在进行火箭结构分析时，需要将气动载荷转换为结构载荷。使用压力插值的转换法可保证局部载荷等效，但这种方法需要结构模型外形与气动模型保持一致，而结构模型往往只保留主要承力结构，忽略整流罩等表面细节。针对这一问题，提出一种基于压力插值和力等效的流-固载荷混合转换方法。对于表面有凸起的火箭模型，可通过对比某个气动压力点与其附近的结构单元中心点到火箭轴心的距离，从而判断该气动压力点处的结构模型是否与气动模型外形一致，划分出结构模型表面一致和不一致的区域。之后对于外形一致的区域采用压力插值法，对于外形不一致区域采用力等效法。对某火箭模型的计算结果表明，载荷转换前后的合力、合力矩误差均小于3%。本方法具有适用范围广、转换过程自动化的特点，具有较好的工程应用潜力。
Structural analysis of rockets entails conversion of aerodynamic loads into structural loads.The transformation method of pressure interpolation can ensure the equivalence of the local loads, meanwhile requiring the shape of the structural model to be consistent with that of the aerodynamic model.However, the structural model usually retains only the main load-bearing structures while neglecting the fairing and other surface details.To solve this problem, this paper proposes a hybrid fluid-to-solid load conversion method based on pressure interpolation and force equivalence.For the rocket model with protuberance on its surface, comparison of the distances between a certain aerodynamic pressure point and the center point of its nearby structural elements to the rocket axis can be conducted to judge whether the structural model near the aerodynamic pressure point is consistent with the aerodynamic model in shape, thereby differentiating the consistent and inconsistent areas on the surface of the structural model.Then the pressure interpolation method is used for the area with the consistent shape, while the force equivalent method is adopted for that with the inconsistent shape.The calculation results of a rocket model show that both the errors of the resultant force and moment before and after the load conversion are smaller than 3%.This method exhibits good engineering applicability potential with characteristics such as wide application range and automatic conversion process.
[1] 余旭东, 徐超, 郑晓亚.飞行器结构设计[M].西安:西北工业大学出版社, 2010:48-88. YU X D, XU C, ZHENG X Y.Aircraft structure design[M].Xi'an:Northwestern Polytechnical University Press, 2010:48-88(in Chinese).
[2] HIMELBLAU H, MANNING J E, PIERSOL A G, et al.Dynamic environmental criteria:NASA-HDBK-7005[S].Washington,D.C.:NASA,2001.
[3] 曹文斌, 沈林, 郭其威.运载火箭风载荷流固耦合分析方法[J].强度与环境, 2018, 45(3):7-14. CAO W B, SHEN L, GUO Q W.The analysis method of wind loads about launch vehicle based on fluid-structure interaction[J].Structure & Environment Engineering, 2018, 45(3):7-14(in Chinese).
[4] NOORIAN M A, HADDADPOUR H, EBRAHIMIAN M.Stability analysis of elastic launch vehicles with fuel sloshing in planar flight using a BEM-FEM model[J].Aerospace Science and Technology, 2016, 53:74-84.
[5] TRIKHA M, MAHAPATRA D R, GOPALAKRISHNAN S, et al.Structural stability of slender aerospace vehicles:Part I:Mathematical modeling[J].International Journal of Mechanical Sciences, 2010, 52(7):937-951.
[6] WU L, XIE C C, YANG C.Aeroelastic stability of a slender missile with constant thrust[J].Procedia Engineering, 2012, 31:128-135.
[7] JEE G, BRINDA V, LALITHAMBIKA V R, et al.Achieving load relief with minimal change in conventional control law of a launch vehicle[J].IFAC PapersOnLine, 2016, 49(1):361-366.
[8] BOER A, VAN ZUIJLEN A H, BIJL H.Review of coupling methods for non-matching meshes[J].Computer Methods in Applied Mechanics and Engineering, 2006, 196(8):1515-1525.
[9] WITTEVEEN J, BIJL H.Explicit mesh deformation using inverse distance weighting interpolation[C]//19th AIAA Computational Fluid Dynamics.Reston:AIAA, 2009.
[10] YANG F, YUE Z F, LU T J.Non-matching meshes data transfer using Kriging model and greedy algorithm[J].Advances in Engineering Software, 2018, 121:197-205.
[11] LIU W, HUANG C D, YANG G W.Time efficient aeroelastic simulations based on radial basis functions[J].Journal of Computational Physics, 2017, 330:810-827.
[12] DOU W Y, ZHANG L L, CHEN G, et al.A combined radial basis function based interpolation method for fluid-structure interaction problems and its application on high-speed trains[J].Advances in Engineering Software, 2019, 131:143-152.
[13] FRANKE R.Scattered data interpolation:Tests of some methods[J].Mathematics of Computation, 1982, 38(157):181-200.
[14] 吴宗敏.径向基函数、散乱数据拟合与无网格偏微分方程数值解[J].工程数学学报, 2002, 19(2):1-12. WU Z M.Radial basis function scattered data interpolation and the meshless method of numerical solution of PDEs[J].Chinese Journal of Engineering Mathematics, 2002, 19(2):1-12(in Chinese).
[15] BUHMANN M D.Radial basis functions[M].Cambridge:Cambridge University Press, 2003.
[16] HARDER R L, DESMARAIS R N.Interpolation using surface splines[J].Journal of Aircraft, 1972, 9(2):189-191.
[17] DUCHON J.Splines minimizing rotation-invariant semi-norms in Sobolev spaces[M].Berlin:Springer Berlin Heidelberg, 1977, 571:85-100.
[18] 《飞机设计手册》总编委会.飞机设计手册(9):载荷、刚度和强度[M].北京:航空工业出版社, 2001:331-333. Editor-in-Chief of "Aircraft Design Manual".Aircraft design manual (9):Load, strength and stiffness[M].Beijing:Aviation Industry Press, 2001:331-333(in Chinese).
[19] 张建刚, 孙仁俊, 唐长红.大型飞机气动载荷向有限元节点等效分配的方法[J].力学与实践, 2017, 39(1):25-29. ZHANG J G, SUN R J, TANG C H.The method of transferring aerodynamic load to FEM nodes for large airplane[J].Mechanics in Engineering, 2017, 39(1):25-29(in Chinese).
[20] 王专利.翼面结构有限元模型节点气动载荷计算[J].洪都科技, 2007(1):7-14. WANG Z L.FEM node load calculation of wing structure[J].Hong Du Science and Technology, 2007(1):7-14(in Chinese).
[21] 徐建新, 王彪.方向舵静强度试验载荷等效计算研究[J].装备制造技术, 2013(1):14-16. XU J X, WANG B.Research of equivalent load calculation in the rudder static strength test[J].Equipment Manufacturing Technology, 2013(1):14-16(in Chinese).
[22] 高尚君,于哲峰,汪海.基于弹簧-悬臂梁模型最小变形能的气动载荷分配方法[J].飞机设计,2013,33(6):1-4,32. GAO S J, YU Z F, WANG H.Conversion of aerodynamic load based on spring-cantilever model with minimal strain energy criterion[J].Aircraft Design,2013,33(6):1-4,32(in Chinese).
CJA