EI、Scopus 收录
中文核心期刊
Volume 53 Issue 5
May  2021
Turn off MathJax
Article Contents
Li Ran, Liu Shutian. ROBUST TOPOLOGY OPTIMIZATION OF STRUCTURES CONSIDERING THE UNCERTAINTY OF SURFACE LAYER THICKNESS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1471-1479. doi: 10.6052/0459-1879-20-419
Citation: Li Ran, Liu Shutian. ROBUST TOPOLOGY OPTIMIZATION OF STRUCTURES CONSIDERING THE UNCERTAINTY OF SURFACE LAYER THICKNESS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(5): 1471-1479. doi: 10.6052/0459-1879-20-419

ROBUST TOPOLOGY OPTIMIZATION OF STRUCTURES CONSIDERING THE UNCERTAINTY OF SURFACE LAYER THICKNESS

doi: 10.6052/0459-1879-20-419
  • Received Date: 2020-12-19
  • Publish Date: 2021-05-18
  • For additively manufactured structure, the poor forming precision and surface roughness may cause surface layer heterogeneity, which leads to uncertain material properties and/or uncertain structure geometry. In order~to obtain a structure with less sensitive to the uncertainty, a rubost topology optimization method accounting for the uncertain surface thickness of structures is proposed, in which two key problems need to be solved to study the surface layer thickness uncertainty caused by the heterogeneity of the structure surface layer. One is accurately identifying the structure surface layer. The other is to carry out propagation analysis and stochastic response estimation of uncertainty. First of all, an erosion-based surface layer identification method is adopted to establishing the equivalent model of surface layer heterogeneity through smooth filtering based on Helmholtz partial differential equation(PDE) as well as discrete mapping based on Heaviside filtering and tanh function, which is called a two-step filtering/projection process. Secondly, while the thickness of the heterogeneous surface layer is regarded as a random variable subject to Gaussian distribution, the uncertain propagation is analyzed and the system stochastic response is predicted based on the perturbation finite element method. Taking the weighted sum of the mean value and standard deviation of structural compliance as the optimization objective, a robust topology optimization model considering the uncertainty of surface layer thickness is established, and the sensitivities of the objective function with respect to design variables are derived. Finally, several numerical examples are given to demonstrate the effectiveness of the proposed method. The numerical results show that the structural configuration with stronger uncertainty resistance can be obtained by considering the influence of surface thickness uncertainty on the structural performance during the design process, which effectively improves the robustness of the structural performance. Therefore, for additive manufacturing structures, it is of great significance to consider the influence of surface layer thickness uncertainty on structural performance in topology optimization design.

     

  • loading
  • [1]
    Bends?e MP, Kikuchi N. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 1988,71(2):197-224
    [2]
    Mei YL, Wang XM. A level set method for structural topology optimization. Computer Methods in Applied Mechanics and Engineering, 2004,35(7):415-441
    [3]
    Zuo ZH, Xie YM, Huang X. Evolutionary topology optimization of structures with multiple displacement and frequency constraints. Advances in Structural Engineering, 2012,15(2):385-398
    [4]
    Zhang WS, Yuan J, Zhang J, et al. A new topology optimization approach based on Moving Morphable Components (MMC) and the ersatz material model. Structural and Multidisciplinary Optimization, 2016,53(6):1243-1260
    [5]
    Luo YF, Chen WJ, Liu ST, et al. A discrete-continuous parameterization (DCP) for concurrent optimization of structural topologies and continuous material orientations. Composite Structures, 2020,236:111900
    [6]
    卢秉恒, 李涤尘. 增材制造(3D打印)技术发展. 机械制造与自动化, 2013,42(4):1-4

    (Lu Bingheng, Li Dichen. Development of the Additive Manufacturing (3D printing) Technology. Machine Building and Automation, 2013,42(4):1-4 (in Chinese))
    [7]
    汤慧萍, 王建, 逯圣路 等. 电子束选区熔化成形技术研究进展. 中国材料进展, 2015,34(3):225-235

    (Tang Huiping, Wang Jian, Lu Shenglu, et al. Research Progress in Selective Electron Beam Melting. Materials China, 2015,34(3):225-235 (in Chinese))
    [8]
    Javaid M, Haleem A. Additive manufacturing applications in medical cases: A literature based review. Alexandria Journal of Medicine, 2017,54(4):411-422
    [9]
    卢秉恒. 增材制造技术 —— 现状与未来. 中国机械工程, 2020,31(1):19-23

    (Lu Bingheng. Additive manufacturing - Current situation and future. China Machine Engineering, 2020,31(1):19-23 (in Chinese))
    [10]
    Meng L, Zhang W, Quan D, et al. Correction to: From topology optimization design to additive manufacturing: Today's success and tomorrow's roadmap. Archives of Computational Methods in Engineering, 2021,21:269
    [11]
    Luo YF, Sigmund O, Li QH, et al. Additive manufacturing oriented topology optimization of structures with self-supported enclosed voids. Computer Methods in Applied Mechanics and Engineering, 2020,372:113385
    [12]
    顾冬冬, 沈以赴. 基于选区激光融化的金属材料零件快速成形现状与技术展望. 航空制造技术, 2012(8):32-37

    (Gu Dongdong, Shen Yifu. Research status and technical prospect of rapid manufacturing of metallic part by sdective laser meIting. Aeronautical Manufacturing Technology, 2012(8):32-37 (in Chinese))
    [13]
    Du W, Bai Q, Wang Y, et al. Eddy current detection of subsurface defects for additive/subtractive hybrid manufacturing. International Journal of Advanced Manufacturing Technology, 2017,95(5-8):1-11
    [14]
    Wang JC, Cui YN, Liu CM, et al. Understanding internal defects in Mo fabricated by wire arc additive manufacturing through 3D computed tomography. Journal of Alloys and Compounds, 2020,840:155753
    [15]
    范慧茹. 考虑表面层异质及其不确定性的增材制造结构拓扑优化方法. [硕士论文]. 大连: 大连理工大学, 2018

    (Fan Huiru. Topology optimization method of additive manufacture structures with surface layer heterogeneity and uncertainty considered. [Master Thesis]. Dalian: Dalian University of Technology, 2018 (in Chinese))
    [16]
    Du J, Sun C. Reliability-based vibro-acoustic microstructural topology optimization. Structural & Multidiplinary Optimization, 2016,55(4):1-21
    [17]
    Wang L, Xia HJ, Zhang XY, et al. Non-probabilistic reliability-based topology optimization of continuum structures considering local stiffness and strength failure. Computer Methods in Applied Mechanics and Engineering, 2019,346:788-809
    [18]
    Asadpoure A, Tootkaboni M, Guest JK. Robust topology optimization of structures with uncertainties in stiffness-Application to truss structures. Computers and Structures, 2011,89(11-12):1131-1141
    [19]
    Sigmund O. Manufacturing tolerant topology optimization. Acta Mechanica Sinica, 2009,25(2):227-239
    [20]
    Sigmund O. Morphology-based black and white filters for topology optimization. Structural & Multidisciplinary Optimization, 2007,33(4):401-424
    [21]
    Wang FW, Jensen JS, Sigmund O. Robust topology optimization of photonic crystal waveguides with tailored dispersion properties. Journal of the Optical Society of America, B, Optical physics, 2011,28(3):387-397
    [22]
    Schevenels M, Lazarov BS, Sigmund O. Robust topology optimization accounting for spatially varying manufacturing errors. Computer Methods in Applied Mechanics and Engineering, 2011,200(49-52):3613-3627
    [23]
    Kang Z, Wu CL, Luo YJ, et al. Robust topology optimization of multi-material structures considering uncertain graded interface. Composite Structures, 2019,208:395-406
    [24]
    Zheng J, Luo Z, Jiang C, et al. Robust topology optimization for concurrent design of dynamic structures under hybrid uncertainties. Mechanical Systems and Signal Processing, 2019,120:540-559
    [25]
    Clausen A, Aage N, Sigmund O. Topology optimization of coated structures and material interface problems. Computer Methods in Applied Mechanics and Engineering, 2015,290:524-541
    [26]
    Chu S, Xiao M, Gao L, et al. Topology optimization of multi-material structures with graded interfaces. Computer Methods in Applied Mechanics and Engineering, 2019,346:1096-1117
    [27]
    Luo YF, Li QH, Liu ST. A projection-based method for topology optimization of structures with graded surfaces. International Journal for Numerical Methods in Engineering, 2019,118(11):654-677
    [28]
    Luo YF, Li QH, Liu ST. Topology optimization of shell-infill structures using an erosion-based interface identification method. Computer Methods in Applied Mechanics and Engineering, 2019,355:94-112
    [29]
    Bourdin B. Filters in topology optimization. International Journal for Numerical Methods in Engineering, 2001,50(9):2143-2158
    [30]
    Bruns TE, Tortorelli DA. Topology optimization of non-linear elastic structures and compliant mechanisms. Computer Methods in Applied Mechanics & Engineering, 2001,190(26-27):3443-3459
    [31]
    Lazarov BS, Sigmund O. Filters in topology optimization based on Helmholtz-type differential equations. International Journal for Numerical Methods in Engineering, 2011,86(6):765-781
    [32]
    Guest JK, Prevost J, Belytschko T. Achieving minimum length scale in topology optimization using nodal design variables and projection functions. International Journal for Numerical Methods in Engineering, 2004,61(2):238-254
    [33]
    Wang FW, Lazarov BS, Sigmund O. On projection methods, convergence and robust formulations in topology optimization. Structural and Multidisciplinary Optimization, 2011,43(6):767-784
    [34]
    亢战, 程耿东. 基于随机有限元的非线性结构稳健性优化设计. 计算力学学报, 2006,23(2):129-135

    (Kang Zhan, Cheng Gengdong. Structural robust design based on perturbation stochastic finite element method. Chinese Journal of Computational Mechanics, 2006,23(2):129-135 (in Chinese))
    [35]
    Da Silva GA, Cardoso EL. Stress-based topology optimization of continuum structures under uncertainties. Computer Methods in Applied Mechanics and Engineering, 2017,313:647-672
    [36]
    Svanberg K. The method of moving asymptotes — A new method for structural optimization. International journal for numerical methods in engineering, 1987,24(2):359-373
    [37]
    Clausen A, Andreassen E. On filter boundary conditions in topology optimization. Structural and Multidisciplinary Optimization, 2017,56(5):1147-1155
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (812) PDF downloads(115) Cited by()
    Proportional views
    Related

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return