考虑局部过热约束的自支撑结构等几何拓扑优化

Isogeometric Topology Optimization of Self-supported Structures Considering Local Overheating Constraint

等几何拓扑优化方法实现结构几何、分析和优化模型的统一,在结构优化领域具有重要的应用潜力。拓扑优化设计的结构构型复杂,通常需要采用增材制造加工成型。为确保结构的可制造性,其必须满足特定的工艺条件,因此,在优化设计阶段考虑制造工艺约束显得尤为重要。针对金属增材制造中常见的局部过热现象和悬垂角要求,提出一种约束局部过热的自支撑结构等几何拓扑优化方法。采用基于等几何分析的变密度法,引入可打印密度的概念,将不满足打印要求的单元过滤,实现结构自支撑;采用稳态热过程模拟模型近似评估结构的局部过热程度,并将其引入等几何拓扑优化模型中加以约束。数值算例和仿真结果表明,相比于传统等几何拓扑优化方法和仅考虑自支撑特性的等几何拓扑优化方法,该方法设计的结构在满足自支撑特性的基础上,能有效缓解增材制造中结构的局部过热现象,从而减小结构的热变形,提高尺寸精度。

The isogeometric topology optimization method realizes the unity of structure geometry,analysis and optimization model,and has important application potential in the field of structure optimization.The structure of topology optimization design is complex and usually needs to be processed by additive manufacturing.In order to ensure the manufacturability of parts,its structural characteristics must meet specific geometric and technological conditions to ensure its manufacturability.Therefore,it is particularly important to consider the manufacturing process constraints in the optimization design stage.An isogeometric topology optimization method such as self-supported structure with local overheating constraint is proposed to solve the common local overheating phenomenon and the requirement of overhang angle in metal additive manufacturing.The variable density method based on isogeometric analysis is used,and the concept of printable density was introduced to filter the elements that did not meet the printing requirements,so as to realize the self-support of the structure.The steady-state thermal process simulation model is used to approximate the local overheating degree of the structure,and it is introduced into the isogeometric topology optimization model to constrain it.Numerical examples and simulation results show that compared with the traditional isogeometric topology optimization method and the isogeometric topology optimization method which only considers the self-supporting characteristics,the proposed method can effectively alleviate the local overheating phenomenon of the structure in additive manufacturing on the basis of satisfying the self-supporting characteristics,hence reducing the thermal deformation of the structure and improving the dimensional accuracy.