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Engineering with Computers (2002) 18: 109115Ownership and Copyright 2002 Springer-Verlag London LimitedStructural Optimization of Automotive Body Components Based onParametric Solid ModelingM. E. BotkinGM R&D Center, Warren, MI, USAAbstract. Parametric modeling was used to build severalmodels of an automotive front structure concept that utilizescarbon fiber composite materials and the correspondingmolding processes. An ultra-lightweight aluminum body frontstructure was redesigned to include an all-composite frontstructure. Two alternative concepts were studied which rep-resent the structure as a bonded assembly of shells. Closedsections result from two pieces an inner and outer. Para-metric modeling was found to be a useful tool for buildingand modifying models to use in optimization concept studies.Such models can be built quickly and both the sketch dimen-sions and location dimensions are particularly useful formaking the adjustments necessary to fit the various bodypieces together. The parametric models then must be joinedtogether as one geometric solid model in order to obtain asurface mesh. Structural optimization input data can then beseamlessly and quickly created from the parametric-model-based finite element model to begin the tradeoff studies. Thisintegrated process in which parametric modeling was coupledwith structural optimization was used to carry out designstudies on the lightweight body front structure. Several car-bon fiber material combinations were studied to determinemass reduction potential of certain types of carbon fiberproducts considered to be lower cost than typical carbonfiber materials used in the past. Structural optimization wasused to compare several composite constructions for thedesign of the bonded front structure. Eight cases were studiedusing various materials and composite lay-ups. Mass savingsestimates from 4564% over steel were obtained. The mostreasonable design consisted of a combination of relativelylow cost chopped carbon fiber and woven carbon fiber andusing a 20 mm balsa core in the top of the shock towerarea. This design had a maximum thickness of 7 mm and amass reduction over steel of approximately 62%.Correspondence and offprint requests to: Mark E. Botkin, Princi-pal Research Engineer, GM R&D Center, Mail Code: 480-106-256, 30500 Mound Rd., Warren, MI 48090-9055, USA.Email: mark.e.botkinL50560Keywords.Automeshing; Automotive; CAD Modeling; Com-posites; Finite Element Modeling; Optimization1. IntroductionThe structure shown in Fig. 1 is a lightweight bodycomposed of several advanced materials. The designof this body was documented in Prsa 1 and wascarried out as a part of the PNGV 2 governmentprogram. With the primary design goal being weightreduction, the PNGV body weighed approximately70% less than the Chrysler Cirrus steel body it isintended to replace. The body is primarily composedof a sandwich construction of carbon fiber skins andaluminum honeycomb. Small amounts of Kevlarwere also used as well as some Nomex core. How-ever, the load-carrying members of the front struc-ture are aluminum. This paper describes a project toredesign an all-carbon fiber front structure. Severalconcepts were considered. The concepts describedin this paper can be characterized as bonded-togethersheets that form closed-section rails. The conceptswere modeled using the parametric modeling fea-tures of Unigraphics(UG) 3, and are shown inthe next sections. The mesh was created automati-cally using the Scenario capability of Unigraphics.Fig. 1. Carbon fiber body.110 M. E. BotkinBecause the mesh was created based upon a solidgeometric model, separate property regions wereautomatically created for each surface face. Thismade the optimization data creation phase mucheasier than previous studies 4. Programs such asPatran5 can create optimization data automati-cally from properly created structural analysis data.This paper also describes the use of Nastran5Solution 200 to carry out design studies for com-posite design concepts for the front-end structure.2. Parametric ModelingThe parametric modeling process begins with two-dimensional parametric cross-sections which areused to create solid models through extrusion alonga straight line or sweeping along a curve. The frontstructure shown in Fig. 1 was modeled, using thisparametric process, as bonded-together compositesheets. The model is composed, primarily, as threemajor components; the upper rail, lower rail, andshock tower. Other secondary panels tie these threecomponents together. As an example, Fig. 2 showsthe parametric cross section of the outer piece ofthe upper rail. The dimensions shown are variablesthat can be changed either by the designer usingthe modeling program or automatically using optim-ization procedures. After a variable is modified, theentire solid model is automatically updated. Figure3 shows the process of creating three-dimensionalgeometry from the two-dimensional sections. As thesection is swept along the curve, solid geometry isautomatically generated. When any of the underlyinginformation is modified, e.g., section dimensions,sweep curve location, etc., the solid geometry isFig. 2. Outer piece of upper rail.automatically updated. Similar operations are usedfor the lower rail and the shock tower to obtain thecomplete parametric solid model that will be usedin this design study, shown in Fig. 4. Figure 4represents a three piece composite structure (upperrail, lower rail, and shock tower/apron) joinedtogether with adhesive.For the purposes of this design study, parametricmodeling was only used as a convenient method tocreate the finite element model. Ultimately, however,a more comprehensive design approach would allowthe parametric model to be an integral part ofoptimization process where the parametric dimen-sions are available to be used as design variables.This is possible, to a large extent, with versions ofUnigraphics 16 and later and has been demonstratedin Botkin 6.3. Finite Element Analysis3.1. Mesh GenerationThe mesh shown in Fig. 5 was created from UGScenariousing the fully-automatic quadrilateralmesh generation capability using a nominal 10 mmelement size. This is an advancing front techniquetypical of those found in most commercial modelingprograms. However, because of the tight integrationbetween the parametric modeler and the mesher, thedistinct surface regions shown in Fig. 4 are main-tained as property regions in the mesh and, as shownin Fig. 6, can be automatically specified as designvariables in the optimization model. The modelshown in Fig. 5 is composed of 11,710 nodes,12,225 elements, 58,877 degrees-of-freedom, and 23different element properties. In addition to 11488shell elements, 737 CBAR elements were used torepresent adhesive bonds that were used to join thecomposite pieces together.3.2. Analysis ModelFigure 5 also shows the load and boundary con-ditions used in this study. The goal of thisoptimization study is to design an all-compositefront structure to have the same stiffness as thecomposite/aluminum structure shown in Fig. 1. Thetorsional stiffness of the structure in Fig. 1 wasfound to be 1 10,246 Nm/deg. It was found byan analysis of the shock tower region that thestiffness is much higher than that of the overallbody at 17,963 N/mm in the vertical direction and111Structural Optimization of Automotive Body ComponentsFig. 3. Tapered upper rail.Fig. 4. Final front structure model.Fig. 5. Final mesh from UG/Scenario.Fig. 6. Material property regions.12,941 N/mm in the lateral direction. That corre-sponds to a limiting deflection of .055 mm for the1000 N load shown in Fig. 5 and .077 mm for asimilar lateral 1000 N load.112 M. E. BotkinFig. 7. Bond model.3.3. Bond ModelingAs noted earlier, the three individual compositepieces are to be joined by the use of adhesives.Figure 7 shows the modeling approach chosen forthis study. The rows of elements along the edgesof each piece are joined by the use of beam elementsfor which the properties are determined from thematerial properties of the adhesive (shown in Table1). The beam properties are the area of the bondconsidered to contribute to nodes A and B (see Fig.7) and the moments of inertia. These values are 50mm2and 416.67 mm4, respectively, assuming anominal element size of 10 mm (square).Table 1. Composite properties 4E1E2H9262 G H9267 XtXcYtYcS(Mpa) (Mpa) (Mpa) (kg/mm3) (Mpa) (Mpa) (Mpa) (Mpa) (Mpa)Chopped Carbon Fiber26000 26000 .34 9701 1.36E-6 178 143 178 143 50Carbon Plain Weave52000 52000 .06 4200 1.43E-6 530 370 530 370 75Uni-directional Material130000 9000. .3 4800. 1.50E-6 1630. 840. 34. 110. 60.HYSOL EA 9395 Adhesive4937. 4937. .34 1842. 55. 96. 55. 96. 27.Baltek D-100 balsa wood core4070. 4070. 159 1.5E-7 13.1 12.9 13.1 12.9 3.0Baltek D-57 balsa wood core2240. 2240. 108. 1.0E-7 6.9 6.5 6.9 6.5 1.84. Optimization StudiesNastran Solution 200 was used to carry out eightcase studies of various combinations of materials.The material properties are given in Table 1. Allof the default Nastran optimization parameters 7were used except the approximate optimizationtechnique which was chosen to be Convex Lin-earization 8,9. As noted in Botkin 4, convexlinearization, which is the most conservative ofthe approximation methods available in Nastran,was used because of the difficulty of approximat-ing the failure constraints.4.1. Objective and Constraint FunctionsThe objective function of the studies was minimummass. The design was, as mentioned earlier, forstiffness-only. Constraints were imposed on thelateral and vertical deflections of 0.077 and 0.055mm, respectively.4.2. Design VariablesAs mentioned previously, the design variables canautomatically be created from the property regionsshown in Fig. 6. Figure 8 shows the panel fromPatran 5 which is displayed when the Design Studytool is used. Although there are 23 design variables,not all are shown on a single panel. Initial valuescan be modified using this panel and then the Sol-ution 200 data input (DESVAR & DVPREL1 cardimages) is automatically created. It should be113Structural Optimization of Automotive Body ComponentsFig. 8. Design variable panel.pointed out that the thickness values shown in Fig.8 are the initial values of 10 mm for the optimizationrun. The 30 mm values for the PCOMP entriesinclude a 10 mm balsa core and two 10 mm com-posite face sheets.Although the optimization method used in thisdesign study, Nastran Solution 200, is capable oftreating composite ply-angle variables as was dem-onstrated in Botkin 4 only woven cloth with afixed, 90, angle was used in an effort to reducefabrication costs.4.3. Design Concept SelectionAlthough Fig. 4 is referred to as a design concept,the parametric solid model can be thought of as ageometrical concept as opposed to a compositedesign concept. The goal of this design study is touse lower cost carbon fiber products such as choppedfiber and the less expensive large tow products.Estimated properties for these composites can beseen in Table 1 along with properties of all materialsused for this study. The lower bound on all designvariables was set at 2 mm which is considered tobe the thinnest parts that can currently be moldedusing liquid molding processes. The cases are separ-ated into three groups by upper bounds: 15, 10, andH1102110 mm. These thicknesses represent the successionof studies that took place in an effort to find adesign with a suitably small maximum thickness.The mass histories of all cases and the thicknessdistributions are summarized in Figs 9 and 10,respectively.It would be most desirable for a capability toexist that would determine an optimum compositeconcept rather than having to compare several selec-ted concepts. Existence of such a capability is notknown to the author.Fig. 9. Mass summary of cases.Fig. 10. Converged design variables.4.4. 15 mm Upper BoundsCase 1The first case will be that of using all choppedcarbon material with no sandwich construction. Thiswould be considered to be the least expensive caseusing the cheapest material and having no core.Cores add to the material and processing cost andare difficult to mold. As with all cases there willbe 23 design variables and a displacement constraintwill be placed at the top of the shock tower tomaintain the target stiffness shown previously. Apreliminary analysis has shown that the initial designviolates the displacement constraint by 33%. Figure9 shows the mass history of this case. Although theinitial stiffness target was violated at approximately13.6 kg, the optimizer was able to find a designthat satisfied the stiffness target at 6.2 kg, or 64%(6.2 kg/64%) mass reduction over the estimatedsteel mass. Considering this is a relatively lowperformance material, these results are remarkable.Figure 10 shows the design variable distribution ofthis case. The initial thickness of all design variableswas 10.0 mm. Several of the variables terminated114 M. E. Botkinat their lower bounds of 2.0 mm which is consideredto be the smallest thickness that can be reasonablymolded using Resin Transfer Molding (RTM) orStructural Reaction Injection Molding (SRIM).Several variables, however, ended at the arbitrarilychosen upper bound of 15 mm. It should be pointedout that the variables which terminated at their upperbounds were more sensitive (in a mathematicalsense) to the constraint than the mass. The remainderof the variables are more sensitive to mass than theconstraint and hence provide the opportunity formass reduction. A 15 mm thickness is consideredto be a rather unrealistic value and leads to aconclusion that the material in those regions needsto be either higher performing or of a sandwichconstruction, which leads to Case 2.Case 2This case adds a 10 mm thick balsa core of 1.0g/cm3(6.5 lb/cf) density to the top of the shocktower, i.e., variables 7 and 10 through 13 as shownin Fig. 6. Due to the added stiffness, the initialdesign in this case is 7.8% stiffer than the targetvalue. Figure 9 shows the mass history of this case.Although the initial design was stiffer, the initialmass was higher due to the weight of the core andthe added face sheet. In addition, even the finaldesign was heavier than in Case 1 (6.62 kg/61.3%).As demonstrated in Botkin 4 when skin thicknessesare very large, sandwich construction may not beeffective. Figure 10 also shows the variable distri-butions. Although several of the variables are drivento their upper bounds, most other variables aresmaller than in Case 1.Case 3This case modifies the surface skin in the sandwichpanel (top of shock tower) to a higher performingmaterial. This will be a woven material in whichthe properties are shown in Table 1. It is assumedthat this material will be made from the low cost50K tow carbon fiber. Figure 9 shows the resultsof this case. As can be seen the final mass is onlyslightly larger (6.65 kg/61.2%) and the thicknesseshave not been reduced, as was desired. Even thoughthe elastic modulus is much greater for the weave,the shear properties are much lower.4.5. 10 mm Upper BoundsThe following cases show the effect of reducing theupper bound on thickness to 10 mm. It is consideredthat 15 mm is excessively thick to be a reasonableconstruction. As one might expect the optimal massincreased in all cases.Case 4This case maintains the all-chopped carbon but witha core. (9.35 kg/45.4%).Case 5This case uses woven material in the shock towerarea (9.09 kg/46.9%).Case 6This case uses two layers of woven material. Theouter layer is 090 and the inner layer is H1100645in order to improve the shear properties of thewoven material. This construction had the desiredeffect of reducing the mass significantly from theother two 10 mm cases. (7.95 kg/53.6%).4.6. H1102110 mm Upper BoundsCase 7This case is an extension of case 6 with a 20 mmcore of 1.5 g/cm3(9.5 lb/cf) density and an upperbound on material thickness of 7 mm. The MTCbody also used a 20 mm core but of aluminumhoneycomb. This case resulted in a mass of 6.55kg or 61.8% mass reduction over steel. This is avery reasonable design with maximum thicknesseswell within the range of practical consideration.Case 8This case adds sandwich construction (a 10 mmbalsa core) to design variable regions 17 and 18shown in Fig. 6. The results of Case 7 indicatedthese regions to be at their upper bounds. Further-more, as shown in Fig. 1, the shock tower also usedsandwich construction in the side walls. Just as inCases 6 and 7 woven material was used with thesame lay-up. The results of this case were veryencouraging in that an upper bound of 6 mm wasobtained. Although the optimal mass is greater thanin Case 7 (6.95 kg/59.4%), if maximum thicknessis an issue, this case may be more desirable.4.7. Strength ConstraintsCase 9In this case, two loading conditions are added toinclude strength constraints to the stiffness-onlydesign (Case 8). The first load condition representsthe average barrier loads from a 35 mph (56.3km/hr) crash applied at the upper (10,000 N) and115Structural Optimization of Automotive Body Componentslower rails (44,000 N), each side. The second load-ing condition represents a commonly-used 3g pot-hole load (6675 N) applied vertically at the shocktower. Constraints were imposed on stresses for thechopped carbon and failure indices 4 for the wovenmaterial. Since the tensile and compressive strengthsof the chopped carbon were different, the moreconservative limit of 150 Mpa was used as thestress constraint. For the failure index (Hoffman), avalue of 1.0 was used as the constraint limit. Theresults of this case are shown as Case 9 in Figs 9and 10. Because the stiffness constraints are verysevere for this lower-stiffness material, the stressconstraints did not play a very important role in thedesign (7.1 kg/58.6%) compared to case 8. It is still,however, important to determine if the stiffness-onlydesigns are realistic.4.8. Case SummaryCase 7 appears