The concurrent optimization of topology and fibre orientation is a promising approach to pursue higher strength and lighter weight of variable-stiffness structures. This paper suggests a novel discrete-continuous scheme for the concurrent optimization. Considering the global convergence, Discrete Material Optimization is first utilized to select a dominant angle for each element from several predefined candidate angles. However, some regions with multiaxial stress make it difficult to select the definite angles for the elements. Therefore, the Sequential Binary-Phase Topology Optimization is suggested to guarantee the uniqueness of the element to candidate angle mapping. Moreover, to obtain better mechanical properties, Continuous Fibre Angle Optimization with a spatial filter is introduced to optimize fibre continuity. Several classic numerical examples are used to verify the excellent performance of the suggested method in terms of fibre angle convergence and show robustness regarding sensitivity to the initial setting.
AcanforaVSellittoARussoA, et al.Experimental investigation on 3D printed lightweight sandwich structures for energy absorption aerospace applications. Aero Sci Technol2023; 137: 108276.
2.
HanHSorokinVTangL, et al.Lightweight origami isolators with deployable mechanism and quasi-zero-stiffness property. Aero Sci Technol2022; 121: 107319.
3.
CrupiVEpastoGGuglielminoE. Comparison of aluminium sandwiches for lightweight ship structures: honeycomb vs. foam. Mar Struct2013; 30: 74–96.
4.
AsnafiNLangstedtGAnderssonC-H, et al.A new lightweight metal-composite-metal panel for applications in the automotive and other industries. Thin-Walled Struct2000; 36: 289–310.
5.
DuanZYanJZhaoG. Integrated optimization of the material and structure of composites based on the Heaviside penalization of discrete material model. Struct Multidiscip Optim2015; 51: 721–732.
6.
WuCGaoYFangJ, et al.Discrete topology optimization of ply orientation for a carbon fiber reinforced plastic (CFRP) laminate vehicle door. Mater Des2017; 128: 9–19.
7.
HaoPLiuXWangY, et al.Collaborative design of fiber path and shape for complex composite shells based on isogeometric analysis. Comput Methods Appl Mech Eng2019; 354: 181–212.
8.
NikbaktSKamarianSShakeriM. A review on optimization of composite structures Part I: laminated composites. Compos Struct2018; 195: 158–185.
9.
LozanoGGTiwariATurnerC, et al.A review on design for manufacture of variable stiffness composite laminates. Proc IME B J Eng Manufact2016; 230: 981–992.
10.
DirkH-JLWardCPotterKD. The engineering aspects of automated prepreg layup: history, present and future. Compos B Eng2012; 43: 997–1009.
11.
YassinKHojjatiM. Processing of thermoplastic matrix composites through automated fiber placement and tape laying methods: a review. J Thermoplast Compos Mater2018; 31: 1676–1725.
12.
van de WerkenNHurleyJKhanboloukiP, et al.Design considerations and modeling of fiber reinforced 3D printed parts. Compos B Eng2019; 160: 684–692.
13.
DemirEYousefi-LouyehPYildizM. Design of variable stiffness composite structures using lamination parameters with fiber steering constraint. Compos B Eng2019; 165: 733–746.
BendsoeMPSigmundO. Topology optimization: theory, methods, and applications. Cham, Switzerland: Springer Science & Business Media, 2013.
16.
WuKC. Design and analysis of tow-steered composite shells using fiber placement. In: American society for composites 23rd annual technical conference, Memphis, Tennessee, 9-11 September 2008.
17.
PedersenNL. On design of fiber-nets and orientation for eigenfrequency optimization of plates. Comput Mech2006; 39: 1–13.
PapapetrouVSPatelCTamijaniAY. Stiffness-based optimization framework for the topology and fiber paths of continuous fiber composites. Compos B Eng2020; 183: 107681.
20.
BalamuruganRRamakrishnanCSinghN. Performance evaluation of a two stage adaptive genetic algorithm (TSAGA) in structural topology optimization. Appl Soft Comput2008; 8: 1607–1624.
21.
MadeiraJFAPinaHRodriguesH. GA topology optimization using random keys for tree encoding of structures. Struct Multidiscip Optim2010; 40: 227–240.
22.
LuhG-CChuehC-H. Multi-modal topological optimization of structure using immune algorithm. Comput Methods Appl Mech Eng2004; 193: 4035–4055.
23.
KavehAHassaniBShojaeeS, et al.Structural topology optimization using ant colony methodology. Eng Struct2008; 30: 2559–2565.
24.
LuhG-CLinC-YLinY-S. A binary particle swarm optimization for continuum structural topology optimization. Appl Soft Comput2011; 11: 2833–2844.
25.
KellerD. Optimization of ply angles in laminated composite structures by a hybrid, asynchronous, parallel evolutionary algorithm. Compos Struct2010; 92: 2781–2790.
26.
SigmundO. On the usefulness of non-gradient approaches in topology optimization. Struct Multidiscip Optim2011; 43: 589–596.
27.
WuC-YTsengK-Y. Topology optimization of structures using modified binary differential evolution. Struct Multidiscip Optim2010; 42: 939–953.
28.
SoaresCMSoaresCMMateusH. A model for the optimum design of thin laminated plate-shell structures for static, dynamic and buckling behaviour. Compos Struct1995; 32: 69–79.
29.
BruyneelMFleuryC. Composite structures optimization using sequential convex programming. Adv Eng Software2002; 33: 697–711.
30.
SvanbergK. The method of moving asymptotes—a new method for structural optimization. Int J Numer Methods Eng1987; 24: 359–373.
31.
PedersenP. On optimal orientation of orthotropic materials. Struct Optim1989; 1: 101–106.
32.
StegmannJLundE. Discrete material optimization of general composite shell structures. Int J Numer Methods Eng2005; 62: 2009–2027.
33.
BruyneelM. SFP—a new parameterization based on shape functions for optimal material selection: application to conventional composite plies. Struct Multidiscip Optim2011; 43: 17–27.
34.
YinLAnanthasureshG. Topology optimization of compliant mechanisms with multiple materials using a peak function material interpolation scheme. Struct Multidiscip Optim2001; 23: 49–62.
35.
GaoTZhangWDuysinxP. A bi‐value coding parameterization scheme for the discrete optimal orientation design of the composite laminate. Int J Numer Methods Eng2012; 91: 98–114.
36.
KiyonoCYSilvaECNReddyJ. A novel fiber optimization method based on normal distribution function with continuously varying fiber path. Compos Struct2017; 160: 503–515.
37.
LuoYChenWLiuS, et al.A discrete-continuous parameterization (DCP) for concurrent optimization of structural topologies and continuous material orientations. Compos Struct2020; 236: 111900.
38.
DingHXuB. A novel discrete–continuous material orientation optimization model for stiffness-based concurrent design of fiber composite. Compos Struct2021; 273: 114288.
39.
WalkerMSmithRE. A technique for the multiobjective optimisation of laminated composite structures using genetic algorithms and finite element analysis. Compos Struct2003; 62: 123–128.
40.
AndreassenEClausenASchevenelsM, et al.Efficient topology optimization in MATLAB using 88 lines of code. Struct Multidiscip Optim2011; 43: 1–16.
41.
LeeJKimDNomuraT, et al.Topology optimization for continuous and discrete orientation design of functionally graded fiber-reinforced composite structures. Compos Struct2018; 201: 217–233.
