Journal of Jilin University(Engineering and Technology Edition) ›› 2021, Vol. 51 ›› Issue (5): 1583-1592.doi: 10.13229/j.cnki.jdxbgxb20200506

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Optimization of multi⁃material and beam cross⁃sectional shape and dimension of skeleton⁃type body

Chao MA1(),Yun-kai GAO1(),Zhe LIU1,Yue-xing DUAN1,Lin-li TIAN2,3   

  1. 1.School of Automotive Studies，Tongji University，Shanghai 201804，China
    2.Hubei Key Laboratory of Advanced Technology for Automotive Components，Wuhan University of Technology，Wuhan 430070，China
    3.Hubei Collaborative Innovation Center for Automotive Components Technology，Wuhan University of Technology，Wuhan 430070，China
  • Received:2020-07-06 Online:2021-09-01 Published:2021-09-16
  • Contact: Yun-kai GAO E-mail:machaomit@163.com;gaoyunkai@tongji.edu.cn

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Abstract:

The study proposes a structural optimization method that takes the material types， cross-sectional shapes and dimensions of beams as discrete design variables for skeleton-type body. A skeleton-type body of a conceptual vehicle was studied. A multi-objective optimization problem was formulated. The total mass， manufacturing cost， the displacements of specified nodes and the maximum axial stresses under multiple load cases were minimized while the first order natural frequency was maximized. An improved non-dominated sorting genetic algorithm， third version， was used to tackle this multi-objective optimization problem. Desirable designs were chosen according to factors of lightweight， cost and performances of the vehicle. The result demonstrates that the proposed method involving multiple types of design variables leads to a better lightweight design as compared to the sizing optimization method.

Key words: vehicle engineering, multi-material, cross-sectional shape and dimension, discrete optimization, lightweight, skeleton-type body

CLC Number: 

  • U463

Fig.1

Schematic of simple frame"

Table 1

Initial material， cross-sectional shapes and dimensions and potential selection of cross-sectional shape of members of simple frame"

杆件编号材料截面形状初始尺寸/mm可用截面形状
DFeB10×10×1.5B、T、H
EFeT10×8B、T、H
FFeC10×10×1B、C
GFeT15×13B、T、C

Fig.2

Schematic of cross-sectional shape and representation of dimension"

Table 2

Mechanical properties and unit prices of steel， Aluminum alloy and Magnesium alloy"

材料弹性模量/ GPa泊松比密度/ （kg·m-3）单位价格/ （元·kg-1）
Fe2100.3079004.62
Al700.33270015.40
Mg450.35184020.00

Table 3

Property library for optimization of simple frame"

截面形状尺寸规格
FeAlMg
B

10×10×1

20×20×2

30×30×2

30×40×2

20×20×2

30×30×2

30×40×2.5

30×50×3

20×20×2

30×30×2

30×40×2.5

30×50×3

T10×8，15×1315×13，20×1815×13，20×18
H

60×30×30×2

70×40×20×2

60×30×30×2

70×40×20×2

70×40×20×2
C

10×10×1

20×20×2

20×20×2

30×30×3

30×30×3

Fig.3

Flowchart of NSGA-III"

Fig.4

Schematic of coding， decoding and generating finite element model"

Fig.5

Flowchart of structural optimization considering multiple materials， cross-sectional shapes and dimensions"

Table 4

Materials， cross-sectional shapes and dimensions of members of simple frame after structural optimization"

杆件编号材料截面形状优化后尺寸/mm
DMgB30×50×3
EMgB20×20×2
FMgB20×20×2
GAlB30×40×2.5

Table 5

Performances of simple frame before and after structural optimization"

项目M/kgf1/Hz

σI，max

/MPa

σII，max

/MPa

dI，x

/mm

dII，y

/mm

优化前3.0022.6254.0011.92.9210.027
优化后2.6843.210.666.60.2950.024

Fig.6

Conceptual skeleton-type body and corresponding members’ number"

Table 6

Materials， cross-sectional shapes and dimensions of members of skeleton-type body before and after structural optimization"

杆件编号优化前优化后
材料截面形状初始尺寸可用截面形状材料截面形状优化后尺寸
1FeB40×20×2.5B、T、H、CFeB40×20×1.5
2FeB50×30×2.5B、T、H、CFeB50×30×2
3FeB38×25×2.5B、TAlB80×60×4
4FeB75×45×2.5B、T、CFeB60×30×2
5FeT25×22.5B、TFeT25×22.5
6FeT25×22.5B、TFeB30×50×2
7FeT25×22.5B、T、HAlT30×25
8FeT25×22.5B、T、HAlT30×25
9FeB75×45×2.5B、TAlT30×25
10FeT25×22.5B、T、CFeT25×22.5
11FeB70×50×2.5B、T、H、CFeB70×50×2
12FeB30×30×2.5B、TFeT20×18
13FeB50×50×2.5B、TFeB50×50×2.5
14FeB30×30×2.5B、T、CFeT20×18
15FeB30×30×2.5B、TFeB40×40×2
16FeB30×30×2.5B、TFeT20×18
17FeB30×30×2.5B、T、CFeT20×18
18FeB30×30×2.5B、TFeT20×18
19FeB30×30×2.5B、TFeT20×18
20FeB70×50×2.5B、T、CFeB50×50×2.5
21FeC70×50×2.5B、T、CAlB80×60×4
22FeB70×50×2.5B、T、CFeB70×50×2
23FeB70×50×2.5B、T、CAlB80×60×4
24FeB70×50×2.5B、T、CFeT27×25
25FeB70×50×2.5B、T、CAlT25×21
26FeB50×50×2.5B、T、CAlT25×21

Fig.7

Illustration for skeleton-type body"

Table 7

Boundary and loading conditions of multiple load cases of skeleton-type body"

工况左前悬置右前悬置左后悬置右后悬置载荷/方向
弯曲（I）2，331，2，31，32 g/-z
扭转（II）001，2，31，32000 N·m
右前轮悬空（III）2，301，2，31，31.3 g/-z
转弯（IV）2，331，2，31，30.4 g/+y、1.3 g/-z
制动（V）2，331，2，31，30.8 g/-x、2 g/-z

Table 8

Comparison among original design and four optimal designs"

性能参数优化前性能设计方案成本设计方案折中设计方案尺寸优化设计方案
m/kg167.4132.0155.8147.1159.9
f1/Hz12.9714.3614.3013.9813.10
dI，z/mm7.36.26.66.57.6
dII，z/mm7.15.96.56.87.8
dIII，z/mm9.38.69.18.810.1
σI，max/MPa155.0129.7143.5134.3170.3
σII，max/MPa109.8101.6110.8115.2132.1
σIII，max/MPa149.4113.6121.3139.7175.1
σIV，max/MPa110.7100.3136.6109.7121.1
σV，max/MPa347.4291.0319.1301.6356.8
Cost/￥773.42302.39984.831252.2738.7

Fig.8

Optimal designs considering performance， cost， both of performance and cost and sizing optimization only， respectively"

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