A generalized discrete fiber angle optimization method for composite structures: bipartite interpolation optimization. (English) Zbl 1537.74301
Summary: This paper proposes a novel fiber angle optimization method for composite, termed bipartite interpolation optimization (BIO), to address high-dimensional design variables and inefficient fiber orientation optimization. The weighting functions of BIO are constructed with the help of multiphase material topology optimization approach. Various permutations and combinations of \(n\) design variables are utilized to represent \(2^n\) discrete candidate angles. Since the weighting functions of the way automatically satisfy the sum constraint, it is unnecessary to address the sum constraints during the optimization process. Compared with the traditional discrete material optimization strategy and solid isotropic material with penalization scheme, the BIO method reduces the dimension of the mathematical model for optimizing fiber angles. Compared to the shape functions with penalization scheme, the BIO method can be extended to the optimization problem of \(2^n\) candidates. Numerical examples of different types demonstrate that the proposed method has higher solution efficiency in the optimization problem of fiber orientation selection and is suitable for three-dimensional shell optimization problems. It provides a new technical means for the structural optimization design of composite laminates.
© 2022 John Wiley & Sons Ltd.
© 2022 John Wiley & Sons Ltd.
MSC:
| 74P10 | Optimization of other properties in solid mechanics |
| 74P15 | Topological methods for optimization problems in solid mechanics |
| 74E30 | Composite and mixture properties |
| 74S99 | Numerical and other methods in solid mechanics |
| 74K20 | Plates |
Keywords:
discrete material optimization; fiber orientation; weighting function; multiphase material topology optimization; plate bendingReferences:
| [1] | HuJ, ZhangL, LinQ, ChengM, ZhouQ, LiuH. A conservative multi‐fidelity surrogate model‐based robust optimization method for simulation‐based optimization. Struct Multidiscipl Optim. 2021;64(4):2525‐2551. |
| [2] | LiM, WangZ. Heterogeneous uncertainty quantification using Bayesian inference for simulation‐based design optimization. Struct Saf. 2020;85:101954. |
| [3] | LiM, WangZ. Surrogate model uncertainty quantification for reliability‐based design optimization. Reliab Eng Syst Saf. 2019;192:106432. |
| [4] | ZhangL, GuoL, RongQ. Single parameter sensitivity analysis of ply parameters on structural performance of wind turbine blade. Energy Eng. 2020;117(4):195‐207. |
| [5] | WangX, MengZ, YangB, ChengC, LongK, LiJ. Reliability‐based design optimization of material orientation and structural topology of fiber‐reinforced composite structures under load uncertainty. Compos Struct. 2022;291:115537. |
| [6] | BendsøeMP. Optimal shape design as a material distribution problem. Struct Optim. 1989;1(4):193‐202. |
| [7] | BendsøeMP, SigmundO. Material interpolation schemes in topology optimization. Arch Appl Mech (Ingenieur Archiv). 1999;69(9-10):635‐654. · Zbl 0957.74037 |
| [8] | EschenauerHA, OlhoffN. Topology optimization of continuum structures: a review*. Appl Mech Rev. 2001;54(4):331‐390. |
| [9] | StolpeM, SvanbergK. An alternative interpolation scheme for minimum compliance topology optimization. Struct Multidiscipl Optim. 2001;22(2):116‐124. |
| [10] | ZhouM, RozvanyGIN. The COC algorithm, part II: topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng. 1991;89(1-3):309‐336. |
| [11] | LundE, StegmannJ. On structural optimization of composite shell structures using a discrete constitutive parametrization. Wind Energy. 2005;8(1):109‐124. |
| [12] | StegmannJ, LundE. Discrete material optimization of general composite shell structures. Int J Numer Methods Eng. 2005;62(14):2009‐2027. · Zbl 1118.74343 |
| [13] | SørensenR, LundE. Thickness filters for gradient based multi‐material and thickness optimization of laminated composite structures. Struct Multidiscipl Optim. 2015;52(2):227‐250. |
| [14] | SørensenSN, LundE. Topology and thickness optimization of laminated composites including manufacturing constraints. Struct Multidiscipl Optim. 2013;48(2):249‐265. |
| [15] | SørensenSN, SørensenR, LundE. DMTO - a method for discrete material and thickness optimization of laminated composite structures. Struct Multidiscipl Optim. 2014;50(1):25‐47. |
| [16] | SørensenSN, StolpeM. Global blending optimization of laminated composites with discrete material candidate selection and thickness variation. Struct Multidiscipl Optim. 2015;52(1):137‐155. |
| [17] | YanJ, DuanZ, LundE, WangJ. Concurrent multi‐scale design optimization of composite frames with manufacturing constraints. Struct Multidiscipl Optim. 2017;56(3):519‐533. |
| [18] | LuoY, ChenW, LiuS, LiQ, MaY. A discrete‐continuous parameterization (DCP) for concurrent optimization of structural topologies and continuous material orientations. Compos Struct. 2020;236:111900. |
| [19] | TianY, PuS, ZongZ, ShiT, XiaQ. Optimization of variable stiffness laminates with gap‐overlap and curvature constraints. Compos Struct. 2019;230:111494. |
| [20] | TianY, ShiT, XiaQ. A parametric level set method for the optimization of composite structures with curvilinear fibers. Comput Methods Appl Mech Eng. 2022;388:114236. · Zbl 1507.74278 |
| [21] | SigmundO, PeterssonJ. Numerical instabilities in topology optimization: a survey on procedures dealing with checkerboards, mesh‐dependencies and local minima. Struct Optim. 1998;16(1):68‐75. |
| [22] | HvejselCF, LundE. Material interpolation schemes for unified topology and multi‐material optimization. Struct Multidiscipl Optim. 2011;43(6):811‐825. · Zbl 1274.74344 |
| [23] | DuanZ, YanJ, ZhaoG. Integrated optimization of the material and structure of composites based on the Heaviside penalization of discrete material model. Struct Multidiscipl Optim. 2014;51(3):721‐732. |
| [24] | SohouliA, YildizM, SulemanA. Design optimization of thin‐walled composite structures based on material and fiber orientation. Compos Struct. 2017;176:1081‐1095. |
| [25] | SohouliA, YildizM, SulemanA. Efficient strategies for reliability‐based design optimization of variable stiffness composite structures. Struct Multidiscipl Optim. 2017;57(2):689‐704. |
| [26] | BruyneelM. SFP—A new parameterization based on shape functions for optimal material selection: application to conventional composite plies. Struct Multidiscipl Optim. 2010;43(1):17‐27. |
| [27] | BruyneelM, DuysinxP, FleuryC, GaoT. Extensions of the shape functions with penalization parameterization for composite‐ply optimization. AIAA J. 2011;49(10):2325‐2329. |
| [28] | GaoT, ZhangW, DuysinxP. A bi‐value coding parameterization scheme for the discrete optimal orientation design of the composite laminate. Int J Numer Methods Eng. 2012;91(1):98‐114. · Zbl 1246.74043 |
| [29] | ZhangY, HouY, LiuS. A new method of discrete optimization for cross‐section selection of truss structures. Eng Optim. 2014;46(8):1052‐1073. |
| [30] | KiyonoCY, SilvaECN, ReddyJN. A novel fiber optimization method based on normal distribution function with continuously varying fiber path. Compos Struct. 2017;160:503‐515. |
| [31] | SigmundO, TorquatoS. Design of materials with extreme thermal expansion using a three‐phase topology optimization method. J Mech Phys Solids. 1997;45:1037‐1067. |
| [32] | GhiasiH, FayazbakhshK, PasiniD, LessardL. Optimum stacking sequence design of composite materials part II: variable stiffness design. Compos Struct. 2010;93(1):1‐13. |
| [33] | YanJ, SunP, ZhangL, HuW, LongK. SGC—a novel optimization method for the discrete fiber orientation of composites. Struct Multidiscipl Optim. 2022;65(4):124. https://doi.org/10.1007/s00158‐022‐03230‐z · doi:10.1007/s00158‐022‐03230‐z |
| [34] | LongK, GuC, WangX, et al. A novel minimum weight formulation of topology optimization implemented with reanalysis approach. Int J Numer Methods Eng. 2019;120(5):567‐579. · Zbl 07859711 |
| [35] | NocedalJ, WrightST. Numerical Optimization. Springer‐Verlag; 2000. |
| [36] | LongK, WangX, GuX. Local optimum in multi‐material topology optimization and solution by reciprocal variables. Struct Multidiscipl Optim. 2018;57:1283‐1295. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
