optimization of elastically tailored tow-placed plates

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American Institute of Aeronautics and Astronautics

OPTIMIZATION OF ELASTICALLY TAILORED TOW-PLACED PLATES WITH HOLES

Dawn C. Jegley*

NASA Langley Research Center, Hampton, Virginia 23681

Brian F. Tatting+

ADOPTECH, Inc., Blacksburg, Virginia 24060

Zafer Gürdal‡

Virginia Tech, Blacksburg, Virginia 24061

Abstract

Elastic stiffness tailoring of laminated composite panelsby allowing the fibers to curve within the plane of thelaminate is a design concept that has been demonstratedto be both beneficial and practical. The objective of thepresent paper is to demonstrate the effectiveness ofstiffness tailoring through the use of curvilinear fibersto reduce stress concentrations around the hole andimprove the load carrying capability of panels.Preliminary panel designs that are to be manufacturedand tested were determined through design studies forflat plates without holes under axial compression usingan optimization program. These candidate designswere then analyzed with finite element models thataccurately reflect the test conditions and geometries inorder to decide upon the final designs for manufactureand testing. An advanced tow-placement machine isused to manufacture the test panels with varying fiberorientation angles. A total of six large panelsmeasuring three feet by six feet, each of which is usedto produce four specimens with or without holes, arefabricated. The panels were machined into specimenswith holes and tested at NASA Langley ResearchCenter. Buckling response and failure of panels withoutholes and with two different hole dimensions arepresented. Buckling and failure loads of tow-steeredspecimens are significantly greater than the bucklingand failure loads of traditional straight-fiber specimens.

Introduction

One of NASA's goals is to reduce the cost of air travelby 50% in the next 20 years. To achieve this goal,NASA has been involved in the development of thetechnologies needed for future low-cost, light-weightstructures by varying the fiber orientations within a

composite structures for commercial transport aircraft.One such technology involves tailoring compositefibrous layer. Traditionally, fibrous layers of acomposite laminate are arranged such that theorientation of the fibers within each layer is constantthroughout a structural component, or only alloweddiscrete jumps from one section of the component toanother. For structures possessing stress states thatvary as a function of location within the laminate, notvarying the fiber orientation angle to match the changein stress state results in inefficient utilization of thedirectional stiffness and strength characteristics of thefibrous composite laminates. Allowing the fibers tocurve within the plane of the laminate furnishes atailoring possibility to account for a non-uniform stressstate, as well as providing other structural advantagessuch as the alteration of principal load paths. One ofthe traditional configurations in which stressdistribution is highly non-uniform is the case of a flatpanel with a central hole subjected to in-plane loading.Therefore, this sample problem will be studied todetermine the effectiveness of stiffness tailoringthrough the use of curvilinear fiber paths to reducestress concentrations around the hole and improve theoverall load carrying capability of the structure.

One of the first approaches to improve compressiveload carrying capability of composite laminates with anopen hole was the experimental work of Chou,1 whoinserted metal pins into woven fabric prior to curing,effectively pushing the fiber tows apart to create amolded hole. The resulting laminates possessedcurvilinear fibers around the hole and exhibitedimproved open-hole strength compared to traditionalstraight-fiber laminates with drilled holes. Hyer andCharette2 were among the first to investigate theinfluence of fiber orientation angle around a cutout fora flat plate with a circular hole. They proposed thatimproved designs could be realized by aligning thefibers with the principal directions of the stress field.Their finite element solution did demonstratesignificant improvement with respect to material failureload levels; however their curvilinear fiber designsshowed no increase in buckling load. A follow-up workby Hyer and Lee3 attempted to increase these buckling

* Senior Aerospace Engineer, Mechanics and Durability Branch, AssociateFellow, AIAA.+ Senior Engineer‡Professor, Departments of Engineering Science and Mechanics, andAerospace and Ocean Engineering, Associate Fellow, AIAA

This material is declared a work of the U.S. Government and is not subject to copyrightprotection in the United States.

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loads by using sensitivity analysis and a gradient searchmethod to determine the optimal fiber orientationangles in different regions of the plate modeled by agrid of finite elements. This method produced designswith substantial increases in buckling loads, mostlythrough the mechanism of transferring the majorstresses from the interior region to the edges of thepanel. Nagendra et al.4 also used finite element analysisto develop manufacturable designs, and demonstratedcomparable increases for plates with central holes.

Within the same time frame, research led by Gürdal andOlmedo5,6 implemented a definition for a variablestiffness ply with continuously varying properties basedon curvilinear fiber paths and formulated closed-formand numerical solutions for simple laminated plates. Afollow-up design study by Waldhart et al.7 againindicated increased buckling performance due to thestiffness variation, which caused re-distribution of theinternal loads toward the simply supported panel edgesand introduced favorable transverse stresses thatprovided additional mechanisms to improve thebuckling load of panels. This investigation alsointroduced several methods to define variable stiffnessplies from a small set of parameters. The methods werebased on a reference path defined by three angles, withsubsequent paths being constructed either “parallel” tothe original curved path or by defining paths identicalto the reference curve but “shifted” in the directionperpendicular to the axis of fiber orientation anglevariation. Considerations for the manufacturability ofthe plies, based on estimates for an advanced tow-placement delivery system, were also included toensure that the designs could be manufactured usingthese tow-steering methods.

The predictions based on these theoretical resultsprompted a need for experimental validation. Researchby the present authors8 led to the fabrication of twopanels using the VIPER® advanced tow-placementmachine developed by Cincinnati Milacron.9 Thepanels were based on prototype “shifted” methoddesigns from the study by Waldhart,7 and were built tovalidate the manufacturability of tow-steering throughthe application of the curvilinear-fiber formats.Photographs of the two panels during manufacture areshown in Fig. 1 and Fig. 2. The panel shown in Fig. 1has individual tow drops that remove any overlapbetween successive paths of the ply, while the panelshown in Fig. 2 allows the tows to overlap to produce apanel with thickness build-ups that act as “integralstiffeners”. Subsequent testing by Wu10,11 confirmedthe increased load-carrying capability of the variablestiffness panels with tow-drop and overlap construction,with gains of up to five times the compressive bucklingload of a straight-fiber panel.

These results illustrate the potential of the process and,therefore, the need for a design tool that can integratethese curvilinear-fiber-ply formats with standardlaminate design methodologies. Additional testing oflaminates constructed with these curvilinear plies isalso required to corroborate the earlier results and tofurther explore the possible benefits of the concept.Thus, the goal of the research presented in this paper isto design, manufacture, and test elastically tailoredplates that exhibit improved performance compared totraditional fiber-reinforced laminates. The configurationconsidered herein is a rectangular flat panel with acentral hole, loaded under axial compression. Theelastic tailoring is accomplished through the variationof the fiber orientation angle within each ply, which canbe manufactured with the aid of advanced towplacement machines. The design study, finite elementmodeling, and experimental results for this structure arepresented.

Laminate Design Utilizing Tow-Steered Plies

Common techniques for designing traditionalcomposite laminates typically utilize the ply-orientationangles of the orthotropic layers as design variables.The objective of the design problem is to find theoptimal stacking sequence that produces the bestlaminate, measured in terms of cost, weight, andperformance. Optimization techniques for discrete-valued design variables, such as genetic algorithms,12

are often used for this process, since laminates aretypically manufactured using discrete ply-orientationangles. For example, ply angle choices are oftenlimited to only 0° , ±45° and 90° orientations tofacilitate construction and reduce scrap. Furthermore,limiting a ply orientation to a set of well-chosendiscrete angles, as opposed to treating them ascontinuous variables, enables the optimizer toinvestigate the global design space more efficiently,since stacking sequence design depends more on thenumber and ordering of the laminae rather then theexact values for the orientation angles.

For plies constructed using advanced tow-placementtechniques, the manufacturability of a given ply angle isno longer limited to a small set of possibilities. Thesecomputer-controlled machines are capable of efficientlyplacing fiber-reinforced tows at almost any orientationdesired while changing the orientation continuouslyfrom one location to another. The only majorconstraints in this process are the turning radius of thetow path (too small of a radius results in wrinkling ofthe tows) and the shape of the surface (the applicatorhead must have sufficient clearance for concavesurfaces). However, this freedom is certainly adisadvantage for the optimizer, since the design spacethat was governed by simple discrete values for each

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ply now becomes a complex continuous variabledomain which depends on spatially-varying orientationangles as well as practical manufacturing constraints. Aremedy for this disadvantage is to use a parametricrepresentation of the fiber orientation within the platestructure. Therefore, the following section will outline auseful parameterization for tow steered plies, whichwas originally proposed by Gürdal,5-8 that reduces thedefinition of a ply to a handful of global variables.These parameters can then be discretized into atractable set to be used with a discrete-valued optimizer(much like the ply orientation angles for typicalstacking sequence optimization), where the set of tow-steered plies can be ensured to satisfy themanufacturing constraints before the design analysesare performed. That is, ensuring manufacturabilityreduces the design space by eliminating thosecombinations of the parameters from consideration. Inthe following sections, methods to analyze and designlaminates that use these tow-steered definitions arediscussed, followed by design results for the sampleproblem of a panel with a central hole.

Parameterization of Tow-Steered Plies

The design parameters used here are based on earlierwork by Gürdal,5-8 who introduced a general referencepath based on a linear variation of the fiber orientationangle in a specified direction. The method assumes thatthe surface to be considered can be represented by two-dimensional surface coordinates (x, y), and is based onthe specification of the paths traveled by the head of thetow-placement machine during fabrication.

A graphical representation of the reference pathdefinition is shown in Fig. 3. The origin and majordirection of the reference path are defined by a point(x0, y0) and angle φ, respectively. The relativetranslation and rotation of a tow-steered ply definitioncan be easily applied. At the origin, the angle T 0

represents the initial orientation of the tows with respectto the major direction of variation. The orientationangle varies linearly in a saw-tooth manner such that itsvalue is T1 at a distance d along the variation axis, andthen changes back to T0 at a distance of 2d . Thevariation is symmetric about the origin of variation.This linear variation of the orientation angle yields asmooth continuous curve which represents the path ofthe centerline of the tow placement machine’sapplicator head (the dotted line in Fig. 3). For theVIPER® tow-placement machine used here forfabrication, the applicator head has a total width of 3inches (24 individual tows, each 1/8 in. wide), resultingin a swath of material being laid down in the mannershown in Fig. 3.

To construct an entire ply using this reference curve,additional courses are laid down by shifting the

reference path in a direction perpendicular to theφ−direction. This shift distance is calculated so that nogaps exist between adjacent courses. Due to thecurvature of the reference path and the shiftedconstruction method used for additional courses,overlaps may exist between tows of adjacent courses(as shown in Fig. 4, in which the light gray arearepresents the overlap region). Two techniques areemployed to handle this overlap. The first, referred toas the “tow-drop” method, instructs the fiber placementmachine to cut/drop individual tows within each pass sothat no thickness build-up occurs in the regions ofoverlapping paths. These fiber terminations result inconstant thickness panels that contain small wedge-likeareas that contain no fibers due to the dropping of theindividual tows. The second construction method iscalled the “overlap” method and allows for full overlapbetween adjacent paths, which leads to considerablethickness build-ups for some areas of the panel (as isevident for the overlap panel shown in Fig. 2).Numerical algorithms were developed to generatecourse data for a given ply-path definition andconstruction method as well as to find the actual fiberorientation angle for a given (x, y) point (note that forthe overlap method, some locations may have twoangles due to the overlap of neighboring paths).

For the present design study, the origin (x0, y0), majordirection φ, and characteristic distance d are determinedby the geometry and expected loading of the structure,and the angles T0 and T1 are the design variables. Such aply is designated by the shorthand notation φ<T0|T1>.Additionally, a calculation of the turning radius alongthe path can be easily performed once all theparameters are defined, and configurations that possessa minimum turning radius below the allowable limit (25in. for the VIPER® tow-placement machine) can beremoved from the allowable set of designs. Furtherdetails on parameter restrictions are discussed in theformulation of the design study.

Analysis of Tow Steered Laminates

Due to the variable nature of the fiber orientation for atow-steered ply, each location has a different stackingsequence that depends on the parameter specification.This variation leads to laminates with spatially-varyingstiffness measures, which require modifications tostandard analysis techniques. Two such techniques usedto assess the performance of tow steered laminates aredescribed in this section.

Finite Element Solutions. For a traditional finiteelement package, the variable stiffness behavior impliesthat each element must have a unique stacking sequenceassociated with it and that the stiffness parameters areconstant over the domain of the element. The nature of

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the finite element technique also requires that thesmooth curves of the tow paths will be discretized bythe geometry of the element mesh, and therefore adense mesh is needed for accurate modeling of thestiffness variation. In general, this mesh requirementleads to large models that require an automaticalgorithm to calculate each stacking sequence and linkit to the corresponding element location. To facilitatethis re-definition, software was developed that cantransform suitable finite element meshes into variable-stiffness laminates that are specified using the tow-steering parameters introduced earlier.

A screenshot of the re-definition software, referred to asLDT for Laminate Definition Tool, is displayed in Fig.5. The necessary parameters for the tow-steeredlaminate definition are entered in the appropriate fields.To perform the transformation, a valid finite elementmodel is selected for the input file name. Presently,models are limited to flat structures lying in the x-yplane, though in general any structure that can berepresented by surface coordinates can be implemented.The input file must be in an acceptable format for thefinite element package that is being used for analysis(GENESIS/NASTRAN13 and STAGS14 are currentlysupported). Subsequent execution reads in the file,calculates a stacking sequence at the centroid of eachelement and assigns it to a unique property, and re-writes the input file with the elements associated withthe new properties. Though the procedure is quitestraightforward, the large number of stacking sequencecalculations and associated input/output leads tosignificant process time. For example, finite elementmodels that were used in this study, consisting of10,800 elements, required approximately five minutesto be transformed into tow steered designs. Though thisis a reasonable allowance for the generation of newmodels, it is generally prohibitive within a designprocess. Moreover, the computational cost of eachfinite element anlaysis is high, making it undesirablefor the repetitive analyses that are needed forconceptual or preliminary design studies. Therefore, amore efficient Rayleigh-Ritz technique that solves theunderlying governing equations for the variablestiffness laminates has been developed for simple flatplates. While the Rayleigh-Ritz technique is veryuseful for initial design work, it is not a substitute forthe more detailed finite element analysis needed forfinal design.

Rayleigh-Ritz Solution. This numerical solutionconcerns a flat rectangular panel with simply-supportededges subject to combined in-plane loading. The panelis constructed of a symmetric laminate using traditionaland curvilinear fiber-reinforced plies. For variable-stiffness laminates, algorithms exist to calculate theClassical Lamination Theory (CLT) stiffness terms (Aij,

B ij, Dij), which are continuous functions of the panelcoordinates, at an arbitrary point based on the tow-steered layup definitions described earlier. For the in-plane response, the loading is introduced throughconstant normal and shear displacements at the edgesand the reaction forces are summed to calculate theaverage stress resultant applied to each edge. Thistechnique is used to allow for stiffness variations withinthe panel that generate non-constant distributions ofstresses along the boundaries. Following the Rayleigh-Ritz technique, typical expansions in terms of doubletrigonometric series are formulated for the in-planedisplacements u and v as well as the variable CLTstiffness parameters. Insertion of these expansions intothe integral representing the total potential energy of thesystem and minimizing with respect to the unknownexpansion coefficients yields a linear system ofequations. For constant-stiffness laminates, theequations reduce to the trivial solution of constantloading. The in-plane solution for the variable stiffnesslaminates is used to measure material failure byinvestigating the stress state for an evenly spaced gridof points within the panel. Additionally, a linearbuckling estimate is performed, where the stressresultants serve as the prebuckling state and the out-of-plane displacement w and bending stiffness matrix Dij

are similarly expanded in trigonometric series andinserted into integrals for the potential energy of thepanel.

The solution just described is formulated as a Fortran90 code. Though both the tow-drop and overlapmethods are implemented, the discontinuities inthickness due to the overlap technique are not asaccurately modeled through the trigonometricexpansions, and require significantly more terms (andtherefore more computation time) than constantthickness laminates for accurate modeling. Thus mostof the computations performed with this algorithmassume no overlaps are present. Computation times fora typical variable stiffness solution (using seven termsin each direction for the expansions of thedisplacements) average around three seconds on atypical 400-MHz PC platform. For traditional straight-fiber laminates, which possess constant stiffnessthroughout the panel, several simplifications can bemade in the equations and the analysis times reduce tosignificantly less than half a second. Comparisons ofthe results of this numerical solution have been madewith dense finite element models, and have been shownto agree well within tolerable limits (less than 1% error)for both the in-plane response and buckling estimate ofa tow-drop design.15

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Design Study for Flat Panel with Central Hole

To assess the potential of the tow-steering concept toincrease buckling loads, a design study is conducted fora flat panel with a central hole under axial compression.Panel dimensions, boundary conditions, and hole sizesare shown in. Fig. 6. The presence of the central holeand the fixed boundary conditions at the top and bottomlead to a highly variable stress state within the structure,for which the curvilinear-fiber formats exhibit promisein increasing buckling and failure loads. A designstudy is performed to assess the increased buckling loadthat is attainable using tow-steered plies.

Design Technique. Since the finite element modeldefinition and analysis for tow-steered laminates arecomputationally expensive, stacking-sequence-designoptimization that utilizes a discrete mathematicalprogramming approach is not suitable due to the largenumber of analysis runs required. Therefore, thesimpler Rayleigh-Ritz solution is used for thepreliminary design phase. Though this approach willenable a thorough investigation of the design space, thesimplified analysis does not take into account thecentral hole, the test fixture boundary conditions, orallow for calculations representing the overlap method.However, earlier results7 have shown that the majormechanism to improve the buckling load using tow-steered plies is to redistribute the load away from thecenter of the panel by having stiffer sections near theedges. Since the tow-drop method can fulfill thisobjective, the simplified analysis for a panel withidentical dimensions as the test specimen is used in thepreliminary design phase. The results will supplyseveral candidate designs that will be further analyzedwith the more accurate finite element techniques. Theprototype designs that will be manufactured and testedare determined. from this set

Design Study Results. The design studies wereconducted using OLGA16,17 (Optimization of Laminatesusing Genetic Algorithms), an in-house laminate designtool that implements tow steered plies for flat panelstructures. Two design studies were conducted. Thefirst design study considered only straight-fiber plies, toserve as a baseline for the tow-steered panels. A 15 in.by 20 in. rectangular panel constructed from AS4/977-3material was defined within OLGA, subject to a 1 lb/in.compressive load in the axial direction. Materialproperties corresponding to a typical AS4/9773 systemwere used in the OLGA and finite element designstudies. Specifically, longitudinal modulus, E1=18.83Msi, transverse modulus, E2=1.34 Msi, shear modulusG1 2=0.64 Msi, Poisson’s ratio ν12=0.36, densityρ=0.058 lb/in3 and ply thickness of 0.0075 inches.

Loads corresponding to buckling and to material failureusing the Tsai-Hill criterion were calculated for thecandidate laminates. Laminates for fabrication wererequired to have greater failure loads than bucklingloads. The laminate was further restricted to besymmetric and constructed of twenty plies. The designvariables were based on the fiber-orientation angles T0

and T1 within each layer and were allowed to vary in15 ° increments. Two-ply stacks of plus/minusorientations were also used to ensure the laminate wasbalanced and to effectively reduce the size of the designspace. The best design from the straight-fiber studywas found to be a laminate with a stacking sequence of[±452/±30/±45/±15]s, which possessed a buckling loadof 7903 lbs.

The second design study used the tow-drop method forthe internal plies. The external plies were constrained tohave straight fibers so that gaps and overlaps did notexist on the exterior of the laminate. The origin of thevariation was placed in the center of the panel, thevariation direction was perpendicular to the loading(φ = 0), and the value of characteristic dimension d waschosen to be one-half the width of the panel. Thebuckling predictions for the five best tow-drop designsare shown in Table 1.

Table 1. Results from OLGA design study

Design Number and LayupBucklingload (lbs)

0 (Baseline): [±452/±30/±45/±15]s 7,903

1: [±45/0±<45|60>2/0±<45|30>/0±<45|15>]s 9,313

2: [±45/0±<45|60>/0±<30|15>/0±<45|60>2]s 9,244

3: [±452/0±<45|60>/0±<30|15>/0±<45|60>]s 9,225

4: [±±±±45/0±±±±<45|60>2/0±±±±<30|15>/0±±±±<45|60>]s 9,211

5: [±45/0±<30|45>/0±<45|60>2/0±<30|15>]s 9,186

To verify the trends found using OLGA, five candidatedesigns were then analyzed with STAGS,14 using both asmall (1.5-in. diameter) and large (3.0-in. diameter)hole. The finite element models for the rectangularpanel with a small or large central hole are shown inFig. 7 and Fig. 8, respectively. The small-hole modelcontains 6206 elements with ~37,000 degrees offreedom, while the large-hole model has 5694 elementsand ~34,500 degrees of freedom. These models aredesigned to accurately model the test fixture to be used.On the top and bottom edges, the two inches of pottingis modeled by allowing displacement only in the axialdirection. The load is introduced through a constantcompressive force at the top of the potted edge, whichis constrained to remain straight, while the bottom edgeis held stationary. Out-of-plane displacement and

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rotation about the x-axis are restrained approximately0.2 inches from each unloaded edge to simulate theeffect of the knife edges in the test. The mesh densityyields elements that are approximately 0.25 in. on eachside, which was determined through parameter studiesto be small enough to accurately model the variations inthickness due to the curvilinear fibers and the overlaps.

Predictions of the buckling loads for the baseline design(0) and the tow-steered designs (1-5) using bothconstruction techniques and based on finite elementanalysis are shown in Table 2.

Table 2. Finite element results for candidate designs

Buckling load (lbs)DesignNumber 1.5-in.

hole3.0-in.hole

1.5-in.hole

3.0-in.hole

0 9,124 8,339 - -

Tow-drop Method Overlap Method

1 10,168 9,388 13,653 12,710

2 9,988 9,141 13,787 12,954

3 9,904 9,096 12,530 11,725

4 10,387 9,557 14,301 13,499

5 10,143 9,306 13,541 12,738

Differences between the buckling loads presented intables 1 and 2 (O L G A predictions and STAGSpredictions, respectively), are attributed to the presenceof the central holes as well as the fixed-end boundaryconditions. From the results of Table 2, the fourthdesign was chosen as the prototype design to be usedfor manufacture and testing and is identified by boldtype in Tables 1 and 2.

Manufacturing of Prototype Designs

The chosen layup for the tow-steered design, denoted as[±45/0±<45|60>2/0±<30|15>/0±<45|60>]s, must betranslated into ply data that can be decoded by the tow-placement machine. Algorithms were produced toperform this task, which at the same time served as auseful tool for visualizing the construction of the plyand improving the design of the laminate. The next twosections discuss alterations that were made to theprototype designs before fabrication to improve thereliability of the test panels. However, due tounavailability of the planned material, a G40-800/977-2material system was substituted. The primarydifference between these two systems is the tapethickness. The original design was for tape with a0.0075-inch thickness but the new material has a tapethickness of 0.0055 inches. Therefore, even though thedesign stacking sequences were used, the final panels

are much thinner and therefore have lower bucklingloads and additional analysis was required to correlateanalysis and test results.

Staggering Technique for Tow-Steered Plies

The prototype tow-steered layup contains two differentsteered-ply groups: a 0±<45|60> group, of which thereare three pairs; and a single pair of 0±<30|15>. Aftercalculating the resulting ply paths for each ply andanalytically assembling the entire laminate, areas ofthickness build-up for the overlap method can beplotted. Such a result is shown in Fig. 9, where thecentral holes to be machined are shown as dashedcircles and the shaded regions represent an increasednumber of plies due to the overlaps between towcourses. However, though the increased plies providegreater stiffness near the unloaded edges of the panel(which is what increases buckling loads), the discreteincrease from 20 plies to 26 plies in the major overlapregions is considered to be too drastic to reliablymanufacture. Therefore, the ability to easily change theorigin of the tow-steered design, through the use of the(x0, y0) parameters, was called upon to stagger the0±<45|60> ply groups in the vertical direction andprovide a more consistent thickness variation for thepanel. Note that this staggering is different from theshifting of the tows discussed previously. The shiftingin the reference path is to account for the non-zerowidth of the tow and is applied to each tow within aply. The staggering is to smooth the overall thicknessand changes the origin of the entire ply. This modifiedlayup, shown in Fig. 10, has the same stackingsequence as the one in Fig. 9 but because of staggeringit has an improved thickness variation as can beobserved from the figure. This alteration was alsoperformed for the tow-drop method to spread out thelocations of the gaps resulting for the tow drops.Although the interweaving reduced the variation inthickness, the buckling load calculated by finite elementanalysis showed no appreciable decrease. The resultingchanges in buckling load were less than 1%. Therefore,this technique of interweaving ply groups isrecommended whenever identical ply groups arepresent in a tow-steered design.

Fabrication and Preparation of Test Specimens

In order to minimize the set-up time and cost offabrication, four test panels with the same layup wereconstructed simultaneously as one large sheet and thenindividual specimens machined after cure.Simultaneous fabrication also reduces overall machinetime and eliminates scrap as the edges always haveunusable tow-start areas, as well as producing testspecimens that are manufactured and cured in the sameenvironment.

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The formulation used to define the curvilinear fibercourses is conducive to defining the layup for the largesheet, since the definition repeats with period 2d (whichis equal to the individual panel width by design). Thepattern for cutting four test specimens from one largepanel is shown in Fig. 11 for the overlap method. Thepattern in the figure shows the thicknesses withoutstaggering the plies and is for illustrative purposes only.Staggering was used in the fabricated panel. In thefigure, the darker regions indicate the increasedthickness build-up due to the three 0±<45|60> plygroups and the 0±<30|15> ply group is the lighter andshallower curves. Note, however, that the overlapregions are symmetric about each panel center due tothe cyclic nature of the tow steering definition, yet theintersections of oppositely oriented overlap regions arenot regularly spaced across the sheet. This artifact isdue to the fact that the locations of the intersections donot depend merely on d, the characteristic distance ofthe fiber orientation definition, but also on the directionof the fiber course and the width of the tow-placementhead. For example, if the general direction of theoverlap regions are aligned at positive and negativeforty-five degrees, the intersections will occur muchmore frequently than if the direction is at fifteendegrees. Therefore, when overlaps are used, the fourspecimens are not exactly identical due to the non-regular spacing of the intersection points.

Finally, in light of the result that the overlap panelsdepend on the width of the tow placement head, aninvestigation was conducted to determine the best headwidth to use for the tow steered designs. The defaultvalue corresponds to 24 tows that are 1/8 inch wide(3.03 inches total, allowing for a 1% space betweentows). Models were constructed and analyzed using 12to 36 tows to determine if the different head widthsdemonstrated increased buckling resistance due to thedifferent location of the overlap intersections.However, the results showed little difference betweendesigns with different head widths (less then 2% overthe total range). Therefore the designs will use thedefault value of 24 tows, which is the maximumnumber of tows in the actual tow placement machineand should minimize fabrication time.

Also shown in Fig. 11 are the locations of the centralholes for testing, which will be machined in when thespecimens are processed. For the tow-steered panels(manufactured using the tow-drop and overlapmethods), two test specimens each for the two differenthole sizes were produced. For the straight-fiber panel,a baseline specimen with no hole was produced, as wellas one with the smaller central hole and two with thelarger hole. The test specimens are labeled anddifferentiated by construction method (A = straight-

fiber; B = tow-drop; C = overlap) and position on thelarge panel (1-4, numbered from left to right).

All specimens were potted in two inches of epoxycompound on each end and the ends ground flat andparallel to each other. A photograph of an overlapspecimen with a large hole (specimen C3) is shown inFig. 12. Knife-edge supports were appliedapproximately 0.2 inches from the unloaded edges asshown in Fig 6. to restrain out-of-plane motion. Thespecimen was instrumented with strain gages andDCDTs (Direct Current Displacement Transducers).Back-to-back strain gages were applied at the mid-length location and 2 inches from the potting for eachspecimen, as shown in Fig. 12. Two DCDTs were usedto measure end-shortening and two were used tomeasure out-of-plane displacement for each specimen.An out-of-plane displacement measurement was takenat the axial quarter point directly above the center of thespecimen and another was taken close to the hole, at themid-length location. Measurement locations are shownin Fig. 6. Shadow Moiré interferometery was also usedto monitor out-of-plane displacement patterns of eachspecimen. Each specimen was loaded to failure at arate of approximately 1,000 lb/min.

Results and Discussion

Buckling load predicted by finite element analysisusing models conforming to the manufactured designs,using the smaller thicknesses of 0.0055 inches per plyfor the as-manufactured panels, are shown in Fig. 13.Experimentally determined buckling and failure loadsare also shown in Fig. 13. All specimens carried loadwell in excess of the buckling load. The overlapspecimens carried significantly more load than thecomparable tow-drop specimens.

Displacement predictions are shown in Fig. 14-16 forstraight-fiber, tow-drop, and overlap specimens withlarge holes (specimens A4, B3, and C3, respectively).Experimental results are also shown in the figures.Reasonable agreement is observed for the straight-fiberspecimen but buckling and post-buckling behavior isnot as accurately predicted for the tow-steeredspecimens. However, the tow-drop specimensgenerally have buckling loads about 10 percent greaterthan the comparable straight-fiber specimens, while theoverlap specimens achieve buckling loads almostdouble that of the constant-stiffness counterparts.Finite element analysis accurately predicts mode shapesand mode shape changes in most cases, as evidenced bythe reversal of displacement shown in figures 14-16 forboth the experiment and the analysis. Experimentalbuckling loads are significantly greater than analyticalpredictions for some cases. Possible explanations forthis difference include the differences in the assumedand actual material properties, thermal effects involved

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in curing anisotropic panels, and imperfections causedby manufacturing irregularities. Since these factorswould contribute significantly to a failure prediction, noanalytical predictions of failure are presented andanalysis was terminated in some cases at load levelsless than the experimental failure load, but alwayscontinued until at least double the initial buckling load.

Out-of-plane displacement patterns reveal that mostspecimens initially buckled into one half-wave in eachdirection. Some specimens changed mode shape byconsequently buckling into two half-waves in the axialdirection. Photographs of out-of-plane displacementpatterns for the large hole specimens are shown in Fig.17-18 (straight-fiber specimen A4), Fig. 19-20 (tow-drop panel B3), and Fig. 21-22 (overlap panel C3) forload levels corresponding to a load just greater than theinitial buckling load and for a load just less than failure.No predictions for failure loads are made. However, asshown in Fig. 13, specimen failure loads aresignificantly greater than buckling loads in all caseswith the overlap specimens carrying loads more thanthree times their buckling loads. Most specimen failureswere in the corners, not at the hole edge.

Concluding Remarks

Software tools developed for the analysis and design oftow-steered composite laminates were used to explorethe benefits of curvilinear fiber concepts for tailoring ofrectangular laminates with circular holes.Parameterization of tow-steered plies using a smallnumber of variables provided an efficient strategy forrigorous optimization based on a simplified analysisprocedure. Software tools also made it possible tointegrate the tow-steered ply definitions with a state-of-the-art finite element program for detailed analysis ofthe laminates under general loading and boundaryconditions representative of experimental conditions.

The systematic procedure from design to fabricationemployed in this project produced an excellent methodfor incorporating manufacturing constraints within thedesign process. By limiting the design choices tofeasible configurations, the optimized designs could bedirectly translated to machine language to provide exactagreement with the prototype parts. The resultspresented here indicate that significant increases inload-carrying capability compared to traditionalstraight-fiber laminates can be realized, anddemonstrate that elastic tailoring is a useful techniquefor improving the performance of composite laminates.Experimental results verify that the tow steeringtechnique can be used to fabricate specimens withincreased buckling and failure loads. To achieve amore accurate analytical results for load beyond thebuckling load for these specimens, a more detailed

finite element analysis taking into account more of themanufacturing irregularities in the fabricated pieceswould be required.

References

1. Yau, S. S., and Chou, T. W., “Strength of Woven-Fabric Composites with Drilled and Molded Holes,”Composite Materials Testing and Design, ASTM STP-972, American Society for Testing and Materials,Philadelphia, PA, 1988, pp. 423-437.

2. Hyer, M. W., and Charette, R. F., “The Use ofCurvilinear Fiber Format in Composite StructureD e s i g n , ” P r o c e e d i n g s o f t h e 3 0 t h

AIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics and Materials (SDM) Conference, NewYork, NY, 1989, paper no 1404..

3 . Hyer, M. W., and Lee, H. H., “The Use ofCurvilinear Fiber Format to Improve BucklingResistance of Composite Plates with Central Holes,”Composite Structures, Vol. 18, 1991.

4 . Nagendra, S., Kodiyalam, A., Davis, J. E., andParthasarathy, V. N., “Optimization of Tow Fiber Pathsfor Composite Design,” Proceedings of the 36t h

AIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics and Materials (SDM) Conference, NewOrleans, LA, April 1995, AIAA paper no. 1275.

5. Gürdal, Z., and Olmedo, R., “In-Plane Response ofLaminates with Spatially Varying Fiber Orientations:Variable Stiffness Concept,” AIAA Journal, Vol. 31,(4), April 1993.

6. Olmedo, R., and Gürdal, Z., “Buckling Responseof Laminates with Spatially Varying FiberOrientat ions,” Proceedings of the 34 t h

AIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics and Materials (SDM) Conference, La Jolla,CA, April 1993, paper no. 1567.

7 . Waldhart, C. J., Gürdal, Z., and Ribbens, C.,“Analysis of Tow Placed, Parallel Fiber, VariableStiffness Laminates,” Proceedings of the 37th

AIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics and Materials (SDM) Conference, Salt LakeCity, UT, April 1996, paper no. 1569.

8 . Tatting, B. F., and Gürdal, Z., “Design andManufacture of Tow-Placed Variable StiffnessComposite Laminates with ManufacturingConsiderations,” Proceedings of the 13th U.S. NationalCongress of Applied Mechanics (USNCAM),Gainesville, FL, 1998.

9. Evans, D. O., Vaniglia, M. M., and Hopkins, P. C.,“Fiber Placement Process Study,” 34th InternationalSAMPE Symposium, May 1989.

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10. Wu, K. C., and Gürdal, Z., “Thermal Testing ofTow-Placed Variable Stiffness Panels,” Proceedings ofthe 42nd AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics and Materials (SDM) Conference,Seattle, WA, April 2001, paper no. 1190.

11. Wu, K. C., Gürdal, Z., and Starnes, J. H.,“Buckling and Postbuckling of Tow-Placed VariableStiffness Panels,” Proceedings of the 43r d

AIAA/ASME/ASCE/AHS/ASC Structures, StructuralDynamics and Materials (SDM) Conference, Denver,CO, April 2002, paper no 1512.

12. Gürdal, Z., Haftka, R.T., and Hajela, P., Designand Optimization of Laminated Composite Materials,John Wiley and Sons, Inc., New York, NY, 1999, pp.185-218.

13. Vanderplaats Research and Development, Inc.,“GENESIS User Manual,” Colorado Springs, CO,2000.

14. Rankin, C. C., Brogan, F. A., Loden, W. A., andCabiness, H. D., “STAGS Users Manual,” LockheedMartin Missiles & Space Co., Inc., Report LMSCP032594, June 2000.

15. Tatting, B., and Gurdal, Z., Design andManufacturing of Elastically Tailored Tow PlacedPlates, NASA/CR 2002-211919, August 2002.

16. Soremekun, G. A. E., and Gürdal, Z., “AdvancedGenetic Algorithms for Designing Complex LaminatedStructures,” Proceedings of the American HelicopterSociety Hampton Roads Chapter, Structure Specialists’Meeting, Williamsburg, VA, October 2001.

17. Tatting, B. F., and Gürdal, Z., “Analysis andDesign of Tow-Steered Variable Stiffness CompositeLaminates,” Proceedings of the American HelicopterSociety Hampton Roads Chapter, Structure Specialists’Meeting, Williamsburg, VA, October 2001.

Fig. 1. Fabricated panel using tow-drop method.

Fig. 2. Fabricated panel using overlap method.

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Reference path

(x0, y0)

x

φ

y

d

T1

Major direction

T0

Fig. 3. Geometry of reference path.

Reference path for first course

x

y

Major direction

Reference path for second course

Overlap region

Shift

Fig. 4. Adjacent courses with overlap region.

Fig. 5. Screenshot of Laminate Definition Tool (LDT).

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D = 1.5, 3

a = 15

∆ Potted end

Potted end

Knife edge

Knife edge

y

x

b = 20 DCDT locationsare marked by

Fig. 6. Geometry of test specimen (lengths in inches).

X

Y

-10 -5 0 5 10

-10

-5

0

5

10

Fig. 7. Finite element mesh for small-hole model.

X

Y

-10 -5 0 5 10

-10

-5

0

5

10

Fig. 8. Finite element mesh for large-hole model.

Plies32313029282726252423222120

Fig. 9. Thickness distribution for original overlap modelwithout staggering plies.

Plies32313029282726252423222120

Fig. 10. Thickness distribution for modified overlapmodel with staggered plies.

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Location of machinedcuts after cure

Holes machinedafter cure

Fig. 11. Panel construction of adjacent specimens. Note that the fabricated panel used the staggered plies rather thanthe original pattern shown here.

Fig. 12. Overlap specimen C3 prior to testing.

0

5,000

10,000

15,000

20,000

25,000

30,000

Predicted buckling loadExperimental first buckling loadFailure load

Load, lb

StraightFibers

Tow dropPattern

Overlap Pattern

1 2 3 4 1 2 3 41 2 3 4

1 No hole for straight fibers, small hole for tailored2 Small hole3 Large hole4 Large hole

Fig. 13. Failure and buckling loads of tested specimens.

Straingage

13


Displacement, inches-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.50

5000

10000

15000

STAGS resultsTest data

Center out-of-planedisplacement

End shorteningMid-heightout-of-planedisplacement

Buckled into twoaxial half-waves

Buckled into oneaxial half-wave

Load,lb

Fig. 14. Displacements for straight-fiber specimen A4.

Displacement, inches-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

0

5000

10000

15000

20000



End shortening

Mid-heightout-of-planedisplacement

Buckled into twoaxial half-waves

Buckled into oneaxial half-wave

Load,lb

Fig. 15. Displacements for tow-drop specimen B3.

Displacement, inches-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.40

5000

10000

15000

20000



End shortening

Mid-heightout-of-planedisplacement

Buckled into twoaxial half-wavesBuckled into one

axial half-wave

Load,lb

Fig. 16. Displacements for overlap specimen C3.

Fig. 17. Out-of-plane displacement straight-fiberspecimen A4 subjected to a load of 4300 lb.

Fig. 18. Out-of-plane displacement pattern for straight-fiber specimen A4 subjected to a load of 11,900 lb.

Fig. 19. Out-of-plane displacement pattern for tow-dropspecimen B3 subjected to a load of 6200 lb.

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Fig. 20. Out-of-plane displacement pattern for tow-dropspecimen B3 subjected to a load of 18,600 lb.

Fig. 21. Out-of-plane displacement pattern for overlapspecimen C3 subjected to a load of 7700 lb.

Fig. 22. Out-of-plane displacement pattern for overlapspecimen C3 subjected to a load of 24,100 lb.

optimization of elastically tailored tow-placed plates

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