几种主要拓扑优化建模方法的分析对比及展望
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摘要
拓扑优化是结构优化设计的一个分支,近十几年来,拓扑优化在各个领域的应用日趋广泛,针对优化模型的开发涌现出大量研究。主要介绍和对比分析了几种主要的连续体拓扑优化建模方法,得出了变密度法为当前最适于工业生产的方法的结论,并提出了今后拓扑优化的发展方向。
Topology optimization is a branch of structural optimization design. In recent ten years,topology optimization has been widely used in various fields,and a large number of researches have emerged on the development of optimization models. This paper mainly introduces and compares several main topology optimization modeling methods of continuum,draws the conclusion that variable density method is the most suitable method for industrial production at present,and puts forward the development direction of topology optimization in the future.
Topology optimization is a branch of structural optimization design. In recent ten years,topology optimization has been widely used in various fields,and a large number of researches have emerged on the development of optimization models. This paper mainly introduces and compares several main topology optimization modeling methods of continuum,draws the conclusion that variable density method is the most suitable method for industrial production at present,and puts forward the development direction of topology optimization in the future.
引文
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[2] GIN ROZVANY,T LEWINSKI.Topology Optimization in Structural and Continuum Mechanics[M]. Vienna:Springer,2014.
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[6]周克民.结构拓扑优化的一些基本概念和研究方法[J].力学与实践,2018,40(03):245-252.
[7] O SIGMUND.Design of material structures using topology optimization[D]. Technical University of Denmark,1994.
[8] RIETZ A.Sufficiency of a finite exponent in SIMP(power law)methods[J].Structural and Multidisciplinary Optimization,2001,21(2):159-163.
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[11] J.A SETHIAN,A WIEGMANN.Structural boundary design via level set and immersed interface methods[J].Computational Physics,2000,163(2):489-528.
[12]张维声.基于水平集方法的应力相关拓扑优化问题研究[D].大连:大连理工大学,2013.
[13] Y.M.XIE,G.P STEVEN.A simple evolutionary procedure for structural optimization[J].Computers&Structures,1993,49(5):885-896.
[14] M QUERIN O,P STEVEN G,Y.M.XIE. Evolutionary optimization(ESO)using a bi-directional algorithm[J].Engineering Computations,1998,15(8):1031-1048.
[2] GIN ROZVANY,T LEWINSKI.Topology Optimization in Structural and Continuum Mechanics[M]. Vienna:Springer,2014.
[3] O SIGMUND,K MAUTE. Topology optimization approaches a comparative review[J].Structural and Multidisciplinary Optimization,2013,48(6):1031-1055.
[4] M.P BENDSOE,N KIKUCHI. Generating optimal topologies in structural design using a homogenization method[J].Computer Methods in Applied Mechanics and Engineering,1988,71:197-224.
[5]杨姝.复杂机械结构拓扑优化若干问题研究[D].大连:大连理工大学,2007.
[6]周克民.结构拓扑优化的一些基本概念和研究方法[J].力学与实践,2018,40(03):245-252.
[7] O SIGMUND.Design of material structures using topology optimization[D]. Technical University of Denmark,1994.
[8] RIETZ A.Sufficiency of a finite exponent in SIMP(power law)methods[J].Structural and Multidisciplinary Optimization,2001,21(2):159-163.
[9] STOLPE MATHLAS,SVANHERG KRISTER. An Alternative Interpolation Scheme for Minimum Compliance Topology Optimization[J]. Structural and Multidiscipline Optimization,2001(22):116-124.
[10] S OSHER,J SETHIAN.Front propagating with curvature dependent speed:algorithms based on Hamilton-Jacobi formulations[J].Computational Physic,1988(78):12-49.
[11] J.A SETHIAN,A WIEGMANN.Structural boundary design via level set and immersed interface methods[J].Computational Physics,2000,163(2):489-528.
[12]张维声.基于水平集方法的应力相关拓扑优化问题研究[D].大连:大连理工大学,2013.
[13] Y.M.XIE,G.P STEVEN.A simple evolutionary procedure for structural optimization[J].Computers&Structures,1993,49(5):885-896.
[14] M QUERIN O,P STEVEN G,Y.M.XIE. Evolutionary optimization(ESO)using a bi-directional algorithm[J].Engineering Computations,1998,15(8):1031-1048.