基于拓扑优化的变密度点阵结构体优化设计方法
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摘要
点阵材料是一种超轻高强的高性能多孔材料,目前主要以等密度构建点阵结构体。在实际情况下,点阵材料的各部分承受着不同的载荷,等密度点阵材料存在性能不能充分发挥的问题。针对上述问题,将拓扑优化引入点阵材料设计中,提出一种基于均匀化方法的多尺度拓扑优化方法,实现了变密度点阵结构体的优化设计,可根据实际载荷设计出最优的变密度点阵结构体,以达到最优性能。以汽车连杆为例,与现有商业软件HyperWorks采用的梁模型点阵优化方法进行对比验证。结果表明,所提出方法优化所得连杆的轻量化效果更好,应力分布更合理。该方法生成的变密度点阵结构有着更优异的性能,更适合变密度点阵结构体的优化设计。
Lattice material is an ultra-light, high-strength, high-performance porous material. At present, the lattice structure is mainly constructed with uniform density. Different parts made of the lattice material are subjected to different loads, which results in a problem that the optimal performance of the lattice material with uniform density cannot be fully achieved. In view of the above problems, a multiscale topology optimization method based on homogenization method is proposed, which realizes the graded-density lattice structure, and the optimal graded-density lattice structure can be obtained according to the actual load to achieve optimal performance. Taking the automobile connecting rod as an example, comparing with the method of beam-model-based lattice optimization from the commercial software HyperWorks, the proposed method has better performance on mass reduction and the stress distribution. Therefore, the method obtains a better-property design, which is more suitable for the optimal design of graded-density lattice structures.
Lattice material is an ultra-light, high-strength, high-performance porous material. At present, the lattice structure is mainly constructed with uniform density. Different parts made of the lattice material are subjected to different loads, which results in a problem that the optimal performance of the lattice material with uniform density cannot be fully achieved. In view of the above problems, a multiscale topology optimization method based on homogenization method is proposed, which realizes the graded-density lattice structure, and the optimal graded-density lattice structure can be obtained according to the actual load to achieve optimal performance. Taking the automobile connecting rod as an example, comparing with the method of beam-model-based lattice optimization from the commercial software HyperWorks, the proposed method has better performance on mass reduction and the stress distribution. Therefore, the method obtains a better-property design, which is more suitable for the optimal design of graded-density lattice structures.
引文
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[13]赵芳垒,敬石开,刘晨燕.局部相对密度映射的变密度多孔结构设计方法[J].机械工程学报,2018,54(19):121-128.ZHAO Fanglei,JING Shikai,LIU Chenyan.Variable density cellular structure design method base on local relative density mapping[J].Journal of Mechanical Engineering,2018,54(19):121-128.
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[18]苏铁熊,吕彩琴,张翼,等.接触问题对连杆有限元分析的影响[J].内燃机学报,2002,20(1):79-83.SU Tiexiong,LüCaiqin,ZHANG Yi,et al.The contact affection to fea of connection rod[J].Transactions of Csice,2002,20(1):79-83.
[2]杜善义.先进复合材料与航空航天[J].复合材料学报,2007,24(1):1-12.DU Shanyi.Advanced composite materials and aerospace engineering[J].Acta Materiae Compositae Sinica,2007,24(1):1-12.
[3]ZHOU O,MAYER R R.Characterization of aluminum honeycomb material failure in large deformation compression,shear,and tearing[J].Journal of Engineering Materials and Technology-Transactions of the Asme,2002,124(4):412-420.
[4]ALHOMOUD M S.Performance characteristics and practical applications of common building thermal insulation materials[J].Building And Environment,2005,40(3):353-366.
[5]KHANOKI S A,PASINI D.Fatigue design of a mechanically biocompatible lattice for a proof-of-concept femoral stem[J].Journal of the Mechanical Behavior of Biomedical Materials,2013,22:65-83.
[6]SMITH M,GUAN Z,CANTWELL W J.Finite element modelling of the compressive response of lattice structures manufactured using the selective laser melting technique[J].International Journal of Mechanical Sciences,2013,67(1):28-41.
[7]柏龙,熊飞,陈晓红,等.SLM制备的Ti6Al4V轻质点阵结构多目标结构优化设计研究[J].机械工程学报,2018,54(5):156-165.BAI Long,XIONG Fei,CHEN Xiaohong,et al.Multi-objective structural optimization design of Ti6Al4Vlattice structure formed by SLM[J].Journal of Mechanical Engineering,2018,54(5):156-165.
[8]周克民,李俊峰,李霞.结构拓扑优化研究方法综述[J].力学进展,2005,35(1):69-76.ZHOU Kemin,LI Junfeng,LI Xia.A review on topology optimization of structures[J].Advances in Mechanics,2005,35(1):69-76.
[9]ROZVANY G.The SIMP method in topology optimization-Theoretical background,advantages and new applications[C]//8th Symposium on Multidisciplinary Analysis and Optimization.Multidisciplinary Analysis Optimization Conferences.American Institute of Aeronautics and Astronautics,Long Beach,CA,U.S.A2006.
[10]COELHO P G,FERNANDES P R,GUEDESJ M,et al.A hierarchical model for concurrent material and topology optimisation of three-dimensional structures[J].Structural&Multidisciplinary Optimization,2008,35(2):107-115.
[11]WANG Y,XU H,PASINI D.Multiscale isogeometric topology optimization for lattice materials[J].Computer Methods in Applied Mechanics&Engineering,2016,316:568-585.
[12]欧阳佳琛.基于改进变密度法的功能梯度材料拓扑优化设计[D].武汉:华中科技大学,2016.OUYANG Jiachen.Topology optimization design of functionally graded materials based on modified variable density method[D].Wuhan:Huazhong University of Science and Technology,2016.
[13]赵芳垒,敬石开,刘晨燕.局部相对密度映射的变密度多孔结构设计方法[J].机械工程学报,2018,54(19):121-128.ZHAO Fanglei,JING Shikai,LIU Chenyan.Variable density cellular structure design method base on local relative density mapping[J].Journal of Mechanical Engineering,2018,54(19):121-128.
[14]ARABNEJAD S,PASINI D.Mechanical properties of lattice materials via asymptotic homogenization and comparison with alternative homogenization methods[J].International Journal of Mechanical Sciences,2013,77(4):249-262.
[15]HOLLISTER S J,KIKUCHI N.A comparison of homogenization and standard mechanics analyses for periodic porous composites[J].Computational Mechanics,1992,10(2):73-95.
[16]SIGMUND O.A 99 line topology optimization code written in Matlab[J].Structural&Multidisciplinary Optimization,2001,21(2):120-127.
[17]山其新.汽车发动机连杆有限元分析与改进设计[D].成都:电子科技大学,2017.SHAN Qixin.Finite element analysis and improved design of connecting rod of automobile engine[D].Chengdu:University of Electronic Science and Technology of China,2017.
[18]苏铁熊,吕彩琴,张翼,等.接触问题对连杆有限元分析的影响[J].内燃机学报,2002,20(1):79-83.SU Tiexiong,LüCaiqin,ZHANG Yi,et al.The contact affection to fea of connection rod[J].Transactions of Csice,2002,20(1):79-83.