基于LSCM与多项式拟合的机翼气动载荷施加方法

Aerodynamic Load Application Method of Wing Based on LSCM and Polynomial Fitting

目的 将由机翼计算的离散气动载荷高精度等效作用于结构有限元节点上。方法 先通过最小二乘保角映射(Least Square Conformal Maps,LSCM)将机翼翼面的气动模型网格和有限元模型网格映射到同一个二维参数平面上,在此平面上用二维切比雪夫多项式拟合气动载荷的分布,然后代入结构有限元映射节点坐标,即可实现结构有限元离散载荷的施加。结果 采用本文方法,即可实现控制合力、压心坐标误差条件下的气动载荷在结构有限元网格上的整体离散施加。结论 采用LSCM方法可以实现大曲率壳向二维平面的保角映射。基于切比雪夫多项式建模与参数识别可以高精度拟合复杂的翼面气动载荷,二者的结合运用使得结构有限元载荷的施加可以兼具效率与精度。

The work aims to allocate the discrete aerodynamic load calculated by the wing to the finite element nodes of the structure precisely and equivalently.Firstly,the aerodynamic mesh and the finite element mesh were mapped to the same two-dimensional intermediate surface by Least Square Conformal Maps(LSCM),and then the distribution of the aerodynamic load was fitted by Chebyshev polynomial on the intermediate surface.Finally,the coordinates after finite element node mapping were substituted to convert the aerodynamic load into finite element load.With the method presented in this paper,the whole discrete allocation of aerodynamic load on the finite element mesh under the condition of control force and center of compres-sion coordinate error can be realized.The LSCMmethod can realize conformal mapping of large curvature shells to two-dimensional planes.The Chebyshev polynomial modeling and parameter identification can fit the complex aerofoil aerody-namic loadwith high precision.The combination of the two methods can make the load conversion process both efficient and accurate.