航天高性能薄壁构件的材料-结构一体化设计综述
收稿日期: 2022-05-12
修回日期: 2022-06-06
录用日期: 2022-06-27
网络出版日期: 2022-07-21
基金资助
国家自然科学基金(51790171)
Material⁃structure integrated design for high⁃performance aerospace thin⁃walled component
Received date: 2022-05-12
Revised date: 2022-06-06
Accepted date: 2022-06-27
Online published: 2022-07-21
Supported by
National Natural Science Foundation of China(51790171)
新一代航天器技术的快速发展对结构件超强承载、极端防热、超高精度和超轻量化提出了越来越苛刻的要求，如何设计并制造出高性能、轻量化、超精密的航天薄壁构件成为先进材料与结构设计制造领域普遍关注的难题。本文综述了近年来薄壁构件高性能设计与制造及其航天应用的主要成果，围绕材料-结构多尺度建模与性能表征、多材料多尺度结构设计与增材制造原理、增材制造材料性能与结构设计的交互作用机制等科学问题，就结构优化中的制造工艺约束建模，增材制造工艺参数对结构性能的影响，高性能构件材料-结构一体化设计方法及其在航天结构中的应用展开论述，并展望了未来典型航天薄壁构件材料-结构一体化设计和制造方法发展前景与应用，为未来相关研究工作和航空航天装备研发提供参考。
张卫红 , 周涵 , 李韶英 , 朱继宏 , 周璐 . 航天高性能薄壁构件的材料-结构一体化设计综述[J]. 航空学报, 2023 , 44(9) : 627428 -627428 . DOI: 10.7527/S1000-6893.2022.27428
The rapid development of the next generation of aerospace technology has imposed more and more stringent requirements for such structural performance as the ultra-strong load-bearing， extreme heat-proof， ultra-precision and ultra-lightweight. Therefore， how to design and fabricate high-performance， lightweight， and ultra-precise aerospace thin-walled structures has become a common concern in the field of advanced material and structural design and manufacturing. This paper reviews the main achievements of high-performance design and manufacture of thin-walled components and their aerospace applications in recent years， focusing on the scientific issues including the mapping law between multi-scale structures and structural performance， the composed manufacturing principle of multi-material and multi-scale structures， and the interaction mechanism between material organization evolution and structural deformation. Moreover， the manufacturing process constraints in structural optimization， the influence of additive manufacturing process parameters on the structural optimization， the material-structure integrated design method of high-performance structures and its application in aerospace structures are discussed. The development prospects and applications of the material-structure integrated design and manufacturing methods of typical aerospace thin-walled structures in the future are also prospected， which can provide references for future related research and aerospace applications.
| 1 | BABU?KA I. Homogenization approach in engineering［M］∥Lecture Notes in Economics and Mathematical Systems. Berlin： Springer Berlin Heidelberg， 1976： 137-153. |
| 2 | ALLAIRE G， GEOFFROY-DONDERS P， PANTZ O. Topology optimization of modulated and oriented periodic microstructures by the homogenization method［J］. Computers & Mathematics With Applications， 2019， 78（7）： 2197-2229. |
| 3 | LU X X， GIOVANIS D G， YVONNET J， et al. A data-driven computational homogenization method based on neural networks for the nonlinear anisotropic electrical response of graphene/polymer nanocomposites［J］. Computational Mechanics， 2019， 64（2）： 307-321. |
| 4 | GHOSH S， LEE K， MOORTHY S. Multiple scale analysis of heterogeneous elastic structures using homogenization theory and voronoi cell finite element method［J］. International Journal of Solids and Structures， 1995， 32（1）： 27-62. |
| 5 | WANG Z Y， LI P F. Voronoi cell finite element modelling of the intergranular fracture mechanism in polycrystalline alumina［J］. Ceramics International， 2017， 43（9）： 6967-6975. |
| 6 | SHEN L L， SHEN Z B， LI H Y， et al. A Voronoi cell finite element method for estimating effective mechanical properties of composite solid propellants［J］. Journal of Mechanical Science and Technology， 2017， 31（11）： 5377-5385. |
| 7 | FEYEL F， CHABOCHE J L. FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials［J］. Computer Methods in Applied Mechanics and Engineering， 2000， 183（3-4）： 309-330. |
| 8 | XIA L， BREITKOPF P. Concurrent topology optimization design of material and structure within FE2 nonlinear multiscale analysis framework［J］. Computer Methods in Applied Mechanics and Engineering， 2014， 278： 524-542. |
| 9 | TIKARROUCHINE E， BENAARBIA A， CHATZIGEOR? GIOU G， et al. Non-linear FE2 multiscale simulation of damage， micro and macroscopic strains in polyamide 66-woven composite structures： analysis and experimental validation［J］. Composite Structures， 2021， 255： 112926. |
| 10 | OTERO F， OLLER S， MARTINEZ X. Multiscale computational homogenization： review and proposal of a new enhanced-first-order method［J］. Archives of Computational Methods in Engineering， 2018， 25（2）： 479-505. |
| 11 | KWON Y R， LEE B C. A mixed element based on Lagrange multiplier method for modified couple stress theory［J］. Computational Mechanics， 2017， 59（1）： 117-128. |
| 12 | MARKOVIC D， IBRAHIMBEGOVIC A. On micro-macro interface conditions for micro scale based FEM for inelastic behavior of heterogeneous materials［J］. Computer Methods in Applied Mechanics and Engineering， 2004， 193（48-51）： 5503-5523. |
| 13 | TANG X D， WHITCOMB J D， KELKAR A D， et al. Progressive failure analysis of 2×2 braided composites exhibiting multiscale heterogeneity［J］. Composites Science and Technology， 2006， 66（14）： 2580-2590. |
| 14 | GOYAL D， WHITCOMB J D， TANG X D. Validation of full 3D and equivalent tape laminate modeling of plasticity induced non-linearity in 2×2 braided composites［J］. Composites Part A： Applied Science and Manufacturing， 2008， 39（5）： 747-760. |
| 15 | CANAL L P， PAPPAS G， BOTSIS J. Large scale fiber bridging in mode I intralaminar fracture. An embedded cell approach［J］. Composites Science and Technology， 2016， 126： 52-59. |
| 16 | GONZáLEZ C， LLORCA J. Multiscale modeling of fracture in fiber-reinforced composites［J］. Acta Materialia， 2006， 54（16）： 4171-4181. |
| 17 | DONG J W， HUO N F. A two-scale method for predicting the mechanical properties of 3D braided composites with internal defects［J］. Composite Structures， 2016， 152： 1-10. |
| 18 | BENSOUSSAN A， LIONS J L， PAPANICOLAOU G. Asymptotic analysis for periodic structures［M］. Providence， R.I.： American Mathematical Society， 2011. |
| 19 | 梁军， 黄富华， 杜善义. 周期性单胞复合材料有效弹性性能的边界力方法［J］. 复合材料学报， 2010， 27（2）： 108-112. |
| LIANG J， HUANG F H， DU S Y. Boundary force method to predict effective elastic properties of periodical unit cell composite material［J］. Acta Materiae Compositae Sinica， 2010， 27（2）： 108-112 （in Chinese）. | |
| 20 | ZHAI J J， CHENG S， ZENG T， et al. Thermo-mechanical behavior analysis of 3D braided composites by multiscale finite element method［J］. Composite Structures， 2017， 176： 664-672. |
| 21 | YVONNET J. A fast method for solving microstructural problems defined by digital images： a space Lippmann-Schwinger scheme［J］. International Journal for Numerical Methods in Engineering， 2012， 92（2）： 178-205. |
| 22 | SCHNEIDER M. Convergence of FFT-based homogenization for strongly heterogeneous media［J］. Mathematical Methods in the Applied Sciences， 2015， 38（13）： 2761-2778. |
| 23 | WILLOT F， ABDALLAH B， PELLEGRINI Y P. Fourier-based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fields［J］. International Journal for Numerical Methods in Engineering， 2014， 98（7）： 518-533. |
| 24 | LIU Z L， BESSA M A， LIU W K. Self-consistent clustering analysis： an efficient multi-scale scheme for inelastic heterogeneous materials［J］. Computer Methods in Applied Mechanics and Engineering， 2016， 306： 319-341. |
| 25 | VOND?EJC J， ZEMAN J， MAREK I. Guaranteed upper-lower bounds on homogenized properties by FFT-based Galerkin method［J］. Computer Methods in Applied Mechanics and Engineering， 2015， 297： 258-291. |
| 26 | LADEVèZE P， LOISEAU O， DUREISSEIX D. A micro-macro and parallel computational strategy for highly heterogeneous structures［J］. International Journal for Numerical Methods in Engineering， 2001， 52（12）： 121-138. |
| 27 | IBRAHIMBEGOVI? A， MARKOVI? D. Strong coupling methods in multi-phase and multi-scale modeling of inelastic behavior of heterogeneous structures［J］. Computer Methods in Applied Mechanics and Engineering， 2003， 192（28-30）： 3089-3107. |
| 28 | CHENG K T， OLHOFF N. An investigation concerning optimal design of solid elastic plates［J］. International Journal of Solids and Structures， 1981， 17（3）： 305-323. |
| 29 | BENDS?E M P， KIKUCHI N. Generating optimal topologies in structural design using a homogenization method［J］. Computer Methods in Applied Mechanics and Engineering， 1988， 71（2）： 197-224. |
| 30 | BENDS?E M P. Optimal shape design as a material distribution problem［J］. Structural Optimization， 1989， 1（4）： 193-202. |
| 31 | BENDS?E M P， SIGMUND O. Material interpolation schemes in topology optimization［J］. Archive of Applied Mechanics， 1999， 69（9）： 635-654. |
| 32 | QUERIN O M， YOUNG V， STEVEN G P， et al. Computational efficiency and validation of bi-directional evolutionary structural optimisation［J］. Computer Methods in Applied Mechanics and Engineering， 2000， 189（2）： 559-573. |
| 33 | XIE Y M， STEVEN G P. A simple evolutionary procedure for structural optimization［J］. Computers & Structures， 1993， 49（5）： 885-896. |
| 34 | WANG M Y， WANG X M， GUO D M. A level set method for structural topology optimization［J］. Computer Methods in Applied Mechanics and Engineering， 2003， 192（1-2）： 227-246. |
| 35 | ALLAIRE G， JOUVE F， TOADER A M. A level-set method for shape optimization［J］. Comptes Rendus Mathematique， 2002， 334（12）： 1125-1130. |
| 36 | ZHU J H， ZHANG W H， XIA L. Topology optimization in aircraft and aerospace structures design［J］. Archives of Computational Methods in Engineering， 2016， 23（4）： 595-622. |
| 37 | LAKES R. Foam structures with a negative poisson’s ratio［J］. Science， 1987， 235（4792）： 1038-1040. |
| 38 | SIGMUND O. Materials with prescribed constitutive parameters： an inverse homogenization problem［J］. International Journal of Solids and Structures， 1994， 31（17）： 2313-2329. |
| 39 | WANG Y Q， CHEN F F， WANG M Y. Concurrent design with connectable graded microstructures［J］. Computer Methods in Applied Mechanics and Engineering， 2017， 317： 84-101. |
| 40 | LI H， LUO Z， GAO L， et al. Topology optimization for concurrent design of structures with multi-patch microstructures by level sets［J］. Computer Methods in Applied Mechanics and Engineering， 2018， 331： 536-561. |
| 41 | 刘书田， 程耿东. 基于均匀化理论的梯度功能材料优化设计方法［J］. 宇航材料工艺， 1995， 25（6）： 21-27. |
| LIU S T， CHENG G D. Optimization design method of functionally graded materials based on homogenization theory［J］. Aerospace Materials & Technology， 1995， 25（6）： 21-27 （in Chinese）. | |
| 42 | 袁振， 吴长春. 复合材料周期性线弹性微结构的拓扑优化设计［J］. 固体力学学报， 2003， 24（1）： 40-45. |
| YUAN Z， WU C C. Topology optimization for periodic linear elastic microstructures of composite materials［J］. Acta Mechanica Solida Sinica， 2003， 24（1）： 40-45 （in Chinese）. | |
| 43 | HUANG X D， ZHOU S W， SUN G Y， et al. Topology optimization for microstructures of viscoelastic composite materials［J］. Computer Methods in Applied Mechanics and Engineering， 2015， 283： 503-516. |
| 44 | XIA L， BREITKOPF P. Design of materials using topology optimization and energy-based homogenization approach in Matlab［J］. Structural and Multidisciplinary Optimization， 2015， 52（6）： 1229-1241. |
| 45 | CADMAN J E， ZHOU S W， CHEN Y H， et al. On design of multi-functional microstructural materials［J］. Journal of Materials Science， 2013， 48（1）： 51-66. |
| 46 | RODRIGUES H， GUEDES J M， BENDSOE M P. Hierarchical optimization of material and structure［J］. Structural and Multidisciplinary Optimization， 2002， 24（1）： 1-10. |
| 47 | ADAMS B L， LYON M， HENRIE B L， et al. Spectral integration of microstructure and design［J］. Materials Science Forum， 2002， 408-412： 487-492. |
| 48 | ZHANG W H， SUN S P. Scale-related topology optimization of cellular materials and structures［J］. International Journal for Numerical Methods in Engineering， 2006， 68（9）： 993-1011. |
| 49 | YAN J， CHENG G D， LIU L. A uniform optimum material based model for concurrent optimization of thermoelastic structures and materials［J］. International Journal for Simulation and Multidisciplinary Design Optimization， 2008， 2（4）： 259-266. |
| 50 | SU W Z， LIU S T. Size-dependent optimal microstructure design based on couple-stress theory［J］. Structural and Multidisciplinary Optimization， 2010， 42（2）： 243-254. |
| 51 | XIA L， BREITKOPF P. Multiscale structural topology optimization with an approximate constitutive model for local material microstructure［J］. Computer Methods in Applied Mechanics and Engineering， 2015， 286： 147-167. |
| 52 | XIA L， BREITKOPF P. Recent advances on topology optimization of multiscale nonlinear structures［J］. Archives of Computational Methods in Engineering， 2017， 24（2）： 227-249. |
| 53 | XU Y J， ZHU J H， WU Z， et al. A review on the design of laminated composite structures： constant and variable stiffness design and topology optimization［J］. Advanced Composites and Hybrid Materials， 2018， 1（3）： 460-477. |
| 54 | NOMURA T， KAWAMOTO A， KONDOH T， et al. Inverse design of structure and fiber orientation by means of topology optimization with tensor field variables［J］. Composites Part B： Engineering， 2019， 176： 107187. |
| 55 | YUAN S Q， LI S Y， ZHU J H， et al. Additive manufacturing of polymeric composites from material processing to structural design［J］. Composites Part B： Engineering， 2021， 219： 108903. |
| 56 | BODDETI N， ROSEN D W， MAUTE K， et al. Multiscale optimal design and fabrication of laminated composites［J］. Composite Structures， 2019， 228： 111366. |
| 57 | BODDETI N， TANG Y L， MAUTE K， et al. Optimal design and manufacture of variable stiffness laminated continuous fiber reinforced composites［J］. Scientific Reports， 2020， 10： 16507. |
| 58 | PAPAPETROU V S， PATEL C， TAMIJANI A Y. Stiffness-based optimization framework for the topology and fiber paths of continuous fiber composites［J］. Composites Part B： Engineering， 2020， 183： 107681. |
| 59 | LEARY M， MERLI L， TORTI F， et al. Optimal topology for additive manufacture： a method for enabling additive manufacture of support-free optimal structures［J］. Materials & Design， 2014， 63： 678-690. |
| 60 | LIU S T， LI Q H， CHEN W J， et al. An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures［J］. Frontiers of Mechanical Engineering， 2015， 10（2）： 126-137. |
| 61 | ZHOU M D， LAZAROV B S， WANG F W， et al. Minimum length scale in topology optimization by geometric constraints［J］. Computer Methods in Applied Mechanics and Engineering， 2015， 293： 266-282. |
| 62 | 王华明. 高性能大型金属构件激光增材制造：若干材料基础问题［J］. 航空学报， 2014， 35（10）： 2690-2698. |
| WANG H M. Materials’ fundamental issues of laser additive manufacturing for high-performance large metallic components［J］. Acta Aeronautica et Astronautica Sinica， 2014， 35（10）： 2690-2698 （in Chinese）. | |
| 63 | HUANG W D， LIN X. Research progress in laser solid forming of high-performance metallic components at the state key laboratory of solidification processing of China［J］. 3D Printing and Additive Manufacturing， 2014， 1（3）： 156-165. |
| 64 | YANG J K， GU D D， LIN K J， et al. Optimization of bio-inspired bi-directionally corrugated panel impact-resistance structures： numerical simulation and selective laser melting process［J］. Journal of the Mechanical Behavior of Biomedical Materials， 2019， 91： 59-67. |
| 65 | 顾冬冬， 张红梅， 陈洪宇， 等. 航空航天高性能金属材料构件激光增材制造［J］. 中国激光， 2020， 47（5）： 0500002. |
| GU D D， ZHANG H M， CHEN H Y， et al. Laser additive manufacturing of high-performance metallic aerospace components［J］. Chinese Journal of Lasers， 2020， 47（5）： 0500002 （in Chinese）. | |
| 66 | 刘建涛， 林鑫， 吕晓卫， 等. Ti-Ti2AlNb功能梯度材料的激光立体成形研究［J］. 金属学报， 2008， 44（8）： 1006-1012. |
| LIU J T， LIN X， Lü X W， et al. Research on laser solid forming of a functionally gradient Ti-Ti2AlNb alloy［J］. Acta Metallurgica Sinica， 2008， 44（8）： 1006-1012 （in Chinese）. | |
| 67 | 杨模聪， 林鑫， 许小静， 等. 激光立体成形Ti60-Ti2AlNb梯度材料的组织与相演变［J］. 金属学报， 2009， 45（6）： 729-736. |
| YANG M C， LIN X， XU X J， et al. Microstructure and phase evolution in Ti60-Ti2AlNb gradient material prepared by laser solid forming［J］. Acta Metallurgica Sinica， 2009， 45（6）： 729-736 （in Chinese）. | |
| 68 | 解航， 张安峰， 李涤尘， 等. 激光金属直接成形Ti6Al4V-CoCrMo梯度材料开裂研究［J］. 中国激光， 2013， 40（11）： 97-103. |
| XIE H， ZHANG A F， LI D C， et al. Research on the cracking of Ti6Al4V-CoCrMo gradient material fabricated by laser metal direct forming［J］. Chinese Journal of Lasers， 2013， 40（11）： 97-103 （in Chinese）. | |
| 69 | SIMONELLI M， TSE Y Y， TUCK C. Effect of the build orientation on the mechanical properties and fracture modes of SLM Ti-6Al-4V［J］. Materials Science and Engineering： A， 2014， 616： 1-11. |
| 70 | EDWARDS P， RAMULU M. Fatigue performance evaluation of selective laser melted Ti-6Al-4V［J］. Materials Science and Engineering： A， 2014， 598： 327-337. |
| 71 | SATO Y， YAMADA T， IZUI K， et al. Manufacturability evaluation for molded parts using fictitious physical models， and its application in topology optimization［J］. The International Journal of Advanced Manufacturing Technology， 2017， 92（1）： 1391-1409. |
| 72 | WANG Y G， KANG Z. Structural shape and topology optimization of cast parts using level set method［J］. International Journal for Numerical Methods in Engineering， 2017， 111（13）： 1252-1273. |
| 73 | HOU J， ZHU J H， HE F， et al. Stiffeners layout design of thin-walled structures with constraints on multi-fastener joint loads［J］. Chinese Journal of Aeronautics， 2017， 30（4）： 1441-1450. |
| 74 | LI Q H， CHEN W J， LIU S T， et al. Topology optimization design of cast parts based on virtual temperature method［J］. Computer-Aided Design， 2018， 94： 28-40. |
| 75 | WANG C， XU B， MENG Q X， et al. Topology optimization of cast parts considering parting surface position［J］. Advances in Engineering Software， 2020， 149： 102886. |
| 76 | LANGELAAR M. Topology optimization for multi-axis machining［J］. Computer Methods in Applied Mechanics and Engineering， 2019， 351： 226-252. |
| 77 | LEE H Y， ZHU M， GUEST J K. Topology optimization considering multi-axis machining constraints using projection methods［J］. Computer Methods in Applied Mechanics and Engineering， 2022， 390： 114464. |
| 78 | GASICK J， QIAN X P. Simultaneous topology and machine orientation optimization for multiaxis machining［J］. International Journal for Numerical Methods in Engineering， 2021， 122（24）： 7504-7535. |
| 79 | MIRZENDEHDEL A M， BEHANDISH M， NELATURI S. Topology optimization with accessibility constraint for multi-axis machining［J］. Computer-Aided Design， 2020， 122： 102825. |
| 80 | MORRIS N， BUTSCHER A， IORIO F. A subtractive manufacturing constraint for level set topology optimization［J］. Structural and Multidisciplinary Optimization， 2020， 61（4）： 1573-1588. |
| 81 | LANGELAAR M. An additive manufacturing filter for topology optimization of print-ready designs［J］. Structural and Multidisciplinary Optimization， 2017， 55（3）： 871-883. |
| 82 | JOHNSON T E， GAYNOR A T. Three-dimensional projection-based topology optimization for prescribed-angle self-supporting additively manufactured structures［J］. Additive Manufacturing， 2018， 24： 667-686. |
| 83 | VAN DE VEN E， MAAS R， AYAS C， et al. Continuous front propagation-based overhang control for topology optimization with additive manufacturing［J］. Structural and Multidisciplinary Optimization， 2018， 57（5）： 2075-2091. |
| 84 | VAN DE VEN E， MAAS R， AYAS C， et al. Overhang control based on front propagation in 3D topology optimization for additive manufacturing［J］. Computer Methods in Applied Mechanics and Engineering， 2020， 369： 113169. |
| 85 | QIAN X P. Undercut and overhang angle control in topology optimization： a density gradient based integral approach［J］. International Journal for Numerical Methods in Engineering， 2017， 111（3）： 247-272. |
| 86 | ZHANG K Q， CHENG G D， XU L. Topology optimization considering overhang constraint in additive manufacturing［J］. Computers & Structures， 2019， 212： 86-100. |
| 87 | ZHANG K Q， CHENG G D. Three-dimensional high resolution topology optimization considering additive manufacturing constraints［J］. Additive Manufacturing， 2020， 35： 101224. |
| 88 | LIU Y C， ZHOU M D， WEI C， et al. Topology optimization of self-supporting infill structures［J］. Structural and Multidisciplinary Optimization， 2021， 63（5）： 2289-2304. |
| 89 | WANG C， ZHANG W H， ZHOU L， et al. Topology optimization of self-supporting structures for additive manufacturing with B-spline parameterization［J］. Computer Methods in Applied Mechanics and Engineering， 2021， 374： 113599. |
| 90 | ALLAIRE G， DAPOGNY C， ESTEVEZ R， et al. Structural optimization under overhang constraints imposed by additive manufacturing technologies［J］. Journal of Computational Physics， 2017， 351： 295-328. |
| 91 | WANG Y G， GAO J C， KANG Z. Level set-based topology optimization with overhang constraint： towards support-free additive manufacturing［J］. Computer Methods in Applied Mechanics and Engineering， 2018， 339： 591-614. |
| 92 | GUO X， ZHOU J H， ZHANG W S， et al. Self-supporting structure design in additive manufacturing through explicit topology optimization［J］. Computer Methods in Applied Mechanics and Engineering， 2017， 323： 27-63. |
| 93 | ZHANG W H， ZHOU L. Topology optimization of self-supporting structures with polygon features for additive manufacturing［J］. Computer Methods in Applied Mechanics and Engineering， 2018， 334： 56-78. |
| 94 | ZHOU L， SIGMUND O， ZHANG W H. Self-supporting structure design with feature-driven optimization approach for additive manufacturing［J］. Computer Methods in Applied Mechanics and Engineering， 2021， 386： 114110. |
| 95 | LI Q H， CHEN W J， LIU S T， et al. Structural topology optimization considering connectivity constraint［J］. Structural and Multidisciplinary Optimization， 2016， 54（4）： 971-984. |
| 96 | ZHOU L， ZHANG W H. Topology optimization method with elimination of enclosed voids［J］. Structural and Multidisciplinary Optimization， 2019， 60（1）： 117-136. |
| 97 | XIONG Y L， YAO S， ZHAO Z L， et al. A new approach to eliminating enclosed voids in topology optimization for additive manufacturing［J］. Additive Manufacturing， 2020， 32： 101006. |
| 98 | GAYNOR A T， JOHNSON T E. Eliminating occluded voids in additive manufacturing design via a projection-based topology optimization scheme［J］. Additive Manufacturing， 2020， 33： 101149. |
| 99 | DUNNING P D. Minimum length-scale constraints for parameterized implicit function based topology optimization［J］. Structural and Multidisciplinary Optimization， 2018， 58（1）： 155-169. |
| 100 | HOANG V N， JANG G W. Topology optimization using moving morphable bars for versatile thickness control［J］. Computer Methods in Applied Mechanics and Engineering， 2017， 317： 153-173. |
| 101 | WANG R X， ZHANG X M， ZHU B L. Imposing minimum length scale in moving morphable component （MMC）-based topology optimization using an effective connection status （ECS） control method［J］. Computer Methods in Applied Mechanics and Engineering， 2019， 351： 667-693. |
| 102 | LIU J K， MA Y S. A new multi-material level set topology optimization method with the length scale control capability［J］. Computer Methods in Applied Mechanics and Engineering， 2018， 329： 444-463. |
| 103 | LIU J K. Piecewise length scale control for topology optimization with an irregular design domain［J］. Computer Methods in Applied Mechanics and Engineering， 2019， 351： 744-765. |
| 104 | 王罡， 任珂， 胡毅森， 等. 基于微观组织特征的航天铝铜合金力学行为研究［J］. 机械工程学报， 2018， 54（9）： 77-85. |
| WANG G， REN K， HU Y S， et al. Microstructural characteristics-based mechanical behavior of aerospace Al-Cu alloys［J］. Journal of Mechanical Engineering， 2018. 54（9）： 77-85 （in Chinese）. | |
| 105 | 王宝善， 贾蔚菊， 渠维猛， 等. 锻造工艺对Ti60合金棒材组织和性能的影响［J］. 钛工业进展， 2011， 28（1）： 8-11. |
| WANG B S， JIA W J， QU W M， et al. Influence of forging processes on microstructure and mechanical properties of Ti60 alloy［J］. Titanium Industry Progress， 2011， 28（1）： 8-11 （in Chinese）. | |
| 106 | 林鑫， 黄卫东. 高性能金属构件的激光增材制造［J］. 中国科学：信息科学， 2015， 45（9）： 1111-1126. |
| LIN X， HUANG W D. Laser additive manufacturing of high-performance metal components［J］. Scientia Sinica （Informationis）， 2015， 45（9）： 1111-1126 （in Chinese）. | |
| 107 | DAI S， DENG Z C， YU Y J， et al. Microstructure and constitutive model for flow behavior of AlSi10Mg by Selective Laser Melting［J］. Materials Science and Engineering： A， 2021， 814： 141157. |
| 108 | SOUZA P M， BELADI H， SINGH R P， et al. An analysis on the constitutive models for forging of Ti6Al4V alloy considering the softening behavior［J］. Journal of Materials Engineering and Performance， 2018， 27（7）： 3545-3558. |
| 109 | 史振学， 刘世忠， 李嘉荣. 一种第四代单晶高温合金不同温度的拉伸性能各向异性［J］. 航空材料学报， 2019， 39（4）： 78-85. |
| SHI Z X， LIU S Z， LI J R. Tensile anisotropy of the fourth generation single crystal superalloy at different temperatures［J］. Journal of Aeronautical Materials， 2019， 39（4）： 78-85 （in Chinese）. | |
| 110 | VIJAY A， PAULSON N， SADEGHI F. A 3D finite element modelling of crystalline anisotropy in rolling contact fatigue［J］. International Journal of Fatigue， 2018， 106： 92-102. |
| 111 | WANG S H， MA Y B， DENG Z C， et al. Implementation of an elastoplastic constitutive model for 3D-printed materials fabricated by stereolithography［J］. Additive Manufacturing， 2020， 33： 101104. |
| 112 | LI S Y， YUAN S Q， ZHU J H， et al. Additive manufacturing-driven design optimization： building direction and structural topology［J］. Additive Manufacturing， 2020， 36： 101406. |
| 113 | LI S Y， WEI H K， YUAN S Q， et al. Collaborative optimization design of process parameter and structural topology for laser additive manufacturing［J］. Chinese Journal of Aeronautics， 2021 （in press）. |
| 114 | LI S Y， YUAN S Q， ZHU J H， et al. Multidisciplinary topology optimization incorporating process-structure-property-performance relationship of additive manufacturing［J］. Structural and Multidisciplinary Optimization， 2021， 63（5）： 2141-2157. |
| 115 | PARK S I， ROSEN D W. Quantifying effects of material extrusion additive manufacturing process on mechanical properties of lattice structures using as-fabricated voxel modeling［J］. Additive Manufacturing， 2016， 12： 265-273. |
| 116 | LI S Y， YUAN S Q， ZHU J H， et al. Optimal and adaptive lattice design considering process-induced material anisotropy and geometric inaccuracy for additive manufacturing［J］. Structural and Multidisciplinary Optimization， 2022， 65（1）： 35. |
| 117 | GAO J， LUO Z， LI H， et al. Topology optimization for multiscale design of porous composites with multi-domain microstructures［J］. Computer Methods in Applied Mechanics and Engineering， 2019， 344： 451-476. |
| 118 | ZHANG Y， XIAO M， GAO L， et al. Multiscale topology optimization for minimizing frequency responses of cellular composites with connectable graded microstructures［J］. Mechanical Systems and Signal Processing， 2020， 135： 106369. |
| 119 | CHU S， GAO L， XIAO M， et al. Multiscale topology optimization for coated structures with multifarious-microstructural infill［J］. Structural and Multidisciplinary Optimization， 2020， 61（4）： 1473-1494. |
| 120 | WANG Y G， KANG Z. Concurrent two-scale topological design of multiple unit cells and structure using combined velocity field level set and density model［J］. Computer Methods in Applied Mechanics and Engineering， 2019， 347： 340-364. |
| 121 | XU Z， ZHANG W H， ZHOU Y， et al. Multiscale topology optimization using feature-driven method［J］. Chinese Journal of Aeronautics， 2020， 33（2）： 621-633. |
| 122 | GROEN J P， SIGMUND O. Homogenization-based topology optimization for high-resolution manufacturable microstructures［J］. International Journal for Numerical Methods in Engineering， 2018， 113（8）： 1148-1163. |
| 123 | WANG C， GU X J， ZHU J H， et al. Concurrent design of hierarchical structures with three-dimensional parameterized lattice microstructures for additive manufacturing［J］. Structural and Multidisciplinary Optimization， 2020， 61（3）： 869-894. |
| 124 | WANG C， ZHU J H， ZHANG W H， et al. Concurrent topology optimization design of structures and non-uniform parameterized lattice microstructures［J］. Structural and Multidisciplinary Optimization， 2018， 58（1）： 35-50. |
| 125 | WHITE D A， ARRIGHI W J， KUDO J， et al. Multiscale topology optimization using neural network surrogate models［J］. Computer Methods in Applied Mechanics and Engineering， 2019， 346： 1118-1135. |
| 126 | WU Z J， XIA L， WANG S T， et al. Topology optimization of hierarchical lattice structures with substructuring［J］. Computer Methods in Applied Mechanics and Engineering， 2019， 345： 602-617. |
| 127 | LIU Z， XIA L， XIA Q， et al. Data-driven design approach to hierarchical hybrid structures with multiple lattice configurations［J］. Structural and Multidisciplinary Optimization， 2020， 61（6）： 2227-2235. |
| 128 | WU T Y， LI S. An efficient multiscale optimization method for conformal lattice materials［J］. Structural and Multidisciplinary Optimization， 2021， 63（3）： 1063-1083. |
| 129 | ZHOU H， ZHU J H， WANG C， et al. Hierarchical structure optimization with parameterized lattice and multiscale finite element method［J］. Structural and Multidisciplinary Optimization， 2022， 65（1）： 39. |
| 130 | WU J， SIGMUND O， GROEN J P. Topology optimization of multi-scale structures： a review［J］. Structural and Multidisciplinary Optimization， 2021， 63（3）： 1455-1480. |
| 131 | CHEN W J， ZHENG X N， LIU S T. Finite-element-mesh based method for modeling and optimization of lattice structures for additive manufacturing［J］. Materials （Basel， Switzerland）， 2018， 11（11）： 2073. |
| 132 | TANG Y L， KURTZ A， ZHAO Y F. Bidirectional Evolutionary Structural Optimization （BESO） based design method for lattice structure to be fabricated by additive manufacturing［J］. Computer-Aided Design， 2015， 69： 91-101. |
| 133 | WANG C， ZHU J H， WU M Q， et al. Multi-scale design and optimization for solid-lattice hybrid structures and their application to aerospace vehicle components［J］. Chinese Journal of Aeronautics， 2021， 34（5）： 386-398. |
| 134 | ZHOU M D， GENG D. Multi-scale and multi-material topology optimization of channel-cooling cellular structures for thermomechanical behaviors［J］. Computer Methods in Applied Mechanics and Engineering， 2021， 383： 113896. |
| 135 | LIU S T， LI Q H， LIU J H， et al. A realization method for transforming a topology optimization design into additive manufacturing structures［J］. Engineering， 2018， 4（2）： 277-285. |
| 136 | JIU L P， ZHANG W H， MENG L， et al. A CAD-oriented structural topology optimization method［J］. Computers & Structures， 2020， 239： 106324. |
| 137 | ZHANG S L， LE C， GAIN A L， et al. Fatigue-based topology optimization with non-proportional loads［J］. Computer Methods in Applied Mechanics and Engineering， 2019， 345： 805-825. |
| 138 | ZHAO L， XU B， HAN Y S， et al. Structural topological optimization with dynamic fatigue constraints subject to dynamic random loads［J］. Engineering Structures， 2020， 205： 110089. |
| 139 | YANG Q， GAO B， XU Z Y， et al. Topology optimisations for integrated thermal protection systems considering thermo-mechanical constraints［J］. Applied Thermal Engineering， 2019， 150： 995-1001. |
| 140 | CHEN F， ZHU J H， DU X X， et al. Shape preserving topology optimization for structural radar cross section control［J］. Chinese Journal of Aeronautics， 2022， 35（6）： 198-210. |
| 141 | CHEN F， ZHU J H， ZHANG W H. Radar cross section minimization for step structures using topology optimization［J］. Structural and Multidisciplinary Optimization， 2022， 65（2）： 51. |
| 142 | YANG D， YIN Y F， ZHANG Z K， et al. Wide-angle microwave absorption properties of multilayer metamaterial fabricated by 3D printing［J］. Materials Letters， 2020， 281： 128571. |
| 143 | SUN P， ZHANG Z D， GUO H， et al. Topological optimization of hierarchical honeycomb acoustic metamaterials for low-frequency extreme broad band gaps［J］. Applied Acoustics， 2022， 188： 108579. |
| 144 | GU X J， YANG K K， WU M Q， et al. Integrated optimization design of smart morphing wing for accurate shape control［J］. Chinese Journal of Aeronautics， 2021， 34（1）： 135-147. |
| 145 | CHEN X， LIU J， LI Q. The smart morphing winglet driven by the piezoelectric Macro Fiber Composite actuator［J］. The Aeronautical Journal， 2022， 126（1299）： 830-847. |
/
| 〈 |
|
〉 |
CJA