基于等几何分析和材料场级数展开模型的简谐激励结构拓扑优化  

Topology optimization of harmonic excitation structures based on isogeometric analysis and material field series expansion model

作　　者：王培金 刘宏亮 张业伟[1] 雷振增 杨迪雄[2] WANG Pei-jin;LIU Hong-liang;ZHANG Ye-wei;LEI Zhen-zeng;YANG Di-xiong(Key Laboratory of Liaoning Province for Composite Structural Analysis of Aerocraft and Simulation,Shenyang Aerospace University,Shenyang 110136,China;State Key Laboratory of Structural Analysis,Optimization and CAE Software for Industrial Equipment,Dalian University of Technology,Dalian 116024,China)

机构地区：[1]沈阳航空航天大学辽宁省飞行器复合材料结构分析与仿真重点实验室,沈阳110136 [2]大连理工大学工业装备结构分析优化与CAE软件全国重点实验室,大连116024

出　　处：《计算力学学报》2024年第5期864-872,共9页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(12002218);工业装备结构分析国家重点实验室开放基金(GZ22108)资助项目。

摘　　要：考虑简谐激励的结构拓扑优化具有重要的研究意义和工程应用价值,尤其对于飞速发展的航空航天领域。为了方便优化设计结果的几何特征提取和控制,同时兼顾计算精度、效率和设计迭代稳定性,本文基于等几何分析和材料场级数展开模型发展一套等几何优化方法用于简谐激励结构拓扑优化。由于等几何分析具有几何建模精确和跨单元高阶连续的特点,在不需要极其细密网格的情况下就可以保证响应分析和灵敏度计算的精度。通过结合材料场级数展开模型,采用降维技术大幅减少了设计参数的数量,提高了设计优化的求解效率,同时能够获得不依赖单元细分且具有清晰几何边界的优化构型。针对动力学拓扑优化可能出现的迭代振荡和不收敛问题,通过采用稳定化方案获得了稳定迭代的收敛设计解。数值算例表明,本文方法能够有效避免灰度模糊区域、锯齿形边界、单元细分依赖性和棋盘格现象等,可以高精度高效率地求解简谐激励结构拓扑优化问题。Topology optimization of structures under a considering harmonic excitation has important research significance and engineering application value,especially for the rapidly developing aerospace field.In order to facilitate the extraction and control of geometric features of the optimal design results,while taking into account the calculation accuracy,efficiency and iteration stability of the design,this paper develops an isogeometric optimization method based on isogeometric analysis and material field series expansion model for topology optimization of structures under a harmonic excitation.Due to the characteristics of geometric modeling accuracy and high-order continuity across elements,the precision of response analysis and sensitivity calculation can be ensured without the need of extremely fine meshes.By combining the material field series expansion model,dimensionality reduction technology is empolyed to greatly reduce the number of design parameters,improve the efficiency of design optimization,and obtain an optimal configuration independent of elemental subdivision and with clear geometric boundaries.In order to avoid iteration oscillation and non-convergence which may occur in dynamic topology optimization,the convergence design solution with stable iteration is obtained by using the stabilization scheme.Numerical examples show that the proposed method can effectively avoid appearance of a gray fuzzy region,sawtooth boundary,mesh dependency and checkerboard phenomenon,and can achieve topology optimization of structures under a hamonie excitation with high accuracy and efficiency.

关 键 词：等几何分析 拓扑优化 简谐激励 稳定化方案 材料场级数展开模型 

分 类 号：O224[理学—运筹学与控制论]