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附錄:外文原文和譯文SIMULTANEOUS STRUCTURE AND MECHANISM DESIGN FOR AN ADAPTIVE WING USING TOPOLOGY OPTIMIZATIONJames J. Joo Aerospace Mechanics Division University of Dayton Research Institute Dayton, OH 45469, USABrian Sanders Air Vehicles Directorate AirForce Research Laboratory Wright-Patterson AFB, Ohio 45433, USAABSTRACTA synthesis technique using a topology optimization scheme for an adaptive wing structure and mechanism design will be described.This enables the design of energy efficient adaptive structures with controllable deformation characteristice.This is accomplished by using a multi-objective function that minimizes strain energy and maximizes mutual potential energy to design the structure and mechanism simultaneously.To enable simultaneous design for structure and mechanism, the reference structure is composed of three layers; a membrane layer for skin, a frame element layer for structure, and truss element layer for an efficient mechanism. The attachment points between mechanism and structure are also identified with linear springs that are located between mechanism and structure layers. We focus on a simultaneous design of a wing structure and mechanism for large shape change applications. The geometrically large deformation analysis scheme is also added to the synthesis to capture nonlinear effects in design and it will be compared with linear synthesis results.INTRODUCTIONAdaptive structures are a multidisciplinary technology that requires the efficient integration of power systems, structures, mechanisms, and actuators to achieve the desired performance. Adaptive systems will have a dramatic impact on the design of air vehicle systems if new devices can be synergistically integrated into systems. The basic research community has suggested a plethora of innovative concepts ranging from structural health monitoring to adaptive shape control using energy intensive smart materials. Smart material technologies have increased its potential application to provide a new opportunity for active/adaptive structure systems that fully integrate actuators and structures. The Defense Advanced Research Projects Agency (DARPA) recognizes the potential of this technology and initiated the Smart Materials and Structures Demonstration Program to demonstrate the use of smart materials to achieve aerodynamic and hydrodynamic flow control and to reduce noise and vibration in a variety of structures (Sanders, et. al, 2004).New materials synthesized at the atomic level to produce new functionality are ideal for this application but the technology is very immature. Until now, smart materials or other adaptive technologies have been added to an existing structure to achieve a desired shape change a structure already designed to avoid deformation. For example, aircraft wings are designed to be stiff as possible to control aeroelastic effects, and then smart materials are attached on to it to get a higher lift coefficient by change airfoil shape. This system becomes very energy inefficient because you are trying to deform a structure that was alreadydesigned to prevent deformation. For this reason, researchers have designed in flexibility for their structure design. Lu and Kota (2003) have designed a compliant leading edge that matches a desired shape with a single actuation force. Others are investigating new design techniques for these applications. Maute et. al. (2005) used the topology optimization technique to design mechanisms in morphing aircraft structures including actuator characteristics. Also Mauteand Reich (2004) showed the simultaneous optimization of the mechanism layout of adaptive wing and aerodynamic tasks outperformed the decomposed two step procedure.Designed properly, these structural concepts have the potential to revolutionize aircraft design and basic functionality. For example, the use of adaptive systems within unmanned air vehicles (UAV) will enable a multi-mission (e.g., hunter-killer) UAV by allowing the vehicle configuration to efficiently adapt to a wide range of mission roles, such as loiter and high speed dash. Here the best wings for each purpose have radically different planforms. Current research on morphing aircraft that exhibit very large shape changes requires more efficient ways of synthesizing out three major components; rigid-body mechanisms, structures and skins. In this paper, we propose to design an energy efficient adaptive structure for shape control purposes by designing structures and mechanisms simultaneously. A three-layer model is developed that is composed of a ground truss layer for mechanism design and a membrane and beam layers for structure design. A multi-objective function to maximize mutual potential energy to increase flexibility in desired direction and minimizing strain energy to withstand drag is adopted here.NOMENCLATUREUo Dummy force in the desired output direction Ui Dummy force in the input direction. Fin Input force Fex External force K Global stiffness matrix d Displacement vector f Force vector Km Element stiffness matrix of membrane element Kt Element stiffness matrix of truss element Kf Element stiffness matrix of frame element Ks Element stiffness matrix of spring element Maximum volume of truss element Maximum volume of frame element N* Maximum number of spring P Penalty f, s, t Density of frame, spring, and truss elements REFERENCE STRUCTUREThe reference element composed of three layers is shown in Figure 1 below; the membrane element layer is for stretchable flexible skin. The truss element layer is for an energy efficient mechanism that generates motion using rigid body rotation rather than the deformation of elements to change the shape. Using frame elements, most of energy will be stored in the mechanism rather than transformed to the output port which results in an inefficient mechanism. Also this truss element with rigid body rotation is more appropriate for large shape changing applications than frame elements due to the similar reason. This truss element layer is connected to the membrane elements layer by springs and this is for identifying connection points between structure and mechanism. Spring stiffness is chosen based on the following criteria (Chandrupatla 1997) to bond mechanism and membrane layer together:C=maxkij10 (1i,j,k,d,o,f) (1)A frame element layer is added to the membrane layer because the membrane element cannot take bending, torque, or out-of-plane load. These frame and membrane element layers are sharing the same nodes. Fig. 1 3 layer model for adaptive wing structure designSKIN THICKNESS VARIATIONThe skin on the conventional stiff wing works in conjunction with beam elements to form a box beam, which is a mass efficient method to obtain the desired torsion and bending stiffness required for aircraft wings However, the property of skins is necessarily different in large wing shape changing applications such as morphing aircraft system. It should be flexible enough to handle large shape and area changes of the wing that enables morphing. It also should be stiff enough to handle drag. The skin property of morphing wing has a major impact on the efficiency of the system that can be maximized by transferring actuation energy to the output port (shape change) without storing energy in the structure in the form of strain energy. Therefore the effect of the variation of the thickness of the skin is investigated here. The flexible wing is modeled as a sandwich beam as shown in Fig. 2. The bending stiffness of the wing, Kb, is formulated as:Kb=3EsI/L=Es/4Lnah+2at+24at(h+t/2) (2)where Es is the elastic modulus representative of the internal structure and mechanism, I is the total moment of inertia of the wing, a is the width of beam (cord), h is the height of the representative of the internal structure and mechanism, L is the length of the beam (span), t is the thickness of skin, and n is the ratio of elastic modulus of skin, Em, to the internal structure and mechanism, Es:n=Em/Es (3)We are interested in the bending and in-plane stiffness change with respect to the skin thickness change. For this investigation, the bending and in-plane stiffness of the wing are differentiated with respect to the skin thickness t. The sensitivity of bending stiffness is Kb=E/4L64at+24a(h+t/2)(h+3t/2) (4)The in-plane stiffness of the wing, Ki, is represented as:Ki=EsAs+EmAm/L=Es(2at+nah)/L (5)The sensitivity of the in-plane stiffness of the wing with respect to the skin thickness t is: Ki=2aEs/L (6)In order to compare the bending and in-plane stiffness of the wing with respect to the thickness change, the ratio of the equation 4 and 6 are put together as: Kb/Ki=3(h+t)/L (7)The equation 7 is less than one as long as the relationatisfies which is generally true because the span (L) of wing is orders of magnitude higher than the thickness of a wing. Then, equation 7 can be represented as:Kb/tKi/t (8)This result implies the in-plane stiffness is more sensitive than the bending stiffness to changes in the skin thickness. This suggests the use a heterogeneous or engineered anisotropic material which is stiff in out-of-plane direction but very flexible in-plane direction rather than using a homogenous material to avoid thickening the skin to prevent out-of-plane deflection.Since this skin modeling capability is not added to the code yet we model the skin using membrane element in this paper to have rubber like characteristic to give in-plane flexibility. Fig. 2 Sandwich beam model for a flexible wingMULTI-CRITERIA OBJECTIVE FUNCTIONHere we are focusing on the qualitative solution of simultaneous design of an aircraft wing structure using energy metric. The exact quantity of the shape change by minimizing the deviation between target shape and deformed shape which aerodynamists may be interest in will be examined later. An adaptive wing structure for large shape change needs to be flexible enough to deform to a desired shape or direction with minimum strain energy stored in the structure and stiff enough to resist external load and avoid deleterious aeroelastic effects. To synthesize an adaptive structure satisfying these two conflicting requirements, flexible and stiff, a multi-criteria optimization scheme is adopted. Figure 3 shows two different loading conditions to capture those requirements.Figure 3a shows a swept wing configuration with actuation force (Fin) and desired output motion. To obtain deflection in the desired direction, maximum deflection along the direction of Uo is needed, where Uo is a dummy load vector. The desired shape could be a curve but, here, a point at the tip of the wing is chosen to simplify the problem. Maximizing the deflection along Uo is equivalent to maximizing Mutual Potential Energy (MPE). MPE is equal to doTFinand the flexible requirement is captured by:MaxK(p)dins.t.K(p)do=Uo (9)K(p)din=FinHowever, MPE tends to approach infinity as stiffness decreases because of an attempt to maximize MPE with force as an input, hence, the input displacement is constrained with a finite value. Fig. 3 Two loading conditions for adaptive wing designSatisfying the second stiffness requirement is equivalent to minimizing the strain energy (SE) with external load applied to the structure. SE is equal to dexTKdex and the rigidity requirement is captured byMins.t.K(p)dex=Fex (10)The multi-criteria objective function is constructed now to capture both flexibility and rigidity requirements:Minimize-MPE(p)+(1-)SE(p)s.t. (11)The two objective functions are linearly combined with weights, and (1-), and (-1) is multiplied to the MPE for maximizing that function. The Method of Moving Asymptotes (MMA) by Svanberg (1987 and 1999) is used as an optimizer for this problem.SENSITIVITY ANALYSISThe MPE is calculated by: (12)The sensitivity of MPE with respect to design variable can be written as following using the adjoint method: (13) (14)For easy formulation of the problem, truss, frame and spring elements already has pre-determined geometry but their stiffness matrices are multiplied by weights, Pt,Pf,Ps,respectively, and these are the design variables of the problemFrom (12)MPE/Pt= (15) (16)Similarly (17)Substitute (16) and (17) in (15). Then, (18)Similarly (19)The SE induced by the external force is calculated bySensitivity of SE is obtained from similar process as before (20)The sensitivity of the displacement at input port is obtained by (21)The sensitivity of the displacement vector d is: (22)Substitute (22) to the equations (21). Then (23)DESIGN EXAMPLESIn-plane shape change example (sweep to unsweep) The goal of this example is to design a simple swept wing with a flexible skin and mechanism that changes its shape to an unswept position (figure 4). Since the motion is in-plane, only truss and membrane elements are used for the design. The skin is attached to the fuselage at x = 0 and the full ground truss element structure layer is attached to the membrane elements with linear springs at each node. The input force is applied to the truss element layer at the second node from the left bottom corner in positive x direction and output node at top right corner needs to move in positive y direction to deform into an unswept position. The external force, a simple representative of a drag force, is applied to the membrane element layer in the opposite direction of output displacement and minimizing strain energy by this force will result in structure that withstand drag force. A dummy force is applied in desired output direction to calculate MPE. The problem here has only single input and output to simplify the problem but the number of inputs and outputs is not limited to this. The material of membrane issilicon rubber (E = 250 psi, = 0.5) and truss is 2024-T3 aluminum (E = 73.1 Gpa = 10.6 Mpsi, = 0.33). The weight, , is carefully chosen to adjust the scale of the two objective functions Fig. 4 Reference structure and boundary conditionFigure 5 shows the linear synthesis result. Dots are the attachment points between mechanism and skin. There are non-negligible springs that exist on other nodes but the truss elements connected to those springs are too thin (inactive) to deform the spring, hence, those are not shown in the figure. Also, notice that the spring is attached between the mechanism and the skin at the input port. The efficiency of this mechanism will not be high because the input energy will be stored in that spring before it can be transferred to the output port. However, it is necessary to resist the external load. We are hoping this spring will disappear when the efficiency objective function is used instead, but we did not try that out with the efficiency formulation because it is out of scope of this paper. The output port of the skin is deformed to the desired direction because the skin is pushed and pulled at several positions through the mechanism. Fig. 5 Linear synthesis resultFigure 6 shows the result using a nonlinear synthesis result for the same problem. The result looks similar but, the input and output ports are directly connected. The linear result does not have this feature and that link is actually pulling the skin at the output port to the desired direction instead of pushing the skin as linear result that may cause wrinkle on the skin and fail. Fig. 6 Nonlinear synthesis result Now frame elements are added to the reference structure. Frame elements are sharing nodes with the membrane elements (Fig. 7) and the boundary conditions are identical to the previous problem. Figure 8 shows a linear synthesis result. The truss elements and frame elements are indicated in the figure and optimization distributes those elements where it is necessary. The input port is attached with a very soft spring which is different from the previous results. The reason is observed as following; Since the structural elements is added to the existing mechanism and skin elements, it helps to resist external force without a spring at the input port of mechanism that was observed in the previous result without frame elements. The optimization chose not to have mechanism and structure separate but to combine mechanism and structure element together to make a multi-functional structure. Fig. 7 Reference structure and boundary condition Fig. 8 Linear synthesis result SUMMARYThis study addressed the simultaneous design of multi-functional structure composed of skin, structure, and mechanism for possible morphing aircraft application. It is shown that when the structure and mechanism are designed together, the structure and mechanism is combined effectively where it is necessary; mechanism uses structural element to transfer force without creating redundant element in the mechanism layer. In this way, we can remove excessive materials for a lighter airplane and may avoid unexpected problem that can be caused by combining those two layers after being designed separately. Further work needs to be done for 3D cases that including out-of-plane load (aerodynamic pressure) applied and explore more realistic cases with more realistic conditions.ACKNOWLEDGMENTSThis work is supported by the Structural Mechanics Program of the Air Force Office of Scientific Research.外文譯文基于優(yōu)化拓撲的自適應機翼的同步結構與機制設計 詹姆斯.J.玉 戴頓大學研究所 布萊斯桑德斯 美國空軍研究實驗室摘要本文將描述一種基于優(yōu)化拓撲的自適應機翼的同步結構與機構設計的合成技術。這使高效的自適結構的設計具備可控制變形的特征。這是通過設計具有多目標函數(shù)的最大化相互勢能增加靈活性和減少所需的方向應變能承受的空氣動力結構和機制同時進行。 要啟用的體制和機制同步設計,該參考結構由三個層次,一個皮膚,一個單元層的結構框架,并建立有效的機制桁架單元層薄膜層。 機制和結構之間的連接點也確定了線性彈簧之間的機制和結構層的位置。 我們專注于一個機翼結構和形狀變化較大的應用機制,同步設計。 幾何大變形分析的計劃也被添加到捕捉到了設計合成的非線性效應,這將是與線性合成結果進行比較。簡介 自適應結構是一個多學科的技術需要有效的整合電源系統(tǒng)、結構,機制,與驅動器實現(xiàn)預期的性能。如果新的設備可以協(xié)同作用集成到系統(tǒng)中,那么自適應系統(tǒng)將在空中交通工具系統(tǒng)的設計上會有很大的影響力?;A研究團體已經(jīng)提出了一些創(chuàng)新的概念,從結構健康監(jiān)測,到采用適應性形狀控制使用能源密集型智能的材料。智能材料技術增加了其潛在的應用提供了一個新的機會主動/自適應結構系統(tǒng),充分整合執(zhí)行機構和結構。美國國防高等研究計劃局(DARPA)承認了這項技術的潛能,啟動智能材料和結構演示程序,驗證了利用智能材料來實現(xiàn)氣動和流體動力學的流控制,以減少噪音和振動在多種結構。合成了新材料在原子水平的生產(chǎn)對新的功能來說是很理想的這個應用程序但技術是非常不成熟的。直到現(xiàn)在,智能材料或其他的自適應技術已經(jīng)被添加到一個已經(jīng)存在的機構,以達到一個理想的形狀變化-一種已經(jīng)設計防止變形的結構。例如,飛機機翼的設計是嚴格的,因為相對而言,可能控制氣動彈性分析智能材料的影響,然后一并附呈到它上面去高升力系數(shù),改變機翼形狀。這個系統(tǒng)會變得非常有能量效率,因為你正試圖變形結構,這是已經(jīng)被設計來防止變形。因為這個原因,鑒于他們的結構設計研究人員設計中賦予靈活性。魯和哥打京(2003)設計了一個可兼容的領先優(yōu)勢,能夠匹配所需要的形狀與對應的驅動力量。其他人正在拓展這些新設計技術的應用。使用拓撲優(yōu)化技術必須設計一種機制變形飛機金屬結構包括驅動器的性能。同時也說明自適應機翼的同步優(yōu)化機構布局和氣動任務分解表現(xiàn)為兩步程序。采用適當?shù)脑O計,這些結構概念具有革新飛行器設計和基本功能的潛力。例如,自適應系統(tǒng)在無人駕駛飛行器(無人機)低空運行的應用將能夠使無人機完成多個任務通過允許飛行器配置來有效地適應各種各樣的任務角色,例如慢行和高速短跑。對于特定的任務選取最適合的完全不同的機翼形狀。目前關于變型飛行器(可以展現(xiàn)非常大的形狀變化)的研究需要更多有效的辦法,其關鍵歸結為三個主要部分剛體的機制,結構,外表層。在本文中,對于達到形狀控制目的我們提出一個高效設計自適應結構,通過設計的結構和機制,同時進行。研制出一種三層模型,它是一種由地面桁架層膜機制設計和梁的層結構設計構成。在這里采用多目標函數(shù),以最大限度地增加相互勢能最小彈性應變能的方向移動和減小阻力。命名法U0虛擬力的期望輸出的方向Ui 虛擬力在輸入方向。Fin輸入力Fex外力K總剛度矩陣
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