基于RBF插值技术的CFD/CSD非线性耦合分析方法研究

基于非结构混合网格的N-S方程求解器和结构柔度影响系数法，发展了一种考虑气动、结构非线性的基于RBF插值技术CFD/CSD耦合分析方法，适用于解决现代大展弦比飞机的非线性静气动弹性问题。该方法采用时间相关法（即求解非定常方程组，用长时间的渐近解趋于定常状态）求解静气弹分析时的定常流动。考虑大展弦比飞机结构变形问题为大变形小应力问题，在利用柔度系数法求解结构方程时，假设每次求解结构方程时应力与应变为线性关系，整体静气弹分析过程为非线性关系，因此每次求解结构方程时要更新柔度影响系数矩阵。在非定常N-S方程每求解一个时间步耦合一次结构有限元分析，由于结构有限元分析的时间相对于气动分析时间是很短的，所以这种方法实际上近似使用了一次求解非定常气动力的时间完成了整个静气动弹性分析的过程。对于气动网格与结构有限元网格不一致性，本文采用径向基函数（RBF）插值方法中的TPS方法进行结构弹性变形和气动载荷插值，采用虚功原理完成气动载荷数据交换。为了节省气弹分析时间，采用动网格方法对气动网格进行更新，本文基于RBF插值方法发展一种适用于混合网格（四面体、三棱柱、金字塔和六面体）变形的动网格方法，可以保证附面层网格的质量与分布从而准确模拟其流动。利用该方法对M6机翼、DLR-F6翼身组合体和某大型客机机翼进行了静气动弹性特性分析，结果验证了本文开发的非线性CFD/CSD耦合分析方法的可行性、精确性和高效性。

A approach to CFD/CSD non-linear coupling based on RBF interpolation technology

An approach to CFD/CSD non-linear coupling based on radial basis functions (RBF) interpolation technology is established,which is based on the Navier-Stokes (N-S) equations of unstructured hybrid grid and the method of structure flexibility coefficient matrix,and is used to analyze the non-linear aeroelasticity of flexible aircraft with high aspect ratio.Steady flow is simulated by the method of time correlation,which calculates unsteady equations for long time to get the solutions of steady N-S equations.The structure equations are solved at every time step.Because CSD analysis spends much less time than CFD solver,so the non-linear computation aeroelasticity method just takes the time of the calculation of unsteady equations to complete the whole process of aeroelasticity.Considering that the flexible aircraft with high aspect ratio is geometric non-linear,an approximate nonlinear method is used in CSD analysis.The RBF interpolation technology is easy to realize,accurate to exchange data and saving time,so it is applied to exchange flexible deformation aerodynamic loads with the principle of virtual power.The mesh motion method based on RBF interpolation method is established instead of re-meshing,which can be used in moving the hybrid mesh of tetrahedron and triangular prism mesh etc,that can make the computation of boundary accurate.The aeroelasticity of M6 wing,DLR-F6 wing body and a wing of aero-transport are simulated.And results show that the approach to nonlinear computational aeroelasticity based on RBF interpolation method is feasible,accurate and efficient.