响应面拟合法在机翼结构优化中的应用研究

在飞机结构优化设计中，针对循环利用有限元软件寻优耗时大、收敛比较慢的状况，本文采用了一种基于响应面多项式拟合方法对机翼结构进行优化。以某平直机翼为例，该方法从建立机翼结构的有限元模型出发，结合正交试验设计方法，经过对比，采用比较新颖的最大差值极小化法，建立机翼的二次响应面近似模型；在此基础上，以整个机翼结构质量最小化为目标，最大位移和最大应力为约束，把机翼划分为多个区域，选取各区域蒙皮厚度和全部肋腹板厚度为设计参数，建立数学优化模型，用ISIGHT集成MATLAB的方法，采用序列二次规划法进行优化。优化的结果表明，采用该方法对该平直机翼进行优化，在满足机翼刚度和强度的情况下，能有效降低机翼质量，并且避免了多次重复调用有限元软件进行计算，迭代次数仅为34次，优化效率明显提高。

The Application of the Method of Response Surface in Optimization Design of Aircraft Wing Structure

Since using finite element software for the cycle takes too much time and leads to slow convergence in the optimization design of aircraft structure, the article use a method based on response surface polynomial fitting to optimize the wing structure. Taking one straight wing as the example, the finite element model of the wing structure is established in the first step, and then two response surface models are built combined with the orthogonal experimental design method. After the error comparison, the maximum difference minimization method is chosen to establish the wing of the quadratic response surface approximation model. On this basis, the target is set to minimize the entire wing structure quality while the maximum displacement and maximum stress are made constraints. The wing is divided into six regions. Selecting each regional skin thickness and rib web thickness as the design parameters, the article establish mathematical optimization model. With the integration of ISIGHT and MATLAB the article optimizes the mathematical model in sequential quadratic programming method. The results show that, using the method in this paper to optimize the straight wing can effectively reduce the quality of the wing while the constraints of the wing stiffness and strength is satisfied, at the same time repeated calls the finite element software to calculate is avoided.Since the number of iterative is only 34, the optimization efficiency is significantly improved.