Lightweight topology optimization of graded lattice structures with displacement constraints based on an independent continuous mapping method  

基于独立连续映射法的位移约束梯度点阵结构轻量化拓扑优化

作　　者：Nan Wei Hongling Ye Xing Zhang Weiwei Wang Yunkang Sui 魏南;叶红玲;张行;王伟伟;隋允康(Faculty of Materials and Manufacturing,Beijing University of Technology,Beijing 100124,China;College of Mechanical and Architectural Engineering,Taishan University,Taian 271000,China)

机构地区：[1]Faculty of Materials and Manufacturing,Beijing University of Technology,Beijing 100124,China [2]College of Mechanical and Architectural Engineering,Taishan University,Taian 271000,China

出　　处：《Acta Mechanica Sinica》2022年第4期128-138,I0003,共12页力学学报（英文版）

基　　金：the National Natural Science Foundation of China(Grant No.11872080);Beijing Natural Science Foundation(Grant No.3192005);Taishan University Youth Teacher Science Foundation(Grant No.QN-01-201901).

摘　　要：This paper presents a novel topology optimization method to design graded lattice structures to minimize the volume subject to displacement constraints based on the independent continuous mapping(ICM)method.First,the effective elastic properties of graded unit cells are analyzed by the strain energy-based homogenization method.A surrogate model using quartic polynomial interpolation is built to map the independent continuous topological variable to the effective elastic matrix of the unit cell and set up the relationship between the macroscale structure and microscale unit cells.Second,a lightweight topology optimization model is established,which can be transformed into an explicitly standard quadratic programming problem by sensitivity analysis and solved by dual sequential quadratic programming.Third,several numerical examples demonstrate that graded lattice structures have a better lightweight effect than uniform lattice structures,which validates the effectiveness and feasibility of the proposed method.The results show that graded lattice structures become lighter with increasing displacement constraints.In addition,some diverse topological configurations are obtained.This method provides a reference for the graded lattice structure design and expands the application of the ICM method.基于独立连续映射(ICM)方法提出一种以位移约束下体积最小为目标的梯度点阵结构拓扑优化设计新方法.首先采用基于应变能的均匀化方法分析了梯度单元的有效弹性特性.建立四次多项式插值的代理模型,将独立的连续拓扑变量映射到单元的有效弹性矩阵,建立了宏观结构与微观单元之间的关系.其次,建立轻量化拓扑优化模型,通过灵敏度分析将其转化为显式标准二次规划问题,并用对偶序列二次规划求解.数值算例表明,与均匀点阵结构相比,梯度点阵结构具有更好的轻量化效果,验证了该方法的有效性和可行性.结果表明,随着位移约束的增加,梯度点阵结构变得更轻.此外,还得到了一些不同的拓扑构型.该方法为梯度点阵结构设计提供参考,并扩展ICM方法的应用范围.

关 键 词：Topology optimization.Graded lattice structures ICM method Displacement constraints Effective properties 

分 类 号：O302[理学—力学]