This study proposed a discrete structural optimization method for a framed automotive body. Up to four types of discrete design variables are considered simultaneously, that is, the sizing, cross-sectional shape, topology, and material variables. Firstly, to solve the nonconvex and nonlinear optimization problem, the original non-dominated sorting genetic algorithm, the third version (NSGA-III), is adapted. An improved extreme points identification scheme and a new mutation operator are proposed to stabilize the normalization of the population and accommodate the manufacturing constraints, respectively. Two test problems demonstrate that the modified NSGA-III can handle continuous and discontinuous multiple objective optimization. Subsequently, the classical 10-bar truss is used to illustrate the proposed method. A weight reduction of 4.5 kg is achieved as compared to previous optimal designs in the literature. Finally, a framed automotive body is optimized for maximizing the first order natural frequency and minimizing the total mass, the maximum stresses and the maximum displacements in different load cases and the manufacturing cost. The results obtained by different optimization procedures are presented and discussed. The results demonstrate the feasibility and effectiveness of the proposed method. A weight reduction of 17.59% is achieved while other structural performances satisfy the design requirements.
MaCGaoYLiuZ, et al. Optimization of multi-material and beam cross-sectional shape and dimension of skeleton-type body. J Jilin Univ2021; 51(5): 1583–1592.
2.
MihaylovaPBaldanziniNPieriniM.Potential error factors in 1D beam FE modeling for the early stage vehicle design. Finite Elem Anal Des2013; 74(15): 53–66.
3.
DondersSTakahashiYHadjitR, et al. A reduced beam and joint concept modeling approach to optimize global vehicle body dynamics. Finite Elem Anal Des2009; 45(6-7): 439–455.
4.
DegertekinSOLambertiLUgurIB.Discrete sizing/layout/topology optimization of truss structures with an advanced Jaya algorithm. Appl Soft Comput2019; 79(6): 363–390.
5.
ChengMYPrayogoDWuYW, et al. A hybrid harmony search algorithm for discrete sizing optimization of truss structure. Autom Constr2016; 69(9): 21–33.
6.
KocieckiMAdeliH.Two-phase genetic algorithm for topology optimization of free-form steel space-frame roof structures with complex curvatures. Eng. Appl. Artif. Intell2014; 32(6): 218–227.
7.
LieuQXDoDTTLeeJ.An adaptive hybrid evolutionary firefly algorithm for shape and size optimization of truss structures with frequency constraints. Comput Struct2018; 195(1): 99–112.
8.
MiguelLFFLopezRHMiguelLFF.Multimodal size, shape, and topology optimisation of truss structures using the firefly algorithm. Adv Eng Softw2013; 56: 23–37.
9.
TejaniGGSavsaniVJPatelVK, et al. Size, shape, and topology optimization of planar and space trusses using mutation-based improved metaheuristics. J Comput Des Eng2018; 5(2): 198–214.
10.
ZhouMRozvanyGI.The COC algorithm, part II: topological, geometrical and generalized shape optimization. Comput Methods Appl Mech Eng1991; 89(1–3): 309–336.
11.
MamKDoutheCLe RoyR, et al. Shape optimization of braced frames for tall timber buildings: influence of semi-rigid connections on design and optimization process. Eng Struct2020; 216: 110692.
12.
QinHGuoYLiuZ, et al. Shape optimization of automotive body frame using an improved genetic algorithm optimizer. Adv Eng Softw2018; 121(7): 235–249.
13.
ZhangXSPaulinoGHRamosAS.Multi-material topology optimization with multiple volume constraints: a general approach applied to ground structures with material nonlinearity. Struct Multidiscipl Optim2018; 57(1): 161–182.
14.
SandersEDRamosASPaulinoGH.A maximum filter for the ground structure method: an optimization tool to harness multiple structural designs. Eng Struct2017; 151(11): 235–252.
15.
DehghaniMMashayekhiMSharifiM.An efficient imperialist competitive algorithm with likelihood assimilation for topology, shape and sizing optimization of truss structures. Appl Math Model2021; 93(2): 1–27.
16.
DedeTAyvazY.Combined size and shape optimization of structures with a new meta-heuristic algorithm. Appl Soft Comput2015; 28: 250–258.
17.
VillarJRVidalPFernándezMS, et al. Genetic algorithm optimisation of heavy timber trusses with dowel joints according to Eurocode 5. Biosyst Eng2016; 144(4): 115–132.
18.
PengLLiuLLongT, et al. An efficient truss structure optimization framework based on CAD/CAE integration and sequential radial basis function metamodel. Struct Multidiscipl Optim2014; 50(2): 329–346.
19.
Ho-HuuVDuong-GiaDVo-DuyT, et al. An efficient combination of multi-objective evolutionary optimization and reliability analysis for reliability-based design optimization of truss structures. Expert Syst Appl2018; 102(7): 262–272.
20.
RichardsonJNFilomeno CoelhoRAdriaenssensS.Robust topology optimization of truss structures with random loading and material properties: aa multiobjective perspective. Comput. Struct2015; 154(7): 41–47.
21.
ZhengtongHZhengqiGXiaokuiM, et al. Multimaterial layout optimization of truss structures via an improved particle swarm optimization algorithm. Comput Struct2019; 222(10): 10–24.
22.
SouzaRRDFadel MiguelLFLopezRH, et al. A procedure for the size, shape and topology optimization of transmission line tower structures. Eng Struct2016; 111(3): 162–184.
SunGTanDLvX, et al. Multi-objective topology optimization of a vehicle door using multiple material tailor-welded blank (TWB) technology. Adv Eng Softw2018; 124(10): 1–9.
25.
FredricsonH.Topology optimization of frame structures—joint penalty and material selection. Struct Multidiscipl Optim2005; 30(3): 193–200.
26.
MoriniAARibeiroMJHotzaD.Early-stage materials selection based on embodied energy and carbon footprint. Mater Des2019; 178: 107861.
27.
SunGGuoXLiS, et al. Comparative study on aluminum/GFRP/CFRP tubes for oblique lateral crushing. Thin-Walled Struct2020; 152: 106420.
28.
SakundariniNTahaZAbdul-RashidSH, et al. Optimal multi-material selection for lightweight design of automotive body assembly incorporating recyclability. Mater Des2013; 50(9): 846–857.
29.
CuiXZhangHWangS, et al. Design of lightweight multi-material automotive bodies using new material performance indices of thin-walled beams for the material selection with crashworthiness consideration. Mater Des2011; 32(2): 815–821.
30.
DebKJainH.An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans Evol Comput2014; 18(4): 577–601.
31.
GaoYMaCLiuZ, et al. Discrete topology optimization of body-in-white welding production platform based on NSGA-III. J Shanghai Jiaotong Univ2020; 54(12): 1324–1334.
32.
ZitzlerEThieleLLaumannsM, et al. Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans Evol Comput2003; 7(2): 117–132.
33.
DebKGulatiS.Design of truss-structures for minimum weight using genetic algorithms. Finite Elem. Anal. Des2001; 37(5): 447–465.
34.
HajelaPLeeE.Genetic algorithms in truss topological optimization. Int J Solids Struct1995; 32(22): 3341–3357.
