同设计。通过悬臂梁结构的设计,验证了所提方法的有效性。

The integrated structural macro-microscopic design was achieved by using the reduction of substructural degrees of freedom,which required the pre-establishment of samples of different substructural configurations.The macroscopic structure optimization might only be interpolated in predefined microscopic configurations,which restricted the optimization space of structural macro and microscopic.A macro-micro collaborative method was proposed for the design of periodic structures by combining substructure degree of freedom reduction and inverse theory.Using the solid isotropic material with penalization(SIMP)method and the substructure method,a substructure-based macro-micro collaborative framework for periodic structures was constructed.The correlation between the material volume variation of macrostructures and microscopic periodic cell was analyzed,and the matching of optimization parameters was given such as penalty factor and variable filter radius at two scales.Then,the sensitivity values of the design variables in the macroscopic structures and microscopic periodic structures were calculated in combination with the traditional structural flexibility minimum optimization model,and the co-design of macro and micro structures was realized.The effectiveness of the proposed method was verified by the design of the cantilever beam structures.