隐式曲面梯度多孔结构拓扑优化设计方法  

A Topology Optimization Design Method of Graded Cellular Structures with Implicit Surfaces

作　　者：孙鹏飞 张跃 尹鹏 刘宏磊 李宝童[1,2] SUN Pengfei;ZHANG Yue;YIN Peng;LIU Honglei;LI Baotong(School of Mechanical Engineering, Xi’an Jiaotong Univeristy, Xi’an 710049, China;Key Laboratory of Education Ministry for Modern Design and Rotor-Bearing System, Xi’an Jiaotong University, Xi’an 710049, China)

机构地区：[1]西安交通大学机械工程学院,西安710049 [2]西安交通大学现代设计及转子轴承系统教育部重点实验室,西安710049

出　　处：《西安交通大学学报》2022年第1期85-95,共11页Journal of Xi'an Jiaotong University

基　　金：国家自然科学基金资助项目(51775414)。

摘　　要：为实现多孔单胞构型对多孔结构功能特性的调控,提出隐式曲面梯度多孔结构拓扑优化设计方法。在三周期极小曲面隐式水平集函数中引入罚函数,保证小体积分数下曲面的连续性。对惩罚的隐式函数线性加权构造混合水平集函数,实现多孔结构混合参数化建模。采用数值均匀化法评估多孔结构的宏观等效弹性属性,并通过径向基插值函数构建等效弹性张量关于混合权重因子的显式表达式。以混合权重因子为设计变量,建立柔度最小化拓扑优化模型并采用优化准则法求解。引入Heaviside函数建立高阶连续插值模型,保证梯度多孔结构的高阶连续性。数值案例和实验结果表明,相比于均布多孔结构,所设计的梯度多孔结构的鲁棒性和承载特性更优,且不同单胞构型的梯度多孔结构功能特性相异。所提方法能有效应用三周期极小曲面梯度多孔结构设计,实现多孔单胞构型对结构功能特性的调控,丰富了多孔结构的力学内涵。To adjust the functional characteristics of cellular structures via cellular configurations, a topology optimization design method of graded cellular structures(GCS) with implicit surfaces is proposed. A penalty function is introduced to the implicit level set function of the triply periodic minimal surface(TPMS) for ensuring the continuity of TPMS under low volume fraction. The punished functions are weighted to construct a hybrid level set function to realize the hybrid parametric modeling of cellular structures. The macroscopic equivalent elastic characteristics of the cellular structures are evaluated by the numerical homogenization method. The explicit expression of the equivalent elasticity tensor with respect to the weight is built with radial basis interpolation function. The structural compliance is minimized to establish the topology optimization model, and the weight factor is taken as the design variable. The model is solved by the optimality criteria method. High-order continuous interpolation model is built by introducing Heaviside function to ensure the high-order continuity of GCS. Numerical examples and experimental results show that compared with the uniform cellular structures, the designed GCSs possess more superior robustness and load-bearing capacity, and the GCSs with different cellular configurations have diverse functional characteristics. The proposed method can be effectively applied to the design of TPMS-based GCS to realize the adjustment of the functional characteristics via cellular configurations, enriching the mechanical connotation of cellular structures.

关 键 词：拓扑优化 三周期极小曲面 梯度多孔结构 数值均匀化法 混合水平集函数 

分 类 号：TH122[机械工程—机械设计及理论]