DESIGN OPTIMIZATION OF CFRP RECTANGULAR BOX SUBJECTED TO ARBITRARY LOADINGS
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1 Munch, Germany, th June DESIGN OPTIMIZATION OF CFRP RECTANGULAR BOX SUBJECTED TO ARBITRARY LOADINGS Q.T. Guo 1*, Z.Y. L 1, T. Ohor 1 and J. Takahash 1 1 Department of Systems Innovaton, School of Engneerng, The Unversty of Tokyo 7-3-1, Hongo, Bunkyo-ku, Tokyo Japan *Emal: guo-qtao@cfrtp.t.u-tokyo.ac.jp, Web Page: Keywords: CFRP, rectangular box, optmzaton, mult materal soluton Abstract Carbon fber renforced plastcs (CFRP) has been sad to have great potental n weght reducton of structures because of ts hgh specfc stffness and strength. However, ths s true only n the case of tensle strength and flexural rgdty of plates as same as other lght metals. In ths study, the best weght lghtenng drecton of a rectangular box made of hollow beams and panels subjected to arbtrary external loads s dscussed by usng Fnte Element Analyss. The materals used are steel, sotropc and ansotropc CFRP. Based on the results, a desgn optmzaton ncludng mult materal soluton s dscussed on the purpose of affordable realzaton of lght-weght structures such as mass producton automoble. 1. Introducton Vehcle weght reducton has been consdered as one of the most mportant solutons to mprove fuel economy and reduce harmful emssons[1]. It s beleved that mult-materal selecton can be the soluton for the vehcle body weght reducton. Flexural rgdty and torsonal rgdty are the major consderaton durng vehcle desgn. In the past several years, varous lghtweght automotve bodes have been developed usng hgh strength steels [2,3], alumnum alloys[4,5] and dfferent composte materals[6]. Among the composte materals, Carbon fber renforced plastcs (CFRP) has been sad to have great potental n weght reducton of structures because of ts hgh specfc stffness and strength[7]. However, most work done n lghtweght materals car body desgn has been lmted to sngle loadng condton. The objectve of ths study s to fnd the lghtest rectangular box structure subjected to arbtrary statc loadngs usng mult-materal soluton and thckness optmzaton. The rectangular box made of hollow beams and panels s smlar to the vehcle structure, the materals used n ths research are steel, and CFRP, ncludng UD(Un-drectonal)materal, CTT(Chopped carbon fber tape renforced thermoplastcs) and UT-CTT(Ultra-chopped carbon fber tape renforced thermoplastcs). 2. Fnte element analyss As Fg.1 shows, the rectangular box s made up of hollow beams and panels, ncludng floor panel, top panel, front panel, rear panel, left panel and rght panel. The dmensons of the box are 2900mm 1400mm 1500mm(Length Wdth Heght). The outer cross-secton sze of hollow beam s 100mm 100mm.
2 Munch, Germany, th June Fgure 1. Three-dmenson model of rectangular box 2.1. Theoretcal calculaton Flexural rgdty calculaton Flexural rgdty EI can be calculated by the followng equaton: F EI (1) Z EI : Flexural rgdty(n/mm) F : Concentrate force (N) Z max : The maxmum flexure deflecton(mm). max Torsonal rgdty calculaton Torsonal rgdty GJ can be calculated by the followng equaton: TL TL GJ U1 U2 180 arctan D GJ : Torsonal rgdty (N mm/rad) T : Torson force (N) L : Wheelbase (mm) : Torson angle (deg) U 1 : The abs value of left measure pont deflecton (mm) U 2 : The abs value of rght measure pont deflecton (mm) D : Dstance between left measure pont and rght measure pont (mm) Fnte element model In ths study, fnte element models shown were establshed by usng Altar HYPERMESH, the hollow beams and panels are modeled as shell element, the thckness of hollow beams and panels are 2mm and 1mm, respectvely. The materal propertes can be found n Table 1. (2)
3 Munch, Germany, th June In flexure modelng Fg. 2(a), the concentrate force F z was loaded at left and rght sde of the mddle part of the rectangular box structure. The boundary condton was to constran translaton n x, y and z- drectons at front sde and rear sde of the rectangular box structure. In torson modelng Fg. 2(b), a par of opposte concentrate forces F z were loaded at front sde of the rectangular box structure. The boundary condton was to constran the translaton n x, y and z- drectons at rear sde of the structure. Table 1. Materal parameters Materal property Steel UD CTT UT-CTT Densty (g/cm 3 ) Elastc Modulus E (GPa) E Shear Modulus (GPa) G G G Posson rato υ Tensle strength σ 1y (MPa) σ 2y Compresson σ 1c strength σ 2c (MPa) Resn matrx - PP PP PA6 Vf (%) Results (a) Flexure modelng Fgure 2. Fnte element model of rectangular box (b) Torson modelng In order to reduce the desgn varables n the followng desgn optmzaton, the senstvty of panels and hollow beams to the flexural and torsonal rgdty should be conducted. The fnte element
4 Munch, Germany, th June modelngs of scaled rectangular box shown n Fg.3 were used to study the relatonshp between components thckness and rgdty for reducng the CPU calculaton tme. (a) Flexure modelng (b) Torson modelng Fgure 3. Fnte element model of scaled rectangular box Fgure 4. The relatonshp between components thckness and rgdty The flexural and torsonal rgdty can be calculated by equaton (1) and (2). As Fg.4 shows, the flexural and torsonal rgdty wll ncrease wth thckness ncreasng. Comparng wth the hollow beams, however, the panels play much more mportant role n flexural and torsonal rgdty whch means that the panels thckness should be consdered as desgn varables durng optmzaton work. Addtonally, the FEA results of steel rectangular box should be made as the comparson wth the results of the optmal structure. From the results of numercal smulaton, the flexural and torsonal rgdty s 5926 N/mm and N mm/rad, respectvely. Correspondngly, the total weght of the structure s 298.7kg. The results wll be reference for the followng optmzaton process.
5 Munch, Germany, th June Optmzaton process In ths study, the materal types rather than materal propertes are ntroduced as desgn varables n order to reduce the desgn varables. Each canddate materal type has been assgned an ID number from 1 to m, whch can be n any arbtrary order. Defne the materal used for th component as a desgn varable named M ( M 1, 2,..., m ). If a materal type s gven to M, all the related propertes of the materal can be dentfed exactly. Besdes, the thckness of hollow beams was set to same wth the steel one due to the panels mportant role n the flexural and torsonal rgdty optmzaton. Besdes, the thckness of front panel and rear panel are same n the real vehcle desgn process, as well as the thckness of left panel and rght panel. Therefore, the thckness of floor panel, top panel, front panel and left panel were consdered as desgn varables durng optmzaton work Flexural and torsonal rgdty optmzaton The optmzaton model can be formulated as follows: Objectve functon: MnmumW W ( T, M ), 1, 2 Constrants: panel panel EI T, M EI ( steel) GJ ( T, M ) GJ ( steel) panel Desgn varables: 1 T floorpanel W : Total weght (kg) T : The thckness of floor panel (mm) floorpanel T toppanel T frontpanel T leftpanel : The thckness of top panel (mm) : The thckness of front panel (mm) : The thckness of left panel (mm) M : The materal used for th component 1 T toppanel 1 T frontpanel 1 T leftpanel M 1, 2,3, Optmzaton results Flexure case Torson case Table 2. The optmzaton results of flexural and torsonal rgdty Before After optmzaton optmzaton Rgdty W M beam M panel T floorpanel T toppanel T frontpanel T leftpanel Rgdty W (kg) (mm) (mm) (mm) (mm) (kg) UD CTT UT- CTT CTT
6 Munch, Germany, th June The optmzaton results n Table 2 show that the optmal structure wth 64.55% weght reducton can be obtaned when the materals of hollow beams and panels are UD and CTT durng flexural rgdty optmzaton, whle the weght reducton of 29.43% can be acheved n the torsonal rgdty case. 4. Conclusons A rectangular box, a representatve lght weght vehcle frame component, whch s made of hollow beams and panels subjected to flexural and torsonal loadngs was optmzed by usng mult-materal soluton and thckness optmzaton. As a result, weght reducton of 64.55% by CFRP can be acheved comparng wth steel one consderng the flexural rgdty, whle weght reducton of 29.43% can be acheved comparng wth steel one n the torsonal rgdty case. Acknowledgements Part of ths study was conducted as Japanese METI project "the Future Poneerng Projects/ Innovatve Structural Materals Project" snce 2013fy. Authors would lke to express sncerely apprecaton to the project members who have provded valuable nformaton and useful dscussons. References [1] X.T. Cu, H.W. Zhang, S.X. Wang, L.H. Zhang and J.H. Ko. Desgn of lghtweght mult-materal automotve bodes usng new materal performance ndces of thn-walled beams for the materal selecton wth crashworthness consderaton. Materals and Desgn, 32: , [2] R. Koehr. Ulsac-lghtweght steel automotve closures. SAE techncal paper, , [3] Y. L, Z. Ln, A. Jang and G. Chen. Use of hgh strength steel sheet for lghtweght and crashworthy car body. Materals and Desgn, 24: , [4] A. Deb, M.S. Mahendrakumar, C. Chavan, J. Karve, D. Blankenburg and S. Storen. Desgn of an alumnum-based vehcle platform for front mpact safety. Internatonal Journal of Impact Engeerng, 30: , [5] D. Carle and G. Blount. The sutablty of alumnum as an alternatve materal for car bodes. Materals and Desgn, 20: , [6] Y. L, Z. Ln, A. Jang and G. Chen. Expermental study of glass-fber mat thermoplastc materal mpact propertes and lghtweght automobles body analyss. Materals and Desgn, 25: , [7] T. Ohor, T. Matsuo, K. Furukawa and J. Takahash. Fnte element analyss of CFRTP hollow beam under flexural load for an applcaton to vehcle body structure. Proceedngs of the 16th European Conference on Composte Materals ECCM-16, Sevlle, Span, June
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