半軸殼體左右兩面孔加工組合機(jī)床的總體設(shè)計(jì)

半軸殼體左右兩面孔加工組合機(jī)床的總體設(shè)計(jì),殼體,左右,擺布,面孔,臉孔,加工,組合,機(jī)床,總體,整體,設(shè)計(jì) SCIENCE CHINA Technological Sciences ? Science China Press and Springer-Verlag Berlin Heidelberg 2014 *Corresponding author (email: aachengang@) ? Article ? February 2015 Vol.58 No.2: 307–315 doi: 10.1007/s11431-014-5744-5 Efficient aero-structural design optimization: Coupling based on reverse iteration of structural model ZUO YingTao 1 , GAO ZhengHong 1 , CHEN Gang 2* , WANG XiaoPeng 3 2 State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, China; 3 Shanghai Electro-Mechanical Engineering Institute, Shanghai 201109, China Received April 29, 2014; accepted August 4, 2014; published online December 24, 2014 Traditional coupled multi-disciplinary design optimization based on computational fluid dynamics/computational structure dynamics (CFD/CSD) aims to optimize the jig shape of aircraft, and general multi-disciplinary design optimization methodol- ogy is adopted. No special consideration is given to the aircraft itself during the optimization. The main drawback of these methodologies is the huge expanse and the low efficiency. To solve this problem, we put forward to optimize the cruise shape directly based on the fact that the cruise shape can be transformed into jig shape, and a methodology named reverse iteration of structural model (RISM) is proposed to get the aero-structural performance of cruise shape. The main advantage of RISM is that the efficiency can be improved by at least four times compared with loosely-coupled aeroelastic analysis and it maintains almost the same fidelity of loosely-coupled aeroelastic analysis. An optimization framework based on RISM is proposed. The aerodynamic and structural performances can be optimized simultaneously in this framework, so it may lead to the true optimal solution. The aerodynamic performance was predicted by N-S solver in this paper. Test shows that RISM predicts the aerody- namic and structural performances very well. A wing-body configuration was optimized by the proposed optimization frame- work. The drag and weight of the aircraft are decreased after optimization, which shows the effectiveness of the proposed framework. aero-structural optimization, reverse iteration, cruise shape, CFD/CSD, true optimum, semi-coupled Citation: Zuo Y T, Gao Z H, Chen G, et al. Efficient aero-structural design optimization: Coupling based on reverse iteration of structural model. Sci China Tech Sci, 2015, 58: 307?315, doi: 10.1007/s11431-014-5744-5 1 Introduction The coupling of aerodynamics and structures are very se- vere for large aspect ratio aircrafts such as large military transport, civil transport and high altitude long endurance UAV. The aerodynamic loads affect the structural defor- mations, which in turn change the aerodynamic shape. So integrated aerodynamic/structural design optimization is necessary to get the optimum wing. The integrated aerody- namic/structural design optimization has been widely inves- tigated during the last 30 years. Most design optimization methods were based on low-fidelity models such as beam models combined with panel methods in the past. Now in view of the importance of high-fidelity analysis methods to the design optimization, high-fidelity models such as N-S equations, finite element method and so forth are preferred today in integrated aerodynamic/structural design optimiza- tion. However, all these high-fidelity models exacerbate the computational burden. Therefore, one of the main tasks of aero-structural design optimization today is to reduce the computational cost and speed up the optimization proce- 308 Zuo Y T, et al. Sci China Tech Sci February (2015) Vol.58 No.2 dure. During the past decade, aero-structural design optimiza- tion has developed significantly. Large amounts of re- searches have been conducted to improve the optimization efficiency. Efficient algorithms were developed by re- searchers such as tightly coupled CFD/CSD method to en- hance the efficiency of static aeroelastic analysis [1]. Some researchers developed effective optimization frameworks for aerodynamic/structural design optimization. These frameworks include optimizations based on genetic algo- rithm and all kinds of surrogate models proposed by Ku- mano et al. [2], Zill et al. [3], Rajagopal and Ganguli [4], Nikbay et al. [5], Lian and Liou [6]. After years of rapid development, the surrogate-based optimization en- tered a bottleneck period, and no breakthrough has been made during recent years. Many researchers construct com- plex multi-fidelity optimization framework to satisfy the various requirement of different phases of aircraft design [7–12]. Many optimization cases have been done about air- craft design engineering. Some others developed gradi- ent-based optimization to increase the optimization effi- ciency, and typical work includes those of Martins and Kennedy et al. [13,14], Barceblos and Maute [15], Fazzolari et al. [16], Ghazlane et al. [17]. In all these researches the jig shape was parameterized and optimized, and these optimization methodologies did not represent the characteristic of the aircraft perfectly. Static aeroelastic analyses have to be carried out in tradi- tional aero-structural optimization to obtain both the cruise shape and its aero-structural performance as the aerody- namic and structural disciplines are coupled. This procedure is very time-consuming if high fidelity models such as Eu- ler/N-S equations are adopted. The CFD/CSD analysis have to be performed iteratively during static aeroelastic analysis to get the aerodynamic performance such as lift, drag and structural performance such as maximum stress and dis- placement of the aircraft. To avoid the repeated aerody- namic/structural analyses, Aly proposed a decoupled ap- proach of aero-structural design optimization [18]. However, the aerodynamic and structural optimizations are conducted sequentially in Aly’s work, which could not lead to the true optimal solution of aero-structural design optimization. One of the characteristics of the aircraft is that the cruise shape may be transformed into the jig shape by a jig shape correction [17]. Jig shape correction gives the jig shape of the aircraft as well as the aerodynamic and structural per- formance of the aircraft. The aerodynamic design variables affect the structural performance of cruise shape if we pa- rameterize and optimize the cruise shape directly, and structural design variables such as the thickness of skin, the area of beam cap and so forth do not affect the aerodynamic performance of cruise shape. Therefore, the system is semi-coupled from the perspective of the cruise shape. Effi- cient methodologies can be constructed to get the aero- structural performance of the aircraft according to the con- vertibility between the jig shape and the cruise shape if we optimize the cruise shape directly, which is one of the main purpose of this paper. Also very efficient optimization framework can be constructed if we optimize the cruise shape directly. The remainder of this paper is organized as follows: Sec- tion 2 describes the two high fidelity models adopted for the multi-disciplinary optimization problem in this paper. Sec- tion 3 presents a novel integrated aero-structural optimiza- tion framework. Section 4 validates the effectiveness of the proposed aero-structural performance prediction methodol- ogy and the optimization framework. The conclusions are drawn in section 5. 2 Aerodynamic and structural analysis method The flow governing equations are the compressible Na- vier-Stokes equations d ? ?ddd· d ·, ?? ??? ?? ?? ? VnSnS t QF G (1) where ? is an arbitrary control volume, ?? is the bound- ary of the control volume, and ?n is the unit normal vector at the boundary. Q is the set of conservative flow variables. F is the inviscid flux tensor, and G is the flux tensor associ- ated with viscosity and heat conduction. These equations are discretized with the cell-centered fi- nite volume method, and Roe scheme is adopted for the space discretization. Turbulent flows are simulated by SA turbulence model. For the time integration, LU-SGS implic- it method is adopted [19]. Structural analysis is carried out by finite element analy- sis. The aero-structural analysis is performed by using a mul- ti-disciplinary analysis. Disciplines are linked through the exchange of coupling variables, which consist of the vector of external forces returned from the aerodynamic analysis, and the vector of displacements determined by the structural analysis. Because the CFD and CSD models used in the simulation are generated independently, a data transfer be- tween these two kinds of solvers is necessary. Many algo- rithms have been developed to transfer data between CFD and CSD models, which include IPS (infinite-plate spline), BEM (boundary element method), CVT (constant-volume tetrahedron), radial basis functions (RBF), etc. [19–24]. The RBF method is used in this paper to convert the pressure and displacements in the interface. 3 The aero-structural optimization framework 3.1 The Aero-structural analysis In common multi-disciplinary design optimization, the jig Zuo Y T, et al. Sci China Tech Sci February (2015) Vol.58 No.2 309 shape is parameterized and a static aeroelastic analysis is needed to get the aerodynamic and structural performance of the aircraft. A typical static aeroelastic simulation meth- od is the loosely coupled aeroelastic simulation. The proce- dure to get the structural and aerodynamic performance is described in Figure 1. The CFD solver is used to feature the aerodynamic characteristics, and the aerodynamic load is transferred onto the structural nodes by interface interpola- tion of fluid-structure interaction (FSI). Then a finite ele- ment analysis is carried out to get the deformed aircraft. The CFD grid of this deformed aircraft is regenerated and aero- dynamic analysis is conducted again. This procedure will be repeated until the deformation converges. Usually 5–10 iterations are expected for this procedure, which is very time-consuming and inefficient. The mass, aerodynamic forces, maximum displacement and maximum stress of the cruise shape are obtained at last. The aerodynamic design variables affect the structural performance of cruise shape from the perspective of jig shape, and the structural design variables that have no impact on the configuration affect the aerodynamic performance of cruise shape too. Therefore, the system is coupled and inefficient. To improve the efficiency, we aim to parameterize and optimize the cruise shape directly based on the fact that jig shape correction gives the aero-structural characteristic of the aircraft. The aerodynamic performance of cruise shape can be obtained easily. To get the structural performance of the aircraft, the jig shape corresponding to the cruise shape is calculated firstly. Then the aerodynamic load, the force of gravity of cruise shape, etc., are cast on the jig shape. Fi- nally the structural performance of the cruise shape is ob- tained by structural analysis. Figure 1 (Color online) Flowchart of typical static aeroelastic analysis. We adopted Aly’s methodology [17] to get the jig shape because it has been widely used in aircraft design. All the forces including the aerodynamic load, force of gravity and so forth are acted in reverse direction on the cruise shape, and the deformed aircraft is the jig shape we wanted. So the displacement of structural nodes can be achieved by solving the following equation: ? ? 1 []{}, ? ?X KF where [K] represents the stiffness matrix of the cruise shape, {X} means the unknown vector of the structural defor- mation, and {F} means the forces including the aerody- namic force, force of gravity, etc., acting on the structure. Adding the coordinates of structural nodes to the corre- sponding displacements produces the expected jig shape. Aly’s methodology was found not very precise. If we ap- ply the aerodynamic load of cruise shape, etc., to the jig shape, we get the deflected jig shape. It is supposed to be the same as the cruise shape, but actually, it has some dif- ference with the cruise shape. This is mainly because of the difference of the stiffness matrices of these two configura- tions. We also get the inaccurate structural performance of this aircraft in this way. It will be discussed further in the next section. That’s why improvements were made to get jig shape in the past few years [25]. The general improved jig shape correction can be described as follows. (1) Call the CFD solver to feature the aerodynamic char- acteristics of the cruise shape and we get the aerodynamic load of the aircraft. (2) Get the jig shape through Aly’s methodology. (3) Aeroelastic analysis of the jig shape is conducted to get the deflected jig shape. (4) Compare the displacement of every structural node of the cruise shape and the deflected jig shape. The coordinate difference vector of the corresponding structural nodes is termed as ?X. If ?X is small enough, the procedure finishes. (5) Add ??X to the structural nodes of jig shape and we get the updated jig shape, where? is a factor between 0 and 1. Go to (3). As can be seen from this procedure, we get the structural performance of the aircraft according to the displacement of the jig shape at last. The computational expense of this pro- cedure is even large than that of the aeroelastic analysis to get the aero-structural performance of the cruise shape. Therefore, it is not suitable for use in optimization. It is no- table that the jig shape deformed into the cruise shape under the forces including the aerodynamic load of the cruise shape at last. This prompts a way of using the loads of the cruise shape to get the deflected jig shape directly without iteratively calling the CFD solver. A novel aero-structural performance prediction methodology named RISM is pro- posed and shown in Figure 2. It can be described as follows. (1) Call the CFD solver to obtain the aerodynamic char- acteristics of cruise shape and we get the aerodynamic load 310 Zuo Y T, et al. Sci China Tech Sci February (2015) Vol.58 No.2 Figure 2 (Color online) Aero-structural analysis. of the aircraft. (2) Get the jig shape through Aly’s methodology. (3) Apply all the aerodynamic forces of the cruise shape, the force of gravity, etc., in the right direction to the jig shape to get the deflected jig shape. (4) Compare the displacement of every structural node of the cruise shape and the deflected jig shape. The coordinate difference vector of the corresponding structural nodes is termed as ?X, where ?X is a vector. Add ??X to the struc- tural nodes of jig shape and we get the updated jig shape, where ? is a factor which is larger than 0 and less than 1. (5) Go to step (3) unless ?X is small enough At least 15 iterations are needed in this procedure throughout which the aerodynamic load is invariable. The vector of converged steady field variables Q has been obtained in the first step of RISM. Based on Q the structural displacement of cruise shape in the second step of RISM is obtained by solving the following equation cruise 1 0,???KUF (2) where K cruise is the structural stiffness matrix of cruise shape, ?U 1 is the structural displacement and F is nodal force vec- tor of the aerodynamic forces of the cruise shape, the gravi- ty and so forth in reverse direction. The above equations can be expressed in the following form 11 (, , ) 0,?? s SQX U (3) where X s1 is coordinate vector of the finite element mesh (FEM) of the cruise shape. We get the jig shape in the sec- ond step of RISM with the following equations: 21 1 .? ?? ss X XU (4) In the third step of RISM, the deflected jig shape is ob- tained by solving the following equations. jig 2 32 2 0, , ss KUF X XU ? ?? ??? (5) where K jig is the structural stiffness matrix of jig shape X s2 is used to construct the structural stiffness matrix of jig shape, Q, etc., are used to construct the nodal force vector. X s3 is the coordinate vector of FEM of the deflected jig shape. The update of the jig shape in the fourth step of RISM can be represented as: 31 22 2221 21 2 22 (), ( ) =(1 ) , . ? ? ??? ?? ? ? ??? ?? ??? ???? ?? ss ss ss s ss ss XXX XX X XXUX X XU XX (6) The essence of RISM is solving the following nonlinear equation: 1 (, ) 0,? ??? s XUUFK (7) where K is the structural stiffness matrix of jig shape, and it depends on the FEM of the cruise shape X s1 and the dis- placement ?U between the jig shape and the cruise shape. The procedure of RISM is very similar to that of the jig shape correction method described in ref. [25]. Their main difference exists in that the aerodynamic load imposed on Zuo Y T, et al. Sci China Tech Sci February (2015) Vol.58 No.2 311 the jig shape. The aerodynamic force of the jig shape in RISM is invariable, whereas it is achieved by aeroelastic analysis in ref. [25]. Obviously, RISM converges at a much reduced computational expense. There lies an interesting comparison between the proce- dure of the static aeroelastic analysis and that of RISM. The FEM is unchangeable and the CFD grid and aerodynamic loads update every iteration in the static aeroelastic analysis, whereas the CFD grid and aerodynamic loads are un- changeable and the FEM updates every iteration in RISM. As can be seen in the procedure of RISM, the CFD solv- er is called only once to get the aerodynamic performance of cruise shape, and CSD solver is called iteratively. We get the aerodynamic and structural performance of the cruise shape by RISM just like what the aeroelastic analysis can do. Usually we call the CFD solver at least five times in general loosely-coupled static aeroelastic analysis. The expense of structural analysis can be neglected compared with that of aerodynamic analysis. Therefore, the efficiency of RISM can be improved by at least four times compared with the loosely coupled aeroelastic analysis. 3.2 The MDO framework based on RISM The widely used optimization framework based on the sur- rogate model and the genetic algorithm is adopted. RISM is used to get the aero-structural performance of the aircraft. The aerodynamic and structural performances are optimized simultaneously. The steps of the proposed algorithm are explained as follows. Latin hypercube is selected as the sampling method to ensure that all portions of the vector space are represented. The performance of aerodynamics and structure is calculat- ed by the above aero-structural analysis. The Kriging model is adopted to get the objective function based on these sam- ples. The genetic algorithm is used to optimize the Kriging models to get the optimum. The optimum has to be validat- ed by the above aero-structural analysis and added to the sample dataset. When the surrogate approximation model has been updated, the genetic algorithm runs again to get a new optimum. This process continues until the variation of objective function is small enough. The flowchart of the design process is shown in Figure 3. 4 Examples To demonstrate the effectiveness of the optimization system, a wing-body configuration is optimized. The freestream Mach number is 0.785, and Reynolds number is set to be 2.49×10 7 . The grid is generated with a size of 1.8 million. Figure 4(a) displays part of the CFD grid of the aircraft. The deformation of the body is not large and it is supposed to have little influence to the aerodynamic characteristics of the wing-body configuration, so the finite element analysis is performed only on the wing. This technique is also adop- ted by many researchers frequently [17]. The main load-carrying components of the wing box are considered, including skins, ribs, wing spars, stringers. The front and rear spar are defined at 15% and 65% along the Figure 3 (Color online) Surrogate model-based optimization process. Figure 4 (Color online) CFD grid of wing-body