基于结构模型反迭代的高效气动/结构多学科优化设计方法

Loosely-coupled static aeroelastic analysis is adopted to get the aerodynamic and structural performances in traditional aero-structural design optimization, and global optimization or gradient-based optimization is conducted. The efficiency of optimization is very low, and the adjoint equations are very hard to converge. Coping with this situation, a methodology named reverse iteration of structural model (RISM) is proposed to calculate the aero-structural performance of aircraft in the preceding research of the applicant. The efficiency is improved by at least 4 times compared with the conventional loosely-coupled static aeroelastic analysis, and so does the global optimization. The purpose of this research is to build the adjoint theory based on RISM to overcome the disadvantage of traditional adjoint equations and traditional adjoint-based optimization. The structural equations are solved after the aerodynamic equations in RISM, so the coupling of structural discipline and aerodynamic discipline is decreased. According to the similarity and symmetry between adjoint problem and original problem, the adjoint equations of RISM feature as follows compared with the traditional adjoint equations which are solved in loosely-coupled way. 1. The coupling of structural and aerodynamic adjoint equations is decreased. The structural and aerodynamic adjoint equations can be solved in sequence, which decreases dimensions of the adjoint equations and increases the convergence property. 2. A number of cross-partial derivatives disappear in the adjoint equations of RISM, which simplifys the formula and decreases the difficulty to programme. Also it reduces the rigidity of the adjoint equations, and accelerates the convergence remarkably. 3. The efficiency to solve the equations can be improved by at least 4 times. The creative ideas of this research include the construction of the adjoint equations of RISM, and the improvement of the convergence property markedly as well as the efficiency of gradient calculation and optimization.

传统飞行器气动/结构多学科设计优化采用松耦合静气动弹性分析获得气动与结构特性，进行全局或梯度优化设计，存在效率低、共轭方程收敛难的问题。针对该问题，申请人的前期工作建立了结构模型反迭代（RISM）方法评估气动与结构特性，较传统的松耦合静气弹分析效率提高4倍以上，全局优化效率也相应提高4倍以上。本项目拟建立RISM下的离散共轭理论以解决传统共轭优化存在的问题。RISM是按照先气动再结构方程的顺序求解的，因此耦合强度降低，依据共轭问题与原问题的对称性及相似性，RISM的共轭方程相比松耦合迭代求解的传统共轭方程将有如下特点：1.耦合程度降低，按照先结构再气动的顺序求解，降低了方程组的规模，易于收敛；2.大量减少共轭方程中的交叉导数，简化理论公式与实现，降低了方程刚性，能显著提高收敛性；3.求解效率提高4倍以上。创新点是建立RISM对应的共轭理论，显著改善共轭方程的收敛性，提高梯度计算与优化效率。

传统飞行器CFD/CSD松耦合多学科设计优化是以型架外形为设计对象，对其进行静气动弹性分析获得巡航外形及其对应的气动特性和应力应变特性等，以此构造多学科的目标函数与约束条件，采用合适的优化方法进行全局或梯度优化设计。该类方法存在的问题是静气动弹性计算量大。为解决这个问题，项目提出了直接以巡航外形为设计对象，CFD方法直接获得巡航构型的气动特性，无需迭代，再采用本项目提出的结构外形反迭代（RISM）方法获得结构特性，解决了目标特性计算效率低的问题。在此基础上开展了基于代理模型与离散共轭方法的优化设计研究，详细推导了基于RISM的离散共轭梯度计算方法，采用GMRES方法对结构共轭方程进行了求解，能够收敛。优化设计中需要对几何外形参数化，本项目采用自由变形参数化方法对外形进行参数化，并完成了一个基于FFD方法的参数化软件。工程设计中需要用升力、阻力等对外形的敏感性云图来指导设计，一般采用升阻力等对几何设计变量的偏导数来构建敏感性云图。对于阻力系数的敏感性云图，由于该方法使用偏导数，因此存在一定的误导性。本项目提出并建立了阻力系数对几何设计变量的全导数的概念与方法，构建了基于全导数的阻力系数敏感性云图，对于飞机设计更具指导性。对于外形的优化设计结果，一般是以离散的表面网格点的形式存在的，无法直接用CAD软件打开和编辑，不利于工程设计。传统方法采用CATIA等软件导入离散点及点云等方式构建几何外形，存在鲁棒性和建模精度不够等问题。本项目采用UG二次开发方法建立了针对结构化表面网格的方式，自动生成高效高精度CAD几何外形文件，解决了工程中存在的问题。