基于图形法的仿生拓扑优化方法

丁友; 周洲; 祝小平

doi:10.13224/j.cnki.jasp.20210013

基于图形法的仿生拓扑优化方法

doi: 10.13224/j.cnki.jasp.20210013

1.
西北工业大学航空学院，西安 710072
2.
西北工业大学无人机特种技术重点实验室，西安 710072

基金项目: 民机专项（MJ-2015-F-009）；陕西省重点研发计划（2018ZDCXL-GY-03-04，2021ZDLGY09-08，2021GY-339）；陕西省自然科学基金（2019JM-044）

详细信息

作者简介:
丁友（1989-），男，博士生，主要从事飞行器结构设计及仿生优化方面的研究。

中图分类号: V224
计量
- 文章访问数: 350
- HTML浏览量: 65
- PDF量: 133
- 被引次数: 0
出版历程
- 收稿日期: 2021-01-15
- 刊出日期: 2021-11-28

Bionic topology optimization method based on graph method

1.
School of Aeronautics，Northwestern Polytechnical University，Xi'an 710072，China
2.
Science and Technology on Unmanned Aerial Vehicle Laboratory，Northwestern Polytechnical University，Xi'an 710072，China

摘要

摘要: 针对图形系统自动生成图形拓扑形式的优势，提出了一种以隐式方式表征结构拓扑形式的分步拓扑优化设计方法。该分步优化方法首先以基结构法（ground structure method）的计算结果为基础，并通过均匀化方法得到设计区域内的离散拓扑信息，利用第一步所得的拓扑数据指导分形系统中每一级新增拓扑结构的生长方向，以类似细胞分裂生长的形式完成整体结构拓扑形式生成。最后以参数化建模方式完成模型的结构有限元的批量计算，并结合进化算法，完成对设计模型的优化。其中第一个案例通过本文仿生方法在多目标优化方法下得到了近似Michell结构的最优拓扑结构，第二个方案中机翼蒙皮的屈曲载荷系数提升了10.61%，并且质量降低了10.85%，验证了本文方法在类平面结构拓扑优化方面的可行性。
- 轻量化设计 /
- 拓扑优化 /
- 基结构法 /
- 仿生结构 /
- 进化算法
Abstract: For taking the advantages of the fractal system in automatically generating graph topological forms，an implicit method was presented to express the structure topology and optimization.This stepped method was firstly based on the results computed by the ground structure method，then a homogenization operation was performed to get the discrete data in the design domain.Through the data got from the previous step to guide the new structure topology direction for the next level from the fractal system，which was similar to the plant growth to get the final structure topology.At last a finite element calculation with parametric modeling was used for the evolution method to get the optimal result.Two cases respectively presented specific implementation process of the optimization system and verified the feasibility of the method.In the first case，an approximate Michell structure was obtained through bionic method under the multi-objective optimization method.In the second case，the buckling load factor of the wing skin was increased by 10.61%，and the mass was reduced by 10.85%，which verified the feasibility of our method to the similar planar structure topology optimization.
- lightweight design /
- topology optimization /
- ground structure method /
- bionic structure /
- evolution method

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参考文献(24)

[1]	DEATON J D,GRANDHI R V.A survey of structural and multidisciplinary continuum topology optimization:post 2000[J].Structural and Multi-disciplinary Optimization,2014,49（1）:1-38.
[2]	ESCHENAUER H A,OLHOFF N.Topology optimization of continuum structures:a review[J].Applied Mechanics Reviews,2001,54（4）:331-390.
[3]	ZHANG X S,DE STURLER E,PAULINO G H.Stochastic sampling for deterministic structural topology optimization with many load cases:density-based and ground structure approaches[J].Computer Methods in Applied Mechanics and Engineering,2017,325:463-487.
[4]	ALLAIRE G,JOUVE F,TOADER A M.Structural optimization using sensitivity analysis and a level-set method[J].Journal of Computational Physics,2004,194（1）:363-393.
[5]	DIMCIC M.Structural optimization of grid shells based on genetic algorithms[D].Stuttgart,Germany:Stuttgart University,2011.
[6]	NAGY D,ZHAO D,BENJAMIN D.Nature-based hybrid computational geometry system for optimizing component structure[C]∥Humanizing Digital Reality.Singapore City,Singapore:Springer Nature Singapore Private Limited,2018:167-176.
[7]	HAMM C.Evolution of lightweight structures:analyses and technical applications[M].Berlin,Germany:Springer,2015.
[8]	MAIER M,SIEGEL D,THOBEN K D,et al.Transfer of natural micro structures to bionic lightweight design proposals[J].Journal of Bionic Engineering,2013,10（4）:469-478.
[9]	DING X,YAMAZAKI K.Adaptive growth technique of stiffener layout pattern for plate and shell structures to achieve minimum compliance[J].Engineering Optimization,2005,37（3）:259-276.
[10]	LI B,HONG J,WANG Z,et al.An innovative layout design methodology for stiffened plate/shell structures by material increasing criterion[J].Journal of engineering materials and technology,2013,135（2）:021012.1-021012.11.
[11]	PEDRO H T C,KOBAYASHI M H.On a cellular division method for topology optimization[J].International Journal for Numerical Methods in Engineering,2011,88（11）:1175-1197.
[12]	HARTL D J,REICH G W,BERAN P S.Additive topological optimization of muscular-skeletal structures via genetic L-system programming[C]∥Proceedings of 24th AIAA/AHS Adaptive Structures Conference.San Diego,US:American Institute of Aeronautics and Astronautics,2016:1569-1582.
[13]	DORN W,GOMORY R E,GREENBERG H G.Automatic design of optimal structures[J].Journal de Mécanique,1964,3（1）:25-52.
[14]	SOKó? T.A 99 line code for discretized Michell truss optimization written in Mathematica[J].Structural and Multidisciplinary Optimization,2011,43（2）:181-190.
[15]	MARTINEZ P,MARTI P,QUERIN O M.Growth method for size,topology,and geometry optimization of truss structures[J].Structural and Multidisciplinary Optimization,2007,33（1）:13-26.
[16]	TALISCHI C,PAULINO G H,PEREIRA A,et al.PolyTop:a Matlab implementation of a general topology optimization framework using unstructured polygonal finite element meshes[J].Structural and Multidisciplinary Optimization,2012,45（3）:329-357.
[17]	SMITH O D S.Generation of ground structures for 2D and 3D design domains[J].Engineering Computations,1998,15（4）:462-500.
[18]	LEWI?SKI T,ROZVANY G I N,SOKó? T,et al.Exact analytical solutions for some popular benchmark problems in topology optimization:Ⅲ L-shaped domains revisited[J].Structural and Multidisciplinary Optimization,2013,47（6）:937-942.
[19]	ZEGARD T,PAULINO G H.GRAND:ground structure based topology optimization for arbitrary 2D domains using MATLAB[J].Structural and Multidisciplinary Optimization,2014,50（5）:861-882.
[20]	ZEGARD T,PAULINO G H.GRAND3:ground structure based topology optimization for arbitrary 3D domains using MATLAB[J].Structural and Multidisciplinary Optimization,2015,52（6）:1161-1184.
[21]	DU Q,GUNZBURGER M.Grid generation and optimization based on centroidal Voronoi tessellations[J].Applied Mathematics and Computation,2002,133（2/3）:591-607.
[22]	LINDENMAYER A.Developmental algorithms for multicellular organisms:a survey of L-systems[J].Journal of Theoretical Biology,1975,54（1）:3-22.
[23]	DE BOER M J M,LINDENMAYER A.Map OL-systems with edge label control:comparison of marker and cyclic systems[C]∥International Workshop on Graph Grammars and Their Application to Computer Science.Berlin:Springer,1986:378-392.
[24]	KUEH A,PELLEGRINO S.ABD matrix of single-ply triaxial weave fabric composites[C]∥Proceedings of 48th AIAA/ASME/AS-CE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.Honolulu,US:American Institute of Aeronautics and Astronautics,2007:2161-2478.