基于共旋有限元格式的非线性连接翼气动弹性响应分析
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摘要
基于Generalized-α算法,推导得出了基于co-rotational(共旋)有限元格式的三角形平板壳结构非线性动力学近似能量守恒算法,该算法在每个时间步长内使用动力学平衡方程预估-校正迭代方法来保证算法的稳定性。结合计算流体力学方法(CFD)和松耦合求解策略发展了薄壳结构非线性气动弹性求解方法。采用本文所述方法,针对Prandtl平板连接翼结构,对其在两种不同飞行条件下的瞬态响应进行了仿真。当攻角为正且动压较大时,连接翼的响应出现了三个振动平衡位置,并且达到静气动弹性平衡时其变形为弦向低头展向向下弯曲;当攻角为正且动压较小时,连接翼的振动响应只出现了一个平衡位置,且其静气动弹性变形构型为弦向低头展向向上弯曲。仿真结果表明,连接翼结构的气动弹性响应较一般单翼更为复杂,因此,在结构设计过程中需要采用高保真度的分析手段对连接翼结构的气动弹性特性进行分析。
An approximate energy conservation algorithm for nonlinear dynamic analysis of triangular flat shells based on co-rotational formulation finite element is derived from Generalized-α method. The numerical stability of this algorithm is satisfied by predictor-corrector iterative procedure of dynamics balance equation in each time step. Combined with computational fluid dynamics(CFD) and loose coupling algorithm, a nonlinear aeroelastic analysis process for thin shell structures is developed. The transient response of a Prandtl plane joined wing is investigated in two different flight conditions(two different dynamic pressure) based on this method. It is found that there are three balance positions in the transient response when the angle of attack is positive and dynamic pressure is large, and when static aeroelastic balance is achieved, the joined wing twists down in chord direction and bends down in span direction; when the angle of attack is positive and dynamic pressure is small, the transient response has only one balance position during vibration and the joined wing twists down in chord direction and bends up in span direction. The simulation results show that the aeroelastic transient response of joined wing is much more complicated than the monoplane, so the high-fidelity analyses should be used for the aeroelastic analysis of joined wing in the process of structure design.
An approximate energy conservation algorithm for nonlinear dynamic analysis of triangular flat shells based on co-rotational formulation finite element is derived from Generalized-α method. The numerical stability of this algorithm is satisfied by predictor-corrector iterative procedure of dynamics balance equation in each time step. Combined with computational fluid dynamics(CFD) and loose coupling algorithm, a nonlinear aeroelastic analysis process for thin shell structures is developed. The transient response of a Prandtl plane joined wing is investigated in two different flight conditions(two different dynamic pressure) based on this method. It is found that there are three balance positions in the transient response when the angle of attack is positive and dynamic pressure is large, and when static aeroelastic balance is achieved, the joined wing twists down in chord direction and bends down in span direction; when the angle of attack is positive and dynamic pressure is small, the transient response has only one balance position during vibration and the joined wing twists down in chord direction and bends up in span direction. The simulation results show that the aeroelastic transient response of joined wing is much more complicated than the monoplane, so the high-fidelity analyses should be used for the aeroelastic analysis of joined wing in the process of structure design.
引文
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[15] 李少华,杨智春,谷迎松,等.复合材料连翼的气动弹性剪裁研究[J].西北工业大学学报,2008,26(3):292-296.
[16] 吴小胜,雷娟棉,胡俊.钻石背弹翼的静气动弹性研究[J].北京理工大学学报,2010,30(12):1387-1390.
[17] 吴小胜,吴甲生.“钻石背” 弹翼颤振的数值计算[J].北京理工大学学报,2007,27(5):385-389.
[18] 雷娟棉,吴甲生.钻石背弹翼外形参数对气动特性的影响[J].北京理工大学学报,2006,26(11):945-948.
[19] 雷娟棉,吴甲生.钻石背弹翼气动特性风洞实验研究[J].兵工学报,2007,28(7):893-896.
[20] 许兆庆,吴军基,薛晓中,等.巡飞弹钻石背折叠翼结构优化设计[J].机械设计与研究,2011,27(1):87-90.
[21] 黄益民,葛森,吴炜,等.钻石背弹翼抗风动力可靠性及其灵敏度分析[J].机械科学与技术,2013,32(3):416-420.
[22] 窦怡彬,张晓宏.连接翼布局的非线性屈曲分析[J].上海航天,2017,34(5):40-45.
[23] CAVALLARO R,IANNELLI A,DEMASI L,et al.Phenomenology of nonlinear aeroelastic responses of highly deformable joined-wings configurations[C]// 55th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.National Harbor,Maryland:[s.n.],2014:1-63.
[24] DEMASI L,LIVNE E.Dynamic aeroelasticity coupling full order geometrically nonlinear structures and full order linear unsteady aerodynamics - the joined wing case[C]// 49th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.Schaumburg:[s.n.],2008:1-32.
[25] 杨劲松,夏品奇.薄壳结构非线性动力学响应的共旋有限元能量守恒与衰减算法[J].中国科学:技术科学,2013,43(1):46-56.
[26] BATOZ J L,BATHE K J,HO L W.A study of three-node triangular plate bending elements[J].International Journal for Numerical Methods in Engineering,1980,15(12):1771-1812.
[27] FELIPPA C A.A study of optimal membrane triangles with drilling freedoms[J].Computer Methods in Applied Mechanics and Engineering,2003,192(16/17/18):2125-2168.
[2] LIVNE E.Aeroelasticity of joined-wing airplane configurations-past work and future challenges-a survey:Proceedings of the 42nd AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics and Materials Conference [C].Seattle,Washington:[s.n.],2001.
[3] WEISSHAAR T A,LEE D H.Aeroelastic tailoring of joined-wing configurations[C]// 43rd AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Confe-rence.Denver,Colorado:[s.n.],2002:1-11.
[4] LEE D H,CHEN P C.Nonlinear aeroelastic studies on a joined-wing with wing buckling effects C]// 45th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.Palm Springs,California:[s.n.],2004:1-12.
[5] DEMASI L,CAVALLARO R,MARQUEZ R A.Postcritical analysis of Prandtl plane joined-wing configurations[J].AIAA Journal,2013,51(1):161-177.
[6] DEMASI L,CAVALLARO R,BERTUCCELLI F.Post-critical analysis of highly deformable joined wings:The concept of snap-divergence as a characterization of the instability[J].Journal of Fluids and Structures,2015,54:701-718.
[7] CAVALLARO R,BOMBARDIERI R,DEMASI L,et al.Prandtl plane joined wing:Body freedom flutter,limit cycle oscillation and freeplay studies[J].Journal of Fluids and Structures,2015,59:57-84.
[8] SOTOUDEH Z,HODGES D H.Incremental method for structural analysis of joined-wing aircraft[J].Journal of Aircraft,2012,48(5):1588-1601.
[9] 潘家正,吕庆风,周欲晓.连接翼布局直接力控制可能性的初步探索[J].飞行力学,1996,14(1):48-53.
[10] 李光里,李国文,黎军,等.连接翼布局气动特性研究[J].空气动力学学报,2006,24(4):513-519.]
[11] 刘杰,张曙光.连接翼布局纵向控制特性[J].航空学报,2008,29(S):91-96.
[12] 冉玉国,李秋彦,金伟,等.大展弦比连接翼飞机考虑预载作用下的非线性模态与颤振特性研究[C]// 第十一届全国空气弹性学术会议,CARS-2009.昆明:中国空气动力学会气动力弹性专业委员会,2009:28-33.
[13] 张书俊,王运涛,孟德虹.大展弦比联接翼静气动弹性研究[J].空气动力学学报,2013,31(2):170-174.
[14] 张波成,万志强,杨超.连翼布局飞行器飞行载荷与颤振分析[J].工程力学,2010,27(8):229-233.
[15] 李少华,杨智春,谷迎松,等.复合材料连翼的气动弹性剪裁研究[J].西北工业大学学报,2008,26(3):292-296.
[16] 吴小胜,雷娟棉,胡俊.钻石背弹翼的静气动弹性研究[J].北京理工大学学报,2010,30(12):1387-1390.
[17] 吴小胜,吴甲生.“钻石背” 弹翼颤振的数值计算[J].北京理工大学学报,2007,27(5):385-389.
[18] 雷娟棉,吴甲生.钻石背弹翼外形参数对气动特性的影响[J].北京理工大学学报,2006,26(11):945-948.
[19] 雷娟棉,吴甲生.钻石背弹翼气动特性风洞实验研究[J].兵工学报,2007,28(7):893-896.
[20] 许兆庆,吴军基,薛晓中,等.巡飞弹钻石背折叠翼结构优化设计[J].机械设计与研究,2011,27(1):87-90.
[21] 黄益民,葛森,吴炜,等.钻石背弹翼抗风动力可靠性及其灵敏度分析[J].机械科学与技术,2013,32(3):416-420.
[22] 窦怡彬,张晓宏.连接翼布局的非线性屈曲分析[J].上海航天,2017,34(5):40-45.
[23] CAVALLARO R,IANNELLI A,DEMASI L,et al.Phenomenology of nonlinear aeroelastic responses of highly deformable joined-wings configurations[C]// 55th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.National Harbor,Maryland:[s.n.],2014:1-63.
[24] DEMASI L,LIVNE E.Dynamic aeroelasticity coupling full order geometrically nonlinear structures and full order linear unsteady aerodynamics - the joined wing case[C]// 49th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference.Schaumburg:[s.n.],2008:1-32.
[25] 杨劲松,夏品奇.薄壳结构非线性动力学响应的共旋有限元能量守恒与衰减算法[J].中国科学:技术科学,2013,43(1):46-56.
[26] BATOZ J L,BATHE K J,HO L W.A study of three-node triangular plate bending elements[J].International Journal for Numerical Methods in Engineering,1980,15(12):1771-1812.
[27] FELIPPA C A.A study of optimal membrane triangles with drilling freedoms[J].Computer Methods in Applied Mechanics and Engineering,2003,192(16/17/18):2125-2168.