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Lightweight Design of CFRP-Laminated Structures by Combining Microscopical Homogenization and Macroscopical Optimization

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Abstract

We developed a new method for the design of carbon-fiber reinforced plastic (CFRP)-laminated structures, which combined the asymptotic homogenization method and ply optimization. The equivalent mechanical properties of a single-layer CFRP were calculated using the asymptotic homogenization method. The ply optimization of the laminated structures was divided into three parts: an initial free-size optimization to identify the optimal ply shapes and locations of patches per ply orientation; an optimization of the final size to identify the optimal thicknesses of each ply; and an optimization of the final ply stacking sequence to obtain the optimal stacking sequence. Using the example of the floor of a body-in-white model, our method provided a reasonable optimization result with reduced mass by 60 %. The proposed method provides an efficient way to investigate laminated structures and has potential for lightweight design and analysis of automobile components.

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Abbreviations

ξ :

small parameter, —

x :

fast variable, —

y :

slow variable, —

ϕ ξ(x):

field variable, —

σ ij :

stress, MPa

u (i) :

displacement field, —

χ mn k :

shape function, —

D iikl :

elastic tensor of solid material, —

f i :

body force, N/m3

Y :

unit-cell domain, —

∣Y∣ :

volume of the unit cell, —

ε :

three (2D) or six (3D) unit strain fields, —

Ω :

unit-cell domain, —

B :

finite-element strain-displacement matrix, —

K :

constitutive matrix, —

α :

characteristic displacement vector, —

f kl :

external force vector, —

E :

elastic modulus, MPa

G :

shear modulus, MPa

μ :

Poisson ratio, —

ρ :

density, T/mm3

t :

thickness of a single layer, mm

n :

number of layers, —

β :

layer direction, —

G m :

mass of the floor, g

U :

deflection, mm

Ū :

rated deflection, mm

h 0 :

total thickness of the layers, mm

CFRP:

carbon-fiber reinforced plastic

AH:

asymptotic homogenization

BIW:

body-in-white

FE:

finite element

H&C:

Halpin-Cai model

W&R:

Whitney-Riley model

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Acknowledgement

This work was supported by the National Science Foundation of China (Grant No. 11502092), the Plan for Education Development of Jilin Province (Grant No. JJKH20190142KJ) and the Plan for Scientific and Technological Development of Jilin Province(Grant No. 2020 0201272JC)..

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Authors and Affiliations

  1. School of Mechanical and Aerospace Engineering, Jilin University, Changchun, 130025, China

    Fei Cheng, Chenggong Zheng, Yunfei Liu, Wenjie Zuo, Xinzhe Wang & Guikai Guo

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  1. Fei Cheng
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  2. Chenggong Zheng
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  3. Yunfei Liu
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  4. Wenjie Zuo
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  5. Xinzhe Wang
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  6. Guikai Guo
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Correspondence to Guikai Guo.

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Cheng, F., Zheng, C., Liu, Y. et al. Lightweight Design of CFRP-Laminated Structures by Combining Microscopical Homogenization and Macroscopical Optimization. Int.J Automot. Technol. 22, 1427–1436 (2021). https://doi.org/10.1007/s12239-021-0124-1

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