Dec.2020Vol.37No.6 Transactions of Nanjing University of Aeronautics and Astronautics
Multidisciplinary Design Optimization of Crash Box with
Negative Poisson’s Ratio Structure
LU Guangchao1，2，SHU Jiahao1，ZHAO Wanzhong1*
1.College of Energy and Power Engineering，Nanjing University of Aeronautics and Astronautics，Nanjing210016，
P.R.China；
2.Department of Information Management，Zhengzhou Metro Company Limited，Zhengzhou450061，P.R.China
（Received9April2019；revid13August2019；accepted25September2019）Abstract:To improve the crashworthiness and energy absorption performance，a novel crash box negative Poisson’s ratio（NPR）structure is propod according to the characteristics of low speed collision of bumper system.Taking the peak collision force and the average collision force as two subsystems，a multidiit百科
sciplinary collaborative optimization design is carried out，and its optimization results are compared with the ones optimized by NSGA-II algorithm.
Simulation results show that the crashworthiness and energy absorption performance of the novel crash box is improved effectively bad on the multidisciplinary optimization method.
Key words：crash box；multidisciplinary optimization；negative Poisson’s ratio；energy absorption；low-speed collision
CLC number：U463.8Document code：A Article ID：1005‑1120（2020）06‑0955‑07
0Introduction
In a low-speed collision，the bumper system and its energy-absorbing parts can absorb the impact energy caud by the collision［1］.As the main ener‑gy absorption component of the anti-collision sys‑tem，the crash box can absorb most of the energy in a short time，and protect the safety of drivers and pasngers.
Owing to the great effect of crash box on the pas‑sive safety，many rearches have been done to im‑prove its energy absorption performance.Li et al.［2］found that increasing the wall thickness pro
perly could improve the energy absorption characteristics of the crash box.However，the wall thickness of the energy absorption box would lead to excessive peak collision force and damage the car body.Liu et al.［3］enhanced the performance of the crash box through the multi-objective optimization design of the posi‑tion and depth.Lan et al.［4］compared and analyzed the energy absorption characteristics of the crash box filled with aluminum foam.They found that the crash box filled with aluminum foam not only could greatly improve the energy absorption capacity，but also had stronger stability in the process of compres‑sion and deformation.
In order to further improve the crashworthiness and energy absorption performance，the negative Poisson’s ratio（NPR）structural material was ud to the crash box［5-7］.The rearch results showed that the NPR crash box could ensure that the system absorb more collision energy during the collision process and improve the collision performance.For the sake of the improvement of crashworthiness per‑formance，some single‑and multi-objective optimi‑zation algorithms have been ud to optimize the structures of crash boxes.However，there is a cou‑pling effect between the optimization objectives of crash boxes.The simple weighting method is diffi‑cult to consider the mutual influence and coupling re‑lationship among the objectives.In this ca，the fi‑nal optimization result is rarely the global optimal
*Corresponding author，E-mail address：************.
How to cite this article:LU Guangchao，SHU Jiahao，ZHAO Wanzhong.Multidisciplinary design optimization of crash box with negative Poisson’s ratio structure［J］.Transactions of Nanjing University of Aeronautics and Astronautics，2020,37(6)：955‑961.
http：//dx.doi/10.16356/j.1005‑1120.2020.06.013
Vol.37 Transactions of Nanjing University of Aeronautics and Astronautics
solution of the energy absorption system.There‑
fore，this work conducts the multidisciplinary opti‑
mization of the NPR crash box to improve the sys‑
tem’s crashworthiness and energy absorption perfor‑
mance.
1Modeling of NPR Unicellular Structure
The Poisson’s ratio is defined as a ratio of the transver strain to the longitudinal strain.As shown in Fig.1，the NPR effect refers to the trans‑ver expansion change of the material within the elastic range when the tensile stress is received.On the contrary，the transver contraction of the mate‑rial changes when it is compresd.
In this paper，the new crash box is established on the basis of a traditional one，which is compod of two parts connected by welding.Its structure size is235mm in length，120mm in width and62mm in height.Bad on this，a NPR inner core is de‑signed to fill into the traditional part shell，and its cellular model is shown in Fig.2.This structure has been proved with good NPR characteristics［8-9］.As shown in Fig.2，the unicellular structure is deter‑mined by four main variables：The ba length a，the hypotenu length b，the angleθand the thick‑ness t.Through Hypermesh software，the finite ele‑ment model of the inner core is established，and it contains52578quadrilateral grid elements and 70536nodes.The main modeling process is shown in Fig.3.渔父李煜
The Ls-Dyna software is applied to simulate the collision process.In the simulation，the rigid wall is t as900kg，and it impacts the other end of crash box at the speed of15km/h.The rigid wall model is built by means of the keyword*RIGID‑WALL_PLANAR.The whole time of the collision simulation is
t to80ms and the time step is t to 1e−6s.The finite element model of the inner core is mainly compod of quadrilateral meshes with the size of2mm×2mm.In addition，both the static friction coefficient and the dynamic friction coeffi‑cient are t as0.2.
Energy conrvation is an important criterion to verify the correctness and reliability of the estab‑lished model.In the collision simulation，it is neces‑sary to ensure that the hourglass energy cannot ex‑ceed5%of the total energy.Fig.4shows the energy change curve of new NPR crash box.It can be en from Fig.4that the total energy is conrved and the hourglass energy accounts for less than10%and 5%of the internal energy and the total energy re‑spectively.Therefore，the established model of new crash box is accurate and can be ud for subquent optimization
design.
Fig.1Deformation characteristics of NPR
structure
Fig.2Modeling process of the new crash box
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No.6LU Guangchao,et al.Multidisciplinary Design Optimization of Crash Box with (2)
Multidisciplinary
Optimization
Design
个人毕业鉴定In this ction ，the multidisciplinary optimiza‑tion design is conducted for the new crash box.The energy absorption E SEA ，the peak collision force F PCF ，and the average collision force F av are lected as the evaluation indexes.The specific energy ab‑sorption E SEA refers to the energy absorbed by per unit mass ，which can characterize the energy absorp‑tion characteristics of the crash box.The peak colli‑sion force F PCF is the maximum collision force of the crash box in the collision process.Moreover ，the av‑erage collision force F av reflects the average energy absorption level of the crash box ［10］.
The framework of the multidisciplinary optimi‑zation is shown in Fig.5.Firstly ，the optimal Latin hypercube design is ud to obtain the sample points
in the range of design variables ，and models are es‑tablished and simulated according to the sample points.Secondly ，bad on the simulation results ，
respon surface models （RSMs ）［11］
are established
to optimize the objectives and constraints.Finally ，the multidisciplinary optimization algorithm and
小学六年级数学题multi -objective optimization algorithm are applied to optimize the parameters ，respectively.
画三角龙In the optimization ，the structural parameters of the cellular NPR structure model are lected as the optimization variables.The included angle θbe‑tween the horizontal cell rib and the inclined cell rib ，the length of the horizontal cell rib a ，the length of the inclined cell rib b ，and the cell wall thickness t are t as the design variables.The ranges of the structural size parameters are shown in Table 1.
In the multidisciplinary optimization ，the col‑laborative optimization （CO ）multidisciplinary algo‑rithm is ud for the NPR crash box.The specific energy absorption is t as the primary system ，and the peak impact force and average impact force are t as two subsystems.The respon surface model of performance objectives and constraints can be pre‑nted as follows.
The RSM of peak impact force F PCF can be giv‑en
as
Fig.3Overall modeling
process
Fig.4
Energy change curves of new NPR crash box
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Vol.37
Transactions of Nanjing University of Aeronautics and Astronautics F PCF =118935.1-1183.8θ-78583.5t -300.9a 2-1342.6b 2+
560.6ab +3775.9am +80.4bθ+1196θt
(1)
The RSM of specific energy absorption E SEA can be expresd as
E SEA =2514946.1+409168.1b +3454355.7m +366.5θ2-1175137.4m 2-3607.6bθ-244886bt +17430.1θt -26026θm
(2)
The RSM of specific energy absorption F av can be expresd as
F av =273.3+9.58a -64.04b -7.749j -45.48t +168.3m -0.759a 2-1.483b 2+
0.0177j 2-41.838t 2-207.797m 2+0.418ab +0.0598aj -1.727at +4.089am +0.023bj -17.976bt +50.21bm +0.198jt +2.543jm +123.27tm
(3)
In general ，it is expected that the specific ener‑gy absorption E SEA can be maximized on the
premi
Fig.5Framework of the multidisciplinary optimization Table 1
Value range of optimization design variables
Design variable
a /mm
b /mm θ/(°)t /mm
Initial design value
12.8734.44958.670.776
Variable lower limit
124550.5
Variable upper limit
166751
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No.6LU Guangchao,et al.Multidisciplinary Design Optimization of Crash Box with …of satisfying conditions.Bad on the CO algo‑rithm ，the optimization model of the primary system E SEA can be expresd as神仙岛
{
Maximize P =E SEA (Z )=F (a,b,θ,t ,m )s.t.R 1≤ε,R 2≤ε
(4)
where R 1and R 2are the constraints of two disci‑plines and εis the relaxation factor with the value of 0.1.
In the collision process ，it is generally required that the peak value of collision force F PCF should be within the permissible range.Furthermore ，in order to make the crash box absorb the energy as much as possible ，F av is expected to increa as much as pos‑sible within a reasonable range.In this paper ，the peak collision force F PCF and the average collision force F av are lected as two subsystems.The nor‑malization of each subsystem can make the objective function converge quickly.
The optimized model of peak collision force subsystem can be expresd as
ìíî
ï
ï
ïï
ïïMinimize F PCF (Z )=F (a ,b ,θ,t ,m )R 1=(1-a /a 1)2+(1-b /b 1)2+(1-θ/θ1)2+(1-t /t 1)2+(1-m /m 1)212<a 1<16,4<b 1<6,55<θ1<75,0.5<t 1<1.0,1.6<m 1<1.8(5)The optimized model of average collision force subsystem can be depicted as
ìíî
ï
ï
ïï
ïïMaximize F av (Z )=F (a ,b ,θ,t ,m )R 2=(1-a /a 2)2+(1-b /b 2)2+(1-θ/θ2)2+(1-t /t 2)2+(1-m /m 2)212<a 2<16,4<b 2<6,55<θ2<75,0.5<t 2<1.0,1.6<m 2<1.8(6)The multi -objective optimization bad on NS‑GA‑II algorithm is further carried out to verify the disciplinary optimization results.In the multi -objec‑tive optimization ，the peak impact force and specific energy absorption are t as optimization objectives to evaluate the energy absorption characteristic.The mathematical model of multi -objective optimization of the new crash box is expresd as
ìí
纪念的近义词î
ï
ïïï
Minimize G (Z )={1/F av (Z );1/E ESA (Z )}s.t.Z =(a ,b ,θ,t ,m )
F (Z )<120,12≤a ≤16,4≤b ≤6,55≤θ≤75,0.5≤t ≤1,1.6≤m ≤1.8(7)Table 2shows the optimized values of the de‑
sign variables and objectives under different optimi‑zations.The optimal solution is obtained bad on NSGA -II optimization algorithm and CO algorithm.As can be en from Table 2，compared with NS‑GA‑II algorithm ，the quality mass of the new crash box optimized by CO algorithm is decread by 0.195kg ，and the specific energy absorption is in‑cread by 251.4kJ/kg.
Figs.6and 7show the impact force and energy absorption of the new crash box with different opti‑mization algorithms.As can be en from Figs.6and 7，bad on no optimization ，multi -objective op‑timization and multidisciplinary collaborative optimi‑zation ，the peak collision force value are the maxi‑mal ，the middle and the minimal respectively ，and the specific energy absorption value are the mini‑mal ，the middle and the maximal respectively.Thus ，the peak force of collision and the specific en‑ergy absorption of NPR crash boxes are all im ‑proved bad on the CO multidisciplinary algorithm.
Table 2Comparison of optimization results Design variable
a /mm
b /mm θ/(°)t /mm
M /kg E SEA /(J⋅kg -1)
Initial NPR design 12.8734.44958.670.7761.8354211.4
NSGA‑II algorithm 12.4774.11571.850.911.7114462.3
拌三丝CO algorithm
166550.531.5164
713.7
Fig.6Impact forces of different optimization
methods
Fig.7Energy absorption of different optimization methods
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