Optimal design, analysis and additive manufacturing for two-level stochastic honeycomb structure

References

• Allaire, G., F. Jouve, and A. M. Toader. 2002. “A Level-Set Method for Shape Optimization.” Comptes Rendus Mathematique 334 (12): 1125–1130. doi:10.1016/S1631-073X(02)02412-3.
   Web of Science ®Google Scholar
• Bendsøe, M. P., A. Ben-Tal, and J. Zowe. 1994. “Optimization Methods for Truss Geometry and Topology Design.” Structural Optimization 7 (3): 141–159. doi:10.1007/BF01742459.
   Web of Science ®Google Scholar
• Bendsøe, M. P., and N. Kikuchi. 1988. “Generating Optimal Topologies in Structural Design Using a Homogenization Method.” Computer Methods in Applied Mechanics & Engineering 71 (2): 197–224. doi:10.1016/0045-7825(88)90086-2.
   Web of Science ®Google Scholar
• Brackett, D., I. Ashcroft, and R. Hague. 2011. “Topology Optimization for Additive Manufacturing.” 22nd Annual International Solid Freeform Fabrication Symposium Austin, University of Texas., United States, August 8–10.
   Google Scholar
• Chang, P. S., and D. W. Rosen. 2013. “The Size Matching and Scaling Method: A Synthesis Method for the Design of Mesoscale Cellular Structures.” International Journal of Computer Integrated Manufacturing 26 (10): 907–927. doi:10.1080/0951192x.2011.650880.
   Web of Science ®Google Scholar
• Chen, Y., Z. Jia, and L. F. Wang. 2016. “Hierarchical Honeycomb Lattice Metamaterials with Improved Thermal Resistance and Mechanical Properties.” Composite Structures 152: 395–402. doi:10.1016/j.compstruct.2016.05.048.
   Web of Science ®Google Scholar
• Chu, C., G. Graf, and D. W. Rosen. 2008. “Design for Additive Manufacturing of Cellular Structures.” Computer-Aided Design and Applications 5 (5): 686–696. doi:10.3722/cadaps.2008.686-696.
   Google Scholar
• Deshpande, V. S., N. A. Fleck, and M. F. Ashby. 2001. “Effective Properties of the Octet-Truss Lattice Material.” Journal of the Mechanics and Physics of Solids 49 (8): 1747–1769. doi:10.1016/S0022-5096(01)00010-2.
   Web of Science ®Google Scholar
• Gibson, L. J., and M. F. Ashby. 2003. Structure and Properties. 2nd ed. Beijing: Tsinghua University Press.
   Google Scholar
• Gibson, L. J., M. F. Ashby, G. S. Schajer, and C. I. Robertson. 1982. “The Mechanics of Two-Dimensional Cellular Materials.” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 382 (1782): 25–42. doi:10.1098/rspa.1982.0088.
   Web of Science ®Google Scholar
• Helou, M., and S. Kara. 2017. “Design, Analysis and Manufacturing of Lattice Structures: An Overview.” International Journal of Computer Integrated Manufacturing 31 (3): 1–19. doi:10.1080/0951192X.2017.1407456.
   Web of Science ®Google Scholar
• Huang, X., and Y. M. Xie. 2007. “Convergent and Mesh-Independent Solutions for the Bi-Directional Evolutionary Structural Optimization Method.” Finite Elements in Analysis & Design 43 (14): 1039–1049. doi:10.1016/j.finel.2007.06.006.
   Web of Science ®Google Scholar
• Kim, G. D., and Y. T. Oh. 2008. “A Benchmark Study on Rapid Prototyping Processes and Machines: Quantitative Comparisons of Mechanical Properties, Accuracy, Roughness, Speed, and Material Cost.” Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 222 (2): 201–215. doi:10.1243/09544054JEM724.
   Web of Science ®Google Scholar
• Kou, X. Y., and S. T. Tan. 2010. “A Simple and Effective Geometric Representation for Irregular Porous Structure Modeling.” Computer-Aided Design 42 (10): 930–941. doi:10.1016/j.cad.2010.06.006.
   Web of Science ®Google Scholar
• Kou, X. Y., and S. T. Tan. 2012. “Microstructural Modelling of Functionally Graded Materials Using Stochastic Voronoi Diagram and B-Spline Representations.” International Journal of Computer Integrated Manufacturing 25 (2): 177–188. doi:10.1080/0951192X.2011.627948.
   Web of Science ®Google Scholar
• Li, X., Y. H. Zhou, and G. Tong. 2017. “In-Plane Dynamic Impact Characteristics of the Quasi-Honeycomb Structure.” Journal of Xi’an Jiaotong University 51 (3): 80–86+110. doi:10.7652/xjtuxb201703014.
   Google Scholar
• Liang, H., T. Ji, Y. Zhang, Y. Wang, and W. Guo. 2017. “Reconstruction with 3d-Printed Pelvic Endoprostheses after Resection of a Pelvic Tumour.” Bone & Joint Journal 99-B (2): 267–275. doi:10.1302/0301-620X.99B2.BJJ-2016-0654.R1.
   PubMedGoogle Scholar
• Lieu, Q. X., and J. Lee. 2017. “A Multi-Resolution Approach for Multi-Material Topology Optimization Based on Isogeometric Analysis.” Computer Methods in Applied Mechanics and Engineering 323: 272–302. doi:10.1016/j.cma.2017.05.009.
   Web of Science ®Google Scholar
• Lu, L., A. Sharf, H. Zhao, Y. Wei, Q. N. Fan, and C. H. Tu. 2014. “Build-To-Last: Strength to Weight 3D Printed Objects.” ACM Transactions on Graphics 33 (4). Article No. 97 doi:10.1145/2601097.2601168.
   PubMed Web of Science ®Google Scholar
• Manogharan, G., R. A. Wysk, and O. L. A. Harrysson. 2016. “Additive Manufacturing–Integrated Hybrid Manufacturing and Subtractive Processes: Economic Model and Analysis.” International Journal of Computer Integrated Manufacturing 29 (5): 473–488. doi:10.1080/0951192X.2015.1067920.
   Web of Science ®Google Scholar
• Meisel, N., and C. Williams. 2015. “An Investigation of Key Design for Additive Manufacturing Constraints in Multimaterial Three-Dimensional Printing.” Journal of Mechanical Design 137 (11). doi:10.1115/1.4030991.
   PubMed Web of Science ®Google Scholar
• Querin, O. M., G. P. Steven, and Y. M. Xie. 1998. “Evolutionary Structural Optimisation (ESO) Using a Bidirectional Algorithm.” Engineering Computations 15 (8): 1031–1048. doi:10.1108/02644409810244129.
   Web of Science ®Google Scholar
• Rahman, K. M., Z. Hu, and T. Letcher. 2018. “In-Plane Stiffness of Additively Manufactured Hierarchical Honeycomb Metamaterials with Defects.” Journal of Manufacturing Science & Engineering - Transactions of the ASME 140 (1). doi:10.1115/1.4038205.
   PubMed Web of Science ®Google Scholar
• Rozvany, G. I. 2009. “A Critical Review of Established Methods of Structural Topology Optimization.” Structural and Multidisciplinary Optimization 37 (3): 217–237. doi:10.1007/s00158-007-0217-0.
   Web of Science ®Google Scholar
• Shi, X. F., P. Xi, Y. W. Song, R. Li, and X. J. Shi. 2016. “Stress Concentration Analysis of Honeycomb with Missing Cell Walls.” Journal of Beijing University of Aeronautics and Astronautics 42 (12): 2662–2668. doi:10.13700/j.bh.1001-5965.2015.0819.
   Google Scholar
• Shuang, F., W. Hu, Y. Shao, H. Li, and H. Zou. 2016. “Treatment of Intercondylar Humeral Fractures with 3d-Printed Osteosynthesis Plates.” Medicine 95 (3). doi:10.1097/md.0000000000002461.
   Web of Science ®Google Scholar
• Song, Y. W., C. H. Yang, X. F. Shi, and P. Xi. 2015. “Parameterized Finite Element Model of Hexagon Honeycombs.” Journal of Computer-Aided Design & Computer Graphics 27 (1): 175–183. doi:10.3969/j.issn.1003-9775.2015.01.022.
   Google Scholar
• Taheri, A. H., and K. Suresh. 2017. “An Isogeometric Approach to Topology Optimization of Multi-Material and Functionally Graded Structures.” International Journal for Numerical Methods in Engineering 109 (5): 668–696. doi:10.1002/nme.5303.
   Web of Science ®Google Scholar
• Tang, Y., A. Kurtz, and Y. F. Zhao. 2015. “Bidirectional Evolutionary Structural Optimization (BESO) Based Design Method for Lattice Structure to Be Fabricated by Additive Manufacturing.” Computer-Aided Design 69 (C): 91–101. doi:10.1016/j.cad.2015.06.001.
   Google Scholar
• Tang, Y., and Y. F. Zhao. 2016. “A Survey of the Design Methods for Additive Manufacturing to Improve Functional Performance.” Rapid Prototyping Journal 22 (3): 569–590. doi:10.1108/RPJ-01-2015-0011.
   Web of Science ®Google Scholar
• Tarsitano, A., S. Battaglia, L. Ciocca, R. Scotti, R. Cipriani, and C. Marchetti. 2016. “Surgical Reconstruction of Maxillary Defects Using a Computer-Assisted Design/Computer-Assisted Manufacturing-Produced Titanium Mesh Supporting a Free Flap.” Journal of Cranio-Maxillofacial Surgery 44 (9): 1320–1326. doi:10.1016/j.jcms.2016.07.013.
   PubMed Web of Science ®Google Scholar
• Taylor, C. M., C. W. Smith, W. Miller, and K. E. Evants. 2011. “The Effects of Hierarchy on the In-Plane Elastic Properties of Honeycombs.” International Journal of Solids and Structures 48 (9): 1330–1339. doi:10.1016/j.ijsolstr.2011.01.017.
   Web of Science ®Google Scholar
• Vogiatzis, P. S., C. X. Wang, T. Li, and L. Wang. 2017. “Topology Optimization of Multi-Material Negative Poisson’s Ratio Metamaterials Using a Reconciled Level Set Method.” Computer-Aided Design 83: 15–32. doi:10.1016/j.cad.2016.09.009.
   Web of Science ®Google Scholar
• Wahl, L., S. Maas, D. Waldmann, A. Zürbes, and P. Frères. 2012. “Shear Stresses in Honeycomb Sandwich Plates: Analytical Solution, Finite Element Method and Experimental Verification.” Journal of Sandwich Structures & Materials 14 (4): 449–468. doi:10.1177/1099636212444655.
   Web of Science ®Google Scholar
• Wang, S. Y., and K. Tai. 2005. “Structural Topology Design Optimization Using Genetic Algorithms with a Bit-Array Representation.” Computer Methods in Applied Mechanics and Engineering 194 (36): 3749–3770. doi:10.1016/j.cma.2004.09.003.
   Web of Science ®Google Scholar
• Wang, Z. W., and Y. Zhu. 2012. “Experimental Investigation and Finite Element Analysis for Impact Compression of Honeycomb Paperboards.” Journal of Mechanical Engineering 48 (12): 49–55. doi:10.3901/JME.2012.12.049.
   Google Scholar
• Xie, Y. M., and G. P. Steven. 1993. “A Simple Evolutionary Procedure for Structural Optimization.” Computers & Structures 49 (5): 885–896. doi:10.1016/0045-7949(93)90035-c.
   Web of Science ®Google Scholar
• Xing, H., S. Jing, H. Zhang, F. L. Zhao, and P. J. Li. 2017. “A Non-Uniform Honeycomb Design Method Based on Topology Optimization Density Mapping.” Journal of Computer-Aided Design & Computer Graphics 29 (4): 734–741. doi:10.3969/j.issn.1003-9775.2017.04.019.
   Google Scholar
• Zuo, W., and K. Saitou. 2017. “Multi-Material Topology Optimization Using Ordered SIMP Interpolation.” Structural and Multidisciplinary Optimization 55 (2): 477–491. doi:10.1007/s00158-016-1513-3.
   Web of Science ®Google Scholar