外文翻譯--符合尾隨邊緣形態(tài)變化的優(yōu)化設計

1、<p>　　符合尾隨邊緣形態(tài)變化的優(yōu)化設計</p><p>　　摘要：自適應機翼一直使用柔和的技術指導變形的后緣，以改善他們的氣動性能，本文介紹了一種在分布壓力下，符合形狀變化的結構設計的系統(tǒng)化方法。為了使需要的形狀與目標形狀偏差盡量最小，這種方法使用MATLAB和ANSYS的方式來優(yōu)化標準分布機制。這種方式通過局部優(yōu)化和遺傳算法來獲得。在優(yōu)化過程中，許多因素應該考慮在內(nèi)，例如：空氣載荷、輸出位移量和幾

2、何非線性。直接搜索法適用于局部優(yōu)化和GA優(yōu)化后的輸入位移量。由此產(chǎn)生的結構可以做出他們在0到90。.之間變化，模型試驗已經(jīng)確認了這種方法的可行性。</p><p>　　關鍵詞：自適應機翼，伺服順從機構，遺傳算法，拓撲最優(yōu)化，分布壓力載荷，幾何非線性</p><p><b>　　1．說明</b></p><p>　　由于傳統(tǒng)的機翼輪廓通常是按照特

3、定的上升系數(shù)和馬赫數(shù)設計的。他們不能隨著環(huán)境的變化而變化。Siclar和Austin指出可變的后緣曲面將會產(chǎn)生比傳統(tǒng)的固定傾角機翼少60%左右的阻力。</p><p>　　有三種去設計可變的曲面機翼的方法。他們中的一種是傳統(tǒng)的鉸鏈機構，然而，他會導致機翼表面的不連續(xù)性和早期氣流分流與阻力的增加。其它的則是智能材料和順從機構，他們能實現(xiàn)平穩(wěn)的形狀變化。盡管如此，與順從機構相比較，由智能材料制成的傳動裝置有許多不足之

4、處。例如：能量不足；反應緩慢；強烈的滯后性；受溫度的限制；控制太多裝置的難度大。由來自柏林工業(yè)大學的用鎳鈦記憶合金作出的自適應可變拱形的機翼可以快速改變他的形狀，但他不能執(zhí)行高頻繁的變化，因為他的彈性依賴于與外部環(huán)境進行的熱量交換。</p><p>　　順從機構是一種單件靈活的機構。他可以通過彈性變形傳送運動和能量。他不僅具有足夠的變形性，而且具有足夠的剛度來抵御外部的載荷。由于他的連接自由性，他沒有傳統(tǒng)所面臨的

5、棘手問題，例如：摩擦、潤滑、噪聲、反沖。因此可以獲得平穩(wěn)的形狀變化。</p><p>　　1994年，一位來自密歇根大學的名叫kota教授首先提出順從機構能夠使用在一項由美國空軍科學研究院辦公室提供贊助的控制靜態(tài)形狀的科學研究之中。Saggere和Kota提出了一種設計順從機構的新方法，他們能夠使優(yōu)化目標函數(shù)曲線中的形狀變化和目標曲線的形狀誤差最小，基于他們的研究成果，Lu提出了一種載荷路徑代表方法。然而，他的研

6、究僅限于節(jié)點情況下的線性分析。來自于福尼亞州立學院的Good使用順從機構和運動漸近法來設計機翼的尾部，保證誤差在尖端最大偏差范圍之內(nèi)。基于F16的數(shù)據(jù)，Kota和Hetrick在2004年時間設計順從軌跡邊緣，他能在0。到15。之間變化并且獲得了專利證書。來自德國航空航天中心的Companaile提出了模擬靜態(tài)程序設計機翼形狀控制合成靈活機構，并指出今后的研究應將空氣載荷和幾何非線性考慮在內(nèi)。來自工業(yè)能源部實驗室的Buhl使用SIMP法

7、和幾何非線性有限元法來設計順從軌跡邊緣。Flxsys Inc在2006年生產(chǎn)的自適應兼容機翼。經(jīng)過了在懷特騎士飛機上的實驗。結果表明，風和標準的能在（-10。—10。）變化。在中國，適應性機翼研究一直集中在智能材料和常規(guī)機構上，幾乎沒</p><p>　　本文介紹了一種基于局部優(yōu)化和遺傳算法形狀可變機構的設計方法，通過使用MATLAB和ANSYS設計，同時將外部載荷和幾何非線性考慮在內(nèi)。</p>&

8、lt;p><b>　　2．優(yōu)化步驟</b></p><p>　　2.1確定后緣模型和目標函數(shù)</p><p>　　如圖一所示，兩條曲線代表不同飛行狀態(tài)的軌跡邊緣。其中一邊（A點）的結構形狀是固定的，另一邊（B點）將水平滑動。</p><p>　　圖一 圖二

9、 </p><p>　　首先設計領域應該由最初曲線形狀所定義，包括輸出位置和邊界狀態(tài)，然后如圖二所示的被光線分成的微量網(wǎng)格模仿鳥的羽毛部分，這就是被稱為局部表面結構方法。</p><p>　　最簡單也是最有效的方法制造出平面兼容機是使用線切割技術。在優(yōu)化過程中，所有的元素使用同樣的寬度等于其厚度的梁。其中每個梁的高度是一個設計變量。</p><p

10、>　　為了使結構的變形接近于目標曲線形狀，在變形曲線和目標曲線間的最小平方差是被定義的客觀職能。LSE的定義是沿曲線上各個點位置數(shù)字的平方和，他的表達式是 </p><p>　　其中i（i=1,2,…，p）是沿曲線上點的數(shù)量，p是點的總數(shù)。和是目標和邊界曲線變形坐標的第i個節(jié)點。約束條件是：</p><p>　　其中j（j=1,2,…，m）是元素的數(shù)量的總和，hi

11、是尺寸變量，hmin 和 hmax是所有元素的下界與上界，hb是邊界元素的極點，dmax是黨邊界曲線上輸入無效節(jié)點時的最大彎曲，必須小于 [d] 以保證結構的剛度，[d]是當輸入處于無效時所允許的最大彎曲變形，拓撲量Tj等于1，否則當元素被淘汰時為0。</p><p><b>　　2.2 GA優(yōu)化</b></p><p>　　遺傳算法是一種在自然界上模擬選擇的優(yōu)化方法

12、。合適的生物能最大可能性存活下來，但是劣質品種也有機會存在。不同于連續(xù)的優(yōu)化方法，他不要求梯度的目標函數(shù)信息。</p><p>　　每一個元素可以表示為一個拓撲量和一個尺寸變量。因此，每個個體科編碼如下： </p><p>　　其中n是除邊界元素之外元素的數(shù)量。有著同樣的高度，在整個優(yōu)化過程中的邊界元素只有一個變量代表hb。</p><p>　　適應性是遺傳

13、算法優(yōu)化的評價標準。他可以從目標函數(shù)轉化為： </p><p>　　其中β是一個只包括雙方較差的個體參數(shù)。他的數(shù)值越小越有價值，兩個個體的適應性會有更多的不同，因此增加了雙方選擇的高度適應性。</p><p>　　選擇控制參數(shù)在遺傳算法的收斂中扮演一個重要的角色?？偟膩碇v，交叉概率的范圍為0.40-0.99；突變的概率為0.00001-0.01，個體的數(shù)量為10-200。</p>

14、;<p>　　該變量將會通過交叉和變異發(fā)生更新，因此，這個設計可能產(chǎn)生遺傳過程。</p><p>　　2.3適應性元素的分析</p><p>　　由于設計變量和目標函數(shù)是有限元的，有限元分析法優(yōu)化模型是不能被用于設計符合變形的機構中，因此，本文在MATLAB中的遺傳算法和在ANSYS中的有限元分析法。在有限元分析法中，僅只考慮幾何非線性和材料的彈性，ANSYS能解決節(jié)點位移和

15、元素壓力，通過刪去低應力的元素，良好的結果能被推算出來。圖三顯示了詳細的過程。</p><p>　　圖三 整個的優(yōu)化過程</p><p><b>　　2.4二次優(yōu)化</b></p><p>　　盡管遺傳算法可以優(yōu)化大型解空間和拓撲結構尺寸。尺寸通常不能直接集中于優(yōu)化中，為了解決這個問題，遺傳算法優(yōu)化后，直接搜索法應該被用來在遺傳算法結果中去尋找

16、。</p><p><b>　　3.優(yōu)化的結果</b></p><p>　　通過參考文獻[5]可以得出，最初的小徑邊緣尺寸減少36%，表一列出了設計參數(shù)的大小。</p><p>　　表一 設計參數(shù)的大小 </p><p>　　由于位移作為輸入的使用，非線性分析難以解決和廚師壓力非常大，但他必須在三十

17、代以后考慮。</p><p>　　圖四 遺傳優(yōu)化的結果 圖五 二次優(yōu)化的結果</p><p>　　圖四和圖五說明了遺傳算法優(yōu)化結果和二次優(yōu)化結果。</p><p>　　表二 兩次優(yōu)化的比較</p><p>　　從表格中可以發(fā)現(xiàn)，通過輸入位移和尺寸優(yōu)化，LSE減少了1.3528mm和改善了3.13%，變更

18、角度增加1.0493。。</p><p>　　圖六 外部載荷的分布</p><p>　　圖六表示的是外部分布壓力從0到10N/mm，改變輸入位移量在最初結構上保持11.3897mm上的參數(shù)影響結果。如果載荷保持在0-5N/mm范圍內(nèi)，優(yōu)化結構看起來有良好的穩(wěn)定性。當外部載荷超過5N/mm時，最大壓力可能超過屈服壓力，因為這個優(yōu)化方法是基于MATLAB和ANSYS的，為了證明結果，嘗試去通過

19、將分析結果分別輸入到ANSYS和PATRAN中，然后是他們之間的比較。如圖七和圖八所示，二者的變更有很大的共同點；在ANSYS中是54097mm，在PATRAN中是54.50mm，他們的不同之處來自個體上。</p><p>　　圖七 在ANSYS上的結果 圖八 在PATRAN上的結果</p><p>　　另一方面，一個使用線切割技術的模型來證實分析法

20、的結果。模型的材料同設計的一樣，都為5mm后。在試驗中，假設分布壓力載荷為零，輸入146N的情況下，輸入位移量為11.3897mm，圖九表示的是模型和測量的結果。變更的溫度為9.3。。尖端為一位53mm，變更的形狀符合設計的結果。如果11.3897mm的位移量強加在模型上，理論的尖端位移量為54.796mm。因為模型和試驗臺之間存在摩擦力，測量材料和適合的結果之間會有少許的差異。</p><p>　　圖九 模型和

21、實驗的結果</p><p><b>　　4.結論</b></p><p>　　通過方針和實驗證明，該方法符合設計變形機制，探索出具有所需的變性效應和承受外部載荷的結果和能力的機構。在優(yōu)化過程中，MATLAB和ANSYS的聯(lián)合呈現(xiàn)程序的簡單和普遍性。堅硬的字模沒有必要頻繁的改變，同時避免有限元法編程的復雜性和使分布載荷變成節(jié)點載荷，拓撲尺寸可以同時由GA進行優(yōu)化，出去再

22、FEA之后的自由元素能加快優(yōu)化，二次優(yōu)化可以提高GA優(yōu)化的結果。</p><p>　　Optimal Design of Compliant Trailing Edge for </p><p>　　Shape Changing</p><p>　　Abstract: Adaptive wings have long used smooth morphing

23、 technique of compliant leading an d trailing edge to improve their aerodynamic characteristics．This paper introduces a systematic approach to design compliant structures to carry out required shape changes under distrib

24、uted pressure loads．In order to minimize the deviation of the deformed shape from the target shape，this method uses M ATLAB and ANSYS to optimize the distributed compliant mechanisms by way of the ground approach and gen

25、etic </p><p>　　Keywords： adaptive wing；compliant mechanism；genetic algorithm ；topology optimization；distributed pressure load；geometric nonlinearity</p><p>　　1 Introduction：</p><p>

26、　　As conventional airfoil contours are usually designed with specific lift coefficients and M ach numbers，they could not change in accordance with the environment changing．Siclari and Austin indicated that the variable c

27、amber trailing edge would produce the drag about sixty percent less than the conventional fixed camber airfoil</p><p>　　There are three methods used to design able camber wings．Of them．one is conventional hi

28、nged mechanism，which，however, will create discontinuities over the wings surface leading to earlier airflow separation an d drag increase． The others are smart material and the compliant mechanism，of which both could rea

29、lize smooth shape changing．Nevertheless，compared to the compliant mechanism，the smart—material—made actuators have many disadvantages，such as deficient in energy ,slow in response，strong in hys</p><p>　　Comp

30、liant mechanism is a kind of one-piece flexible structure，which can transfer motion and power through its own elastic deformation．It is not only flexible enough to deform，but also has enough stiffness to withstand extern

31、al loads．Thanks to its joint—free nature，it does not have the trouble some problems confronted by conventional mechanism such as friction，lubrication，noise and recoiling，thereby achieving smooth shape changing.</p>

32、<p>　　In 1 994，Kota，a professor from University of Michigan，firstly pointed out that compliant mechanism could be used to control static shape changing under the sponsorship of the Air Force Of ice of Scientific R

33、esearch in USA．Saggere and Kota</p><p>　　suggested a new method to design compliant adaptive structures，which made the least square errors between the shape—changed curve and the target curve as the objectiv

34、e function for optimization．Based on their work，Lu put forward a load path</p><p>　　representation method．However, her work was limited to only linear analysis under consideration of nodal loads．Good[ from V

35、irginia Polytechnic Institute of State University used the compliant mechanism and the Moving Asymptotes method to design the fuselage tail within the allowable range of its tip maximal deflection．Kota and He trick in200

36、4 designed a compliant trailing edge on the base</p><p>　　of the F16s data，which can change from 0。to 15。and obtained a patent．Campanile from German Aerospace Center presented a modal procedure to design syn

37、thetic flexible mechanisms for airfoil shape control，and pointed out that the future re—search should take into account the air load and the geometric nonlinearity．Buhl from Riso National Laboratory of the Wind Energy De

38、partment in Denmark used the SIM P method and geometrically nonlinear finite element method to design compliant trailing edge flaps</p><p>　　elasticity technology．Chen and Huang separately investigated the m

39、orphing of the compliant leading edge from the viewpoints of discreteness and continuity.</p><p>　　This paper presents a method to design the shape changeable structure by MATLAB and AN—SYS associated with d

40、istributed compliant mechanism on the base of the ground structure approach and genetic algorithm (GA)taking into account the external distributed loads and geometric nonlinearity.</p><p>　　2 Optimization Pr

41、ocess:</p><p>　　2．1 Defining the trailing edge model and objective function</p><p>　　As shown in Fig．1，both curves represent two ideal shapes of the trailing edge in the different flying states．

42、One side point)of the structure is supposed to be fixed，and the other side point) to be sliding horizontally. Firstly, the design domain should be defined by the initial curve shape．the input location and the boundary co

43、nditions．Then．it is divided with abeam element network simulating the bird’s feather as shown in Fig．2．This is termed the partial ground structure method.</p><p>　　Fig．1 Initial shape and target shape

44、Fig．2 Discretization of the design domain </p><p>　　The simplest and most effective way to manufacture the planar compliant mechanism is to use wire—cutting technology．In the optimization pro—gram，all the e

45、lements are of rectangular beams with the same width equal to the thickness of the material，every beams height being a design variable．</p><p>　　In order to make the structure’s deformation come close to the

46、 target shape curve，the least square error(LSE)between the deformed curve and the target curve is defined as the objective function．LSE is the sum of squares of position differences of various points along the curves Its

47、 expression is </p><p>　　where I (=1，2，?，P)is the number of the points along the curves，P is the total number of points．a(chǎn)ndare the coordinates of it h node on the target and deformed boundary curve

48、respectively．</p><p>　　The constraints are </p><p>　　Where J (=1，2，?， )is the number of elements，miss the tota1 number of elements，，hi the dimension variable，hmin and hmax are the lower and

49、upper bounds of the element beam height for all elements with the value dependent on manufacturing，hb the height of the boundary elements， the maximumnoda1 deformation of the nodes on the curve boundary when the input po

50、int is inactive，and should be smaller than[d]to ensure structure stiffness，[d] the allowable maximum displacement when the input point is inact</p><p>　　2．2 GA optimization</p><p>　　GA is an opt

51、imization method which simulates the heuristic selection rule in nature，where the fit．test living things have the most chance to survive，but the inferior ones also have the opportunity to exist． Different from the contin

52、uous optimization method，it does not require the gradient-based in—formation of the objective function.</p><p>　　Every element could be expressed as a topology variable and a dimension variable． There—fore，e

53、ach individua1 could be coded as follows</p><p>　　where ，2 is the number of elements except the boundary ones．With the same heights，the boundary elements throughout the optimizing process are</p><

54、p>　　represented by only one variable，hb.</p><p>　　The fitness is the criterion of the GA optimization．It could be transformed from the objective function into </p><p>　　where βis a coefficien

55、t deciding the compulsive selection of the betterindividua1．The smaller the value，the more different would be between the two individuals’fitness thus increasing the compulsiveness of choosing the individual of higher fi

56、tness．</p><p>　　The selection of control parameters plays an important role in the convergence of the GA．Generally speaking．the cross probability ranges 0．40—0．99；the mutation probability is 0．000 01-0．01．a(chǎn)n

57、d the number of individuals 1 0．200．</p><p>　　The variable would be updated through the crossover and mutation，so the possible design could generate in the GA process．</p><p>　　2．3 Finite elemen

58、t analysis(FEA)</p><p>　　Because of the limited design variables and the target function，the optimization module of FEA software could not be used to design the compliant morphing mechanism．Therefore，this pa

59、per programmed the GA in MATLAB and the FEA in ANSYS．In the FEA，taking only account of geo—metric nonlinearities and the material being of linear elasticity, ANSYS could solve the node displacements and the element stres

60、ses．Then by deleting the elements with low stress，the fitness could be calculated．Fig．3 shows the </p><p>　　Fig．3 Flowchart of the structural optimization program．</p><p>　　2．4 Second optimizati

61、on</p><p>　　Although the GA could optimize the topology and dimension simultaneously in a large solution space，the dimension usually could not directly converge to the optimization．In order to solve this pro

62、blem，after the GA，the Direct Search method</p><p>　　should be used to find the best values of the input displacement and the dimensions of the elements which remain in the results after the GA．</p>&l

63、t;p>　　For morphing of compliant mechanism，F(xiàn)ig．3describes the whole optimization process．It mainly contains initialization of the design domain，F(xiàn)EA，GA optimization and second optimization.</p><p>　　3 Prese

64、ntation of Results:</p><p>　　Adopted from Ref，the sizes of the initial and the target trailing edge are reduced by sixty percent．，I1ab1e 1 lists the design parameters.</p><p>　　Because the displ

65、acement is used as the input，the nonlinear analysis could hardly converge and the stress of the initia1 solutions is very large．Which should be considered after thirtieth generation.</p><p>　　Table 1 Design

66、parameters </p><p>　　Fig．4 and Fig．5 illustrate the results from the GA optimization and the second optimization respectively．</p><p>　　Fig．4 Results after the GA optimization Fig．

67、5 Results after the second </p><p>　　optimization．</p><p>　　Form Table 2，it could be found that through the second optimization of the in

68、put displacement and the dimension，the LSE is reduced by 1．352 8mmand improved by 3．13％ ．The altered angle is increased by 1．049 3</p><p>　　Table 2 Results after the two optimization </p><p>　　F

69、ig．6 Stability of final optimal structure</p><p>　　Fig．6 shows the influences of the parameters when the outside distributed pressure load changes from 0 to 1 0 N／mm and the input displacement re—mains 1 1．3

70、89 7 mm on the optimal structure．It could be seen that the optimal structure has a good stability if the load is kept in the range Of 0—5 N／mm．As the external load exceeds 5 N／mm，the max stress is likely to exceed the yi

71、eld stress．</p><p>　　Because this optimization program is based on the M ATLAB and ANSYS．in order to verify the results．a(chǎn)n attempt is made to introduce the analytical results of the optimized structure into

72、ANSYS and PATRAN respectively, and then a comparison is made between them．As shown in Fig．7 and Fig．8，the two altered shapes are in good agreement：for in ANSYS the tip displacement is 54．97mm and in PATRRAN 54．50mm．The m

73、inor difference between them is from the software．</p><p>　　Fig．7 Results of FEA in ANSYS Fig．8 Results of FEA in PATRAN</p><p>　　On the other hand，a model is made by wire—cutting techn

74、ology to verify the analytical results．The material of the mode1．identical with that of the design，is 5 mm thick．In the experiment，the distributed pressure load is assumed to be zero．The input displacement 11．389 7mm wit

75、h the required input load 146 N．Fig．9 shows the model and the experimental result．The altered angle is measured9．3。．a(chǎn)nd the tip displacement 53mm．The altered shape well accords to the optimized result．If a displacement o

76、f 11．</p><p>　　Fig．9 The model and experimental result</p><p>　　4 Conclusions：</p><p>　　Proved by the simulation and experiments，the proposed method to design morphing compliant mec

77、hanism is effectual in turning out a trailing edge with required morphing effects and ability of with—standing external loads．The combination of MAT—LAB and ANSYS in the optimization renders the program simple and univer