CONCEPTUAL DESIGN AND OPTIMIZATION OF A HIGH ASPECT RATIO UAV WING MADE OF COMPOSITE MATERIAL

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1 ICAS 000 CONGRESS CONCEPTUAL DESIGN AND OPTIMIZATION OF A HIGH ASPECT RATIO UAV WING MADE OF COMPOSITE MATERIAL K. Widmaier, F. M. Catalano Aircrat Laboratory University o São Paulo Brail Abstract The applicability o an optimiation routine included in the Ansys sotware applied to iber reinorced structures was analyed via a practical eample. A laminated wing was modeled and optimiation parameters were deined such as weight, iber orientation angle and ailure criteria. Two optimiation methods were used. Results are analyed and the method restrictions are discussed and other methods are proposed. Notation b Cl E F cu FLTHK F su F tu G L MAXFC ν ρ S θy θ u u V WEBTHK ξ wing span lit coeicient Young s modulus ultimate load in compression lange thickness ultimate shear load ultimate load in tension shear modulus lit ma ailure criteria Poisson ratio Density wing surace area stress ailure stress rotation in y rotation in displacement in direction displacement in direction velocity web thickness ailure criteria value Introduction Unmanned air vehicles (UAV's) ly typically long endurance missions, at high altitudes. Thereore, it is very important that the aircrat has a high lit to drag ratio. That can be accomplished using a high aspect ratio wing which its inherent low induced drag. Also advanced materials like laminated composites can be employed. They have a high strength to weight ratio, allow an eellent inishing (less riction drag) and can have his properties changed easily, by changing his lamination orientation and sequence, in order to optimie it. E-GLASS/EPOXY TWO- DIRECTIONAL POLYURETHANE FOAM ρ = 00 kg/m 3 ρ = 35kg/m 3 E = 5,9 Gpa E = 0,3 Mpa E = 5,9 Gpa ν = 0,5 E 33 = 8,7 Gpa G = 4, Mpa ν = 0,0 F tu = 50 Kpa ν 3 = 0,8 F cu = 50 Kpa ν 3 = 0,8 F tu y = 50 Kpa G = 4, Gpa F cu y = 50 Kpa G 3 =,9 Gpa G 3 =,9 Gpa F tu = 8 Mpa F cu = 65 Mpa F tu = 8 Mpa F cu = 65 Mpa F su = 50 Mpa Table. Mechanical properties o the bi-directional laminated o E-Glass (60%) with Epoy matri and o the polyurethane oam. Moreover, the minimiation o the structural mass o the aircrat is a primary objective o the manuacturers. In 743.

2 K. Widmaier, F. M. Catalano consequence, a large number o very eicient private and commercial systems are being created, by using optimiation routines together with inite elements modeling []. Here one o those commercially available FABRIC FOAM Figure. Typical sandwich lamination sequence ( ). Figure. Central wing section cut view. routines will be studied. It is included in Ansys, and here is applied to the optimiation o laminate composite structures. The use o iber reinorced composite leads to many optimiation possibilities. Due to the orthotropic characteristic o the composite, it is possible to design the material, avoring the properties o the composite in the "low" directions o the tensions. Another advantage is the easiness o obtaining comple orms, and the easy alteration o the laminated characteristics, such as thickness, orientation o the iber and number o layers. The wing here modeled is laminated, with a sandwich sequence o lamination as seen in igure. Bi-directional Glass abric is used with a matri o Epoy resin and polyurethane oam, whose properties are in the Table. In igure can be seen a cut o the wing. The initial sequence o lamination obeys the pattern , symmetrical to the central oam layer. The I spar section is positioned where the section o the wing has the largest thickness. The langes o the spar are unidirectional woven, aligned with the ais o the spar. Two ribs were placed. One in the root and other in the tip o the wing. For the siing o the wing it is necessary to determine which are the cases in that the wing suers a maimal loading. Here or simplicity just one case will be considered, equivalent to an abrupt pitch o the airplane lying in the maimum speed o maneuver, VA. In this situation the wing reaches the maimum Cl. Theoretical considerations For the ail analysis in the laminated the Tsai- Wu ailure criteria was used. It leads to the lightest structures []. This theory postulates that or an orthotropic material [3] and [4], ail occurs when <, being: ξ = B A B A A (.) A = y y y t yt t c ( y ) ( y ) ( ) C t y B = t y yt C yt yt y y t c y C t t c t c (.) (.3) 743.

3 CONCEPTUAL DESIGN AND OPTIMIZATION OF A HIGH ASPECT RATIO UAV WING MADE OF COMPOSITE MATERIAL where, Cy = coeicient o joining -y or theory o Tsai-Wu (=Fy) Cy = coeicient o joining -y or theory o Tsai-Wu (=Fy) C = coeicient o joining -y or theory o Tsai-Wu (=F) where Fij are tension tensors, i the principal tensions and i - the ultimate tensile loads. For the determination o the loading, the distribution o Cp along the wing chord was ound using a simple panel method, that resulted in the distribution shown in igure 3. Then it was approimated or a polynomial using Mathematica or the upper and lower wing surace. Along the span the pressure distribution varies elliptically. The distribution can then be approimated using the ollowing equation: Cp(Y) y = (.4) b Figure 3. Chord Cp distribution (α = o ). 3 Modeling description Structural Optimiation is a technique that tries to determine an optimum design [5]. For "optimum" design we understand one that satisies all the requested speciications but with a minimum ependiture o certain actors as weight, supericial area, volume, tension, cost, etc. In other words, the optimum design is usually the one that is so eective as possible. Beore describing the optimiation procedure, some basic deinitions will be given: design variable, state variable, objective unction, analysis ile, etc. Design Variables (DVs) are independent quantities that are varied with the objective o obtaining the best design. Superiors and inerior limits are speciied to serve as "contour" in the design variables. State Variables (SVs) are quantities that deine the speciications o the design. They are also known as "dependent" variables, and are typically resulting quantities that are unction o the design variables. The Objective Function is the dependent variable that is being minimied. It should be a unction o the design variables. The analysis ile is an input ile o Ansys that contains a sequence o complete analysis, (pre-processing, solution, postprocessing). The model has to be deined parametrically, where the parameters are all the optimiation variables. Ater having ound the solution, the variables o interest are recovered or use in the optimiation routine. Starting rom this ile, a ile optimiation loop is created and used automatically by the sotware to accomplish the analysis loops. First was used a optimiation tool called Random Design Generation, where the program accomplishes a speciic number o analysis loops using random values o design variables or each loop. This is a good tool to arrive quickly to an initial coniguration o parameters that can be used with a more adequate optimiation method. Then was used an optimiation technique called Subproblem Approimation Method. This is an advanced ero-order method that uses curve itting to all dependent variables. As the problem possesses symmetry, just hal o the wing was modeled. The mesh was generated automatically on the surace. An element o laminated shell was used, shell99. It can be triangular or quadratic, with 6 or 8 nodes. It allows the calculation o the interlaminar tensions and o the value o the ailure criteria, besides the displacements and deormations

4 K. Widmaier, F. M. Catalano Figure 4. Pressure distribution over the wing model. For the application o the loading, a constant pressure was applied on each element (see igure 4), whose value was previously calculated or the center o each element using the equations obtained in the previous section. The orce resulting normal to the light direction, lit, is obtained o the ollowing well known equation, being considered that the low is bidimensional: V L = Clρ.. S (3.) For the situation o the wing lying with an angle o incidence o o (angle o stall o the airoil) at 5 Km/h (here deined arbitrarily, as being VA), the lit orce is 4737,9N. All the spar nodes in the root o the wing were constrained in u, u, θ and θy. Two nodes, in the position where the wing torsion pins would be, in the main rib, were constrained in u and uy, according to igure 5. The initial lamination sequence was previously deined. The skin o the wing was divided in 5 sections o equal length, and the irst in the root has 0 layers o abric and one o oam, in the center. Each ollowing section has minus two layers, until the last, that has only three (see igure 6). The spar has 5 layers in the web, including the oam. The langes were modeled as a unique layer o unidirectional abric (igure 5). Figure 5. Node constrains and spar mesh. Figure 6. Skin proprieties changing along span. Twelve design variables were deined, the thickness and the orientation o each layer o the skin and o the spar. The intervals o layer thickness were restricted to the maimum and minimum abric thickness available commercially. As state variable was deined the value o the ailure criteria, that should be below 0,8, giving a margin o saety o 5%. The objective unction to be minimied was deined as being the volume, that is proportional to the weight. Following are presented some data o the modeling: 743.4

5 CONCEPTUAL DESIGN AND OPTIMIZATION OF A HIGH ASPECT RATIO UAV WING MADE OF COMPOSITE MATERIAL Variable Min Ma Tolerance MAXFC 0, E-04 0, E00 0, E-0 THK 0, E-03 0, E-03 0, E-05 THK 0, E-03 0, E-03 0, E-05 THK3 0, E-03 0, E-03 0, E-05 THK4 0, E-03 0, E-03 0, E-05 THK5 0, E-03 0, E-03 0, E-05 WEBTHK 0, E-03 0, E-03 0, E-05 FLTHK 0, E-0 0, E-0 0, E-03 TETHA 0, E-0 0, E0 0, E00 TETHA 0, E-0 0, E0 0, E00 TETHA3 0, E-0 0, E0 0, E00 TETHA4 0, E-0 0, E0 0, E00 TETHA5 0, E-0 0, E0 0, E00 VOLUME - - 0, E-0 Table. Parameters variables o the optimiation. 4 Results analysis Ater 5 loops, a coniguration that doesn't ail was reached, although saety's margin has been below 5%. In Figure 7 can be observed that the area close to the wing root has the smallest margin o saety. It is also possible to notice that close to the tip o the wing the tensions are low, and it would be possible to obtain a more eective optimiation modiying the lamination sequence (etension o each layer, igure 6). It is still noticed the leading edge area is a stress concentration area. In igure 7 and 8 can be seen the distribution o the ailure criteria or the skin and spar. Variable Type Value MAXFC (SV) 0,9074 THK (DV) 0,3996E-03 THK (DV) 0,45E-03 THK3 (DV) 0,540E-03 THK4 (DV) 0,35088E-03 THK5 (DV) 0,30880E-03 WEBTHK (DV) 0,9509E-03 ESPML (DV) 0,75797E-0 TETHA (DV) 37,97 TETHA (DV) 40,546 TETHA3 (DV) 7,87 TETHA4 (DV) 60,55 TETHA5 (DV) 83,85 VOLUME (OBJ) 0,75349E-0 Table 3. Values o the variables obtained ater the optimiation. # OF ELEMENTS 639 DEGREES OF FREEDOM 68 ELEMENTS MATRIX,5 MB TRIANGULAR MATRIX 4, MB PROCES TIME p/ LOOP 4 min # de LOOPS 5 FINAL MASS OF THE WING 55,6 Kg Figure 7. Tsai-Wu ailure criteria distribution along the wing skin. Table 4. Process data

6 K. Widmaier, F. M. Catalano Figure 8. Tsai-Wu ailure criteria distribution along the spar. 5 Laminate composite optimiation using genetic algorithms (GA) GA are powerul tools or the optimiation o laminate composite [6]. The GA handles easily with the discrete nature o the stacking problem. Optimiation o laminate composite structures involve not just orientation to speciic thickness, but also the number o layers, the kind o abric o each layer and the total thickness. Gürdal et all [6] ound, optimiing composite panels under combined in-plane loads, structures that were 5.7% lighter. They ound also that GA leads to many dierent easible solutions due to its random characteristics. 6 Conclusion With the present work it was veriied that Ansys allows the use o optimiation routines applied to composite laminated structures. The ollowing diiculties were noticed: -diiculty in deining as design variable the number o layers o the laminate. The diiculty is due the way that the properties o the element shell99 are deined, and the impossibility o just attributing integer values to the design variable. -in practice, change the thickness would be only possible or ew discreet values, that would be the commercially available abric thickness. But that could not be made also. Deined the variable, the program attributes any real value that is inside the deined interval. A possible solution would be to eliminate that design variable, and to use dierent models with dierent conigurations o that variable. Or still, just use a sequence o pre-deined abrics, and to optimie the etension o each layer in the laminated along the surace o the wing. The diiculty in this case would be the need o a variable mesh. -it is not possible to deine the mass directly as objective unction, and in the case o variable density elements, as in the laminated sandwich, it would be more appropriate. The two irst diiculties are easily solved using a GA based optimiation routine. Currently a GA based on ANSYS Parametric Design Language (APDL) is been developed to work as a user optimiation subroutine at the Ansys session. It would be also interesting to do, and the program allows it, a sensitive analysis o each design variable in the objective unction, allowing a better evaluation o the project parameters. Reerences [] Anastasiadis, P.T. The Inluence on Optimal Structural Designs o the Modeling Process and Design Concepts. Aeronautical Journal, May, pp 65-75, 996. [] Kam, T. Y., Lai, F. M., Liao, S. C. Minimum weight design o laminated composite plates subject to strength constraint. AIAA Journal, Vol. 34, No. 8, p , 996. [3] Ansys User s Manual, Volume IV, Theory. Swanson Analysis Systems Inc [4] Jones, R. M. Mechanics o Composite Materials, New York, M C Graw-Hill, 975. [5] Ansys User s Manual, Volume I, Procedures. Swanson Analysis Systems Inc [6] Gürdal Z, Hatka R T and Nagendra S. Genetic algorithms or the design o laminated composite panels. SAMPE journal, Vol. 30, No 3, pp 9-35,