基于图形法的仿生拓扑优化方法

Bionic topology optimization method based on graph method

针对图形系统自动生成图形拓扑形式的优势,提出了一种以隐式方式表征结构拓扑形式的分步拓扑优化设计方法。该分步优化方法首先以基结构法(ground structure method)的计算结果为基础,并通过均匀化方法得到设计区域内的离散拓扑信息,利用第一步所得的拓扑数据指导分形系统中每一级新增拓扑结构的生长方向,以类似细胞分裂生长的形式完成整体结构拓扑形式生成。最后以参数化建模方式完成模型的结构有限元的批量计算,并结合进化算法,完成对设计模型的优化。其中第一个案例通过本文仿生方法在多目标优化方法下得到了近似Michell结构的最优拓扑结构,第二个方案中机翼蒙皮的屈曲载荷系数提升了10.61%,并且质量降低了10.85%,验证了本文方法在类平面结构拓扑优化方面的可行性。

For taking the advantages of the fractal system in automatically generating graph topological forms,an implicit method was presented to express the structure topology and optimi-zation. This stepped method was firstly based on the results computed by the ground structure method,then a homogenization operation was performed to get the discrete data in the design do-main. Through the data got from the previous step to guide the new structure topology direction for the next level from the fractal system, which was similar to the plant growth to get the final structure topology. At last a finite element calculation with parametric modeling was used for the evolution method to get the optimal result. Two cases respectively presented specific implementa-tion process of the optimization system and verified the feasibility of the method. In the first case,an approximate Michell structure was obtained through bionic method under the multi -objective optimization method. In the second case,the buckling load factor of the wing skin was increased by 10. 61%,and the mass was reduced by 10. 85%,which verified the feasibility of our method to the similar planar structure topology optimization.