A review on the topology optimization of the fiber-reinforced composite structures

Zheng Hu

Abstract


According to the requirements of the aerospace industry for high strength, high stiffness, and lightweight structural parts, topology optimization has been proved to be an effective product design method. As one of the most conceptual and prospective structural optimization design methods, topology optimization intends to seek the optimal layout of materials in an allowed design region under a given load and boundary conditions. Thus, the object of study in the article is the method of topological optimization of aircraft structures. The goal of this article is to analyze the existing approaches, algorithms, as well as application of the method of topological optimization in the aerospace field in applied problems. The tasks are to describe the existing various approaches methods, features, and research directions of topological optimization as well as to study the possibility of application in the manufacturing process of composite structures. The following results were obtained. The optimization methods are briefly explained and compared, and the advantages and limitations of each approach are discussed. The various ways of simultaneous optimization of fiber orientation and structural topology were described and analyzed. The features of different methods of continuous fiber orientation optimization method were reviewed. The discrete fiber orientation optimization methods were represented. The possibility of multi-scale concurrent topological optimization was described. The combination of topology optimization and additive manufacturing was considered. Finally, the topology optimization of FRC structures which have been resolved in literature are reviewed and the potential research fields requiring more investigation are pointed out. Conclusions. In the article, a comprehensive review of the topology optimization design of FRC structures was presented. The promising way is to combine topology optimization with additive manufacturing techniques. However, these proposed methods may not suitable for other more complex problems, such as bucking stability and natural frequency. Hence, the topology optimization design of complex FRC components under complicated conditions is the main challenge in the future. This can be a new trend in the topology design of FRC structures.

Keywords


fiber-reinforced composite structure; additive manufacturing; simultaneous optimization; multi-scale optimization; topology optimization

Full Text:

PDF

References


Hossein Ghiasi, D. P., Larry, Lessard. Optimum stacking sequence design of composite materials Part I: Constant stiffness design. Composite Structures, 2009, vol. 90, no. 1, pp. 1-11. DOI: 10.1016/J.COMPSTRUCT.2009.01.006.

Ghiasi, H., Fayazbakhsh, K., Pasini, D., et al. Optimum stacking sequence design of composite materials Part II: Variable stiffness design. Composite Structures, 2010, vol. 93, no. 1, pp. 1-13. DOI: 10.1016/j.compstruct.2010.06.001.

Nikbakt, S., Kamarian, S. and Shakeri, M. A review on optimization of composite structures Part I: Laminated composites. Composite Structures, 2018, vol. 195, pp. 158-185. DOI: 10.1016/j.compstruct.2018.03.063.

Xu, Y., Zhu, J., Wu, Z., et al. A review on the design of laminated composite structures: constant and variable stiffness design and topology optimization. Advanced Composites and Hybrid Materials, 2018, vol. 1, pp. 460-477. DOI: 10.1007/s42114-018-0032-7.

Sigmund, O., Maute, K. Topology optimization approaches. Structural and Multidisciplinary Optimization, 2013, vol. 48, pp. 1031-1055. DOI: 10.1007/s00158-013-0978-6.

Zhu, J.-H., Zhang, W.-H., Xia, L. Topology optimization in aircraft and aerospace structures design. Archives of Computational Methods in Engineering, 2016, vol. 23, pp. 595-622. DOI: 10.1007/s11831-015-9151-2.

Stegmann, J., Lund, E. Nonlinear topology optimization of layered shell structures. Structural and Multidisciplinary Optimization, 2005, vol. 29, pp. 349-360. DOI: 10.1007/s00158-004-0468-y.

Tong, X., Ge, W., Sun, C., et al. Topology optimization of compliant adaptive wing leading edge with composite materials. Chinese Journal of Aeronautics, 2014, vol. 27, no. 6, pp. 1488-1494. DOI: 10.1016/j.cja.2014.10.015.

Tong, X., Ge, W., Zhang, Y., et al. Topology design and analysis of compliant mechanisms with composite laminated plates. Journal of Mechanical Science and Technology, 2019, vol. 33, pp. 613-620. DOI: 10.1007/s12206-019-0115-6.

Dai, Y., Feng, M., Zhao, M. Topology optimization of laminated composite structures with design-dependent loads. Composite Structures, 2017, vol. 167, pp. 251-261. DOI: 10.1016/j.compstruct.2017.01.069.

Hu, Z., Vambol, O. Topological designing and analysis of the composite wing rib. Aerospace technic and technology, 2020, no. 6, pp. 4-14. DOI: 10.32620/aktt.2020.6.01.

Pedersen, P. On optimal orientation of orthotropic materials. Structural optimization, 1989, vol. 1, pp. 101-106. DOI: 10.1007/BF01637666.

Cheng, H., Kikuchi, N., Ma, Z. An improved approach for determining the optimal orientation of orthotropic material. Structural optimization, 1994, vol. 8, pp. 101-112. DOI: 10.1007/BF01743305.

Luo, J., Gea, H. Optimal orientation of orthotropic materials using an energy based method. Structural optimization, 1998, vol. 15, pp. 230-236. DOI: 10.1007/BF01203536.

Fuchs, M., Paley, M., Miroshny, E. The Aboudi micromechanical model for topology design of structures. Computers & structures, 1999, vol. 73, no. 1-5, pp. 355-362. DOI: 10.1016/S0045-7949(98)00260-0.

Ma, Z.-D., Kikuchi, N., Pierre, C., et al. Multidomain topology optimization for structural and material designs. ASME J. Appl. Mech., 2006. vol. 73, pp. 565–573. DOI: 10.1115/1.2164511.

Caivano, R., Tridello, A., Paolino, D., et al. Topology and fibre orientation simultaneous optimisation: A design methodology for fibre-reinforced composite components. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 2020, vol. 234, no. 9, pp. 1267-1279. DOI: 10.1177/1464420720934142.

Papapetrou, V. S., Patel, C., Tamijani, A. Y. Stiffness-based optimization framework for the topology and fiber paths of continuous fiber composites. Composites Part B: Engineering, 2020, vol. 183, no. 4, pp. 107681. DOI: 10.1016/j.compositesb.2019.107681.

Gea, H., Luo, J. On the stress-based and strain-based methods for predicting optimal orientation of orthotropic materials. Structural and Multidisciplinary Optimization, 2004, vol. 26, pp. 229-234. DOI: 10.1007/s00158-003-0348-x.

Yan, X., Xu, Q., Huang, D., et al. Concurrent topology design of structures and materials with optimal material orientation. Composite Structures, 2019, vol. 220, pp. 473-480. DOI: 10.1016/j.compstruct.2019.04.028.

Liu, S., Hou, Y., Sun, X., et al. A two-step optimization scheme for maximum stiffness design of laminated plates based on lamination parameters. Composite Structures, 2012, vol. 94, no. 12, pp. 3529-3537. DOI: 10.1016/j.compstruct.2012.06.014.

Peeters, D., van Baalen, D., Abdallah, M. Combining topology and lamination parameter optimisation. Structural and Multidisciplinary Optimization, 2015, vol. 52, pp. 105-120. DOI: 10.1007/s00158-014-1223-7.

Tong, X., Ge, W., Zhang, Y. Optimal fiber orientations and topology of compliant mechanisms using lamination parameters. 2015 International Conference on Advanced Mechatronic Systems (ICAMechS), IEEE, 2015, pp. 370-374. DOI: 10.1109/ICAMechS.2015.7287091.

Tong, X., Ge, W., Gao, X., et al. Optimization of Combining Fiber Orientation and Topology for Constant-Stiffness Composite Laminated Plates. Journal of Optimization Theory and Applications, 2019, vol. 181, pp. 653-670. DOI: 10.1007/s10957-018-1433-z.

Tong, X., Ge, W., Gao, X., et al. Simultaneous optimization of fiber orientations and topology shape for composites compliant leading edge. Journal of Reinforced Plastics and Composites, 2019, vol. 38, no. 15, pp. 706-716. DOI: 10.1177/0731684419842292.

De Leon, D., De Souza, C., Fonseca, J., et al. Aeroelastic tailoring using fiber orientation and topology optimization. Structural and Multidisciplinary Optimization, 2012, vol. 46, pp. 663-677. DOI: 10.1007/s00158-012-0790-8.

Tong, X., Ge, W., Zhang, Y. Optimal fiber orientation and topology design for compliant mechanisms with fiber-reinforced composites. Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 2017, vol. 231, no. 12, pp. 2302-2312. DOI: 10.1177/0954406216631783

Cheng Changzheng, B. G., Wang, Xuan., Long, Kai., Li, Jingchuang., Wu, Qiaoguo. Fundamental frequency maximization design for continuous fiber-reinforced composite structures. Chinese Journal of Theoretical and Applied Mechanics, 2020, vol. 52, no. 5, pp. 1442-1430. DOI: 10.6052/0459-1879-20-083.

Zowe, J., Kočvara, M., Bendsøe, M. P. Free material optimization via mathematical programming. Mathematical programming, 1997, vol. 79, pp. 445-466. DOI: 10.1007/BF02614328.

Henrichsen, S. R., Lindgaard, E., Lund, E. Free material stiffness design of laminated composite structures using commercial finite element analysis codes. Structural and Multidisciplinary Optimization, 2015, vol. 51, pp. 1097-1111. DOI: 10.1007/s00158-014-1199-3.

Nomura, T., Dede, E. M., Lee, J., et al. General topology optimization method with continuous and discrete orientation design using isoparametric projection. International Journal for Numerical Methods in Engineering, 2015, vol. 101, no. 8, pp. 571-605. DOI: 10.1002/nme.4799.

Lee, J., Kim, D., Nomura, T., et al. Topology optimization for continuous and discrete orientation design of functionally graded fiber-reinforced composite structures. Composite Structures, 2018, vol. 201, no. 1, pp. 217-233. DOI: 10.1016/j.compstruct.2018.06.020.

Ranaivomiarana, N., Irisarri, F.-X., Bettebghor, D., et al. Concurrent optimization of material spatial distribution and material anisotropy repartition for two-dimensional structures. Continuum Mechanics and Thermodynamics, 2019, vol. 31, pp. 133-146. DOI: 10.1007/s00161-018-0661-7.

Zhou, Y., Nomura, T., Saitou, K. Multi-component topology and material orientation design of composite structures (MTO-C). Computer Methods in Applied Mechanics and Engineering, 2018, vol. 342, pp. 438-457. DOI: 10.1016/j.cma.2018.07.039.

Zhou Y., Nomura T. and Saitou K. Anisotropic multicomponent topology optimization for additive manufacturing with build orientation design and stress-constrained interfaces. Journal of Computing and Information Science in Engineering, 2021, vol. 21, no. 1, pp. 011007. DOI: 10.1115/1.4047487.

Nomura, T., Kawamoto, A., Kondoh, T., et al. Inverse design of structure and fiber orientation by means of topology optimization with tensor field variables. Composites Part B: Engineering, 2019, vol. 176, pp. 107187. DOI: 10.1016/j.compositesb.2019.107187.

Smith, H., Norato, J. A. Topology optimization with discrete geometric components made of composite materials. Computer Methods in Applied Mechanics and Engineering, 2021, vol. 376, pp. 113582. DOI: 10.1016/j.cma.2020.113582.

Luo, Y., Chen, W., Liu, S., et al. A discrete-continuous parameterization (DCP) for concurrent optimization of structural topologies and continuous material orientations. Composite Structures, 2020, vol. 236, pp. 111900 DOI: 10.1016/j.compstruct.2020.111900.

Setoodeh, S., Abdalla, M. M., Gürdal, Z. Combined topology and fiber path design of composite layers using cellular automata. Structural and Multidisciplinary Optimization, 2005, vol. 30, pp. 413-421. DOI: 10.1007/s00158-005-0528-y.

Li, H., Gao, L., Li, H., et al. Full-scale topology optimization for fiber-reinforced structures with continuous fiber paths. Computer Methods in Applied Mechanics and Engineering, 2021, vol. 377, pp. 113668. DOI: 10.1016/j.cma.2021.113668.

Lund, E., Stegmann, J. On structural optimization of composite shell structures using a discrete constitutive parametrization. Wind Energy: An International Journal for Progress and Applications in Wind Power Conversion Technology, 2005, vol. 8, no. 1, pp. 109-124. DOI: 10.1002/we.132.

Niu, B., Olhoff, N., Lund, E., et al. Discrete material optimization of vibrating laminated composite plates for minimum sound radiation. International Journal of Solids and Structures, 2010, vol. 47, no. 16, pp. 2097-2114. DOI: 10.1016/j.ijsolstr.2010.04.008.

Hvejsel, C. F., Lund, E. Material interpolation schemes for unified topology and multi-material optimization. Structural and Multidisciplinary Optimization, 2011, vol. 43, pp. 811-825. DOI: 10.1007/s00158-011-0625-z.

Lund, E., Kuhlmeier, L., Stegmann, J. Buckling optimization of laminated hybrid composite shell structures using discrete material optimization, 6th World Congress on Structural and Multidisciplinary Optimization, Rio de Janeiro, Citeseer, 2005. Corpus ID: 15398461.

Lund, E., Stegmann, J. Eigenfrequency and buckling optimization of laminated composite shell structures using discrete material optimization. IUTAM symposium on topological design optimization of structures, machines and materials, Springer, 2006, vol. 137, pp. 147-156. DOI: 10.1007/1-4020-4752-5_15

Sørensen, S. N., Lund, E. Topology and thickness optimization of laminated composites including manufacturing constraints. Structural and Multidisciplinary Optimization, 2013, vol. 48, pp. 249-265. DOI: 10.1007/s00158-013-0904-y.

Bruyneel, M. SFP–a new parameterization based on shape functions for optimal material selection: application to conventional composite plies. Structural and Multidisciplinary Optimization, 2011, vol. 43, pp. 17-27. DOI: 10.1007/s00158-010-0548-0.

Gao, T., Zhang, W., Duysinx, P. A bi-value coding parameterization scheme for the discrete optimal orientation design of the composite laminate. International Journal for Numerical Methods in Engineering, 2012, vol. 91, no. 1, pp. 98-114. DOI: 10.1002/nme.4270.

Gao, T., Zhang, W. H., Duysinx, P. Simultaneous design of structural layout and discrete fiber orientation using bi-value coding parameterization and volume constraint. Structural and Multidisciplinary Optimization, 2013, vol. 48, pp. 1075-1088. DOI: 10.1007/s00158-013-0948-z.

Duan, Z., Yan, J., Zhao, G. Integrated optimization of the material and structure of composites based on the Heaviside penalization of discrete material model. Structural and Multidisciplinary Optimization, 2015, vol. 51, pp. 721-732. DOI: 10.1007/s00158-014-1168-x

Luo, C., Guest, J. K. Optimizing topology and fiber orientations with minimum length scale control in laminated composites. ASME 2019 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, August 18-21, 2019, Anaheim, California, USA, pp. 1-10. DOI: 10.1115/DETC2019-98386.

Sohouli, A., Yildiz, M., Suleman, A. Design optimization of thin-walled composite structures based on material and fiber orientation. Composite Structures, 2017, vol. 176, pp. 1081-1095. DOI: 10.1016/j.compstruct.2017.06.030.

Hansel, W., Becker, W. Layerwise adaptive topology optimization of laminate structures. Engineering computations, 1999, vol. 16, no. 7, pp. 841-851. DOI: 10.1108/02644409910298156.

Hansel, W., Treptow, A., Becker, W., et al. A heuristic and a genetic topology optimization algorithm for weight-minimal laminate structures. Composite Structures, 2002, vol. 58, no. 2, pp. 287-294. DOI: 10.1016/S0263-8223(02)00048-X.

Hu, Z., Vambol, O., Sun, S. A hybrid multilevel method for simultaneous optimization design of topology and discrete fiber orientation. Composite Structures, 2021, vol. 266, pp. 113791. DOI: 10.1016/j.compstruct.2021.113791.

Gao, X., Ma, H. A modified model for concurrent topology optimization of structures and materials. Acta Mechanica Sinica, 2015, vol. 31, pp. 890-898. DOI: 10.1007/s10409-015-0502-x.

Coelho, P., Guedes, J., Rodrigues, H. Multiscale topology optimization of bi-material laminated composite structures. Composite Structures, 2015, vol. 132, pp. 495-505. DOI: 10.1016/j.compstruct.2015.05.059.

Yan, X., Xu, Q., Hua, H., et al. Concurrent optimization of macrostructures and material microstructures and orientations for maximizing natural frequency. Engineering Structures, 2020, vol. 209, pp. 109997. DOI: 10.1016/j.engstruct.2019.109997.

Kim, D., Lee, J., Nomura, T., et al. Topology optimization of functionally graded anisotropic composite structures using homogenization design method. Computer Methods in Applied Mechanics and Engineering, 2020, vol. 369, pp. 113220. DOI: 10.1016/j.cma.2020.113220.

Parandoush, P., Lin, D. A review on additive manufacturing of polymer-fiber composites. Composite Structures, 2017, vol. 182, pp. 36-53. DOI: 10.1016/j.compstruct.2017.08.088.

Liu, J., Yu, H. Concurrent deposition path planning and structural topology optimization for additive manufacturing. Rapid Prototyping Journal, 2017, vol. 23, no. 5, pp. 930-942. DOI: 10.1108/RPJ-05-2016-0087.

Wang, T., Li, N., Link, G., et al. Load-dependent path planning method for 3D printing of continuous fiber reinforced plastics. Composites Part A: Applied Science and Manufacturing, 2021, vol. 140, pp. 106181. DOI: 10.1016/j.compositesa.2020.106181.

Li, N., Link, G., Wang, T., et al. Path-designed 3D printing for topological optimized continuous carbon fibre reinforced composite structures. Composites Part B: Engineering, 2020, vol. 182, pp. 107612. DOI: 10.1016/j.compositesb.2019.107612.

Jiang, D., Hoglund, R., Smith, D. E. Continuous fiber angle topology optimization for polymer composite deposition additive manufacturing applications. Fibers, 2019, vol. 7, no. 2, pp. 14. DOI: 10.3390/fib7020014.

Chandrasekhar, A., Kumar, T., Suresh, K. Build optimization of fiber-reinforced additively manufactured components. Structural and Multidisciplinary Optimization, 2020, vol. 61, pp. 77-90. DOI: 10.1007/s00158-019-02346-z.

Chen, Y., Ye, L. Topological design for 3D-printing of carbon fibre reinforced composite structural parts. Composites Science and Technology, 2021, vol. 204, pp. 108644. DOI: 10.1016/j.compscitech.2020.108644




DOI: https://doi.org/10.32620/aktt.2021.3.07