振荡函数的移动最小二乘逼近方法

移动最小二乘法在求解偏微分方程数值解中得到广泛使用,但是用等距节点逼近振荡函数时逼近精度不高,针对这一问题,用适应函数变化的非均匀节点离散求解区域,与之相适应,移动最小二乘法中权函数的支撑域半径也随节点密度变化,这里用基于领域搜索算法确定支撑域半径。数值算例表明,在移动最小二乘法中,用适应节点变化的节点集及基于领域的搜索算法确定支撑域半径能够有效减小逼近误差。     

Stagnation temperature effect on the supersonic axisymmetric minimum length nozzle design with application for air

When the stagnation temperature of a perfect gas increases, the specific heats and their ratio do not remain constant any more and start to vary with this temperature. The gas remains perfect; its state equation remains always valid, except, it is named in more by calorically imperfect gas. The aim of this work is to trace the profiles of the supersonic axisymmetric minimum length nozzle to have a uniform and parallel flow at the exit section, when the stagnation temperature is taken into account, lower than the dissociation threshold of the molecules, and to have for each exit Mach number and stagnation temperature shape of nozzle. The method of characteristics is used with the algorithm of the second order finite differences method. The form of the nozzle has a point of deflection and an initial angle of expansion. The comparison is made with the calorically perfect gas.     

改进Hicks-Henne型函数法在翼型参数化中的应用

翼型参数化是翼型优化中的重要组成部分.以最常用的Hicks-Henne型函数法为基础,分析了此型函数对翼型后缘描述不精确的原因,并提出了改进方法.由于Hicks-Henne型函数在使用中需确定型函数峰值位置,即站位点和型函数的幅值大小,利用站位点生成函数,结合改变型函数幅值的思想,通过优化算法来自动调节站位点分布和型函...     

基于随机减量的运行模态频域分析方法

以高层建筑、大跨桥梁等难以进行人工激励的大型复杂结构为对象,提出并实现了一种基于随机减量技术和复模态指示因子函数法的新型频域运行状态模态参数识别方法.由随机运行响应估计随机减量函数,然后通过时频域变换得到频域的半功率谱密度函数,并用复模态指示因子函数法从半功率谱密度函数中识别结构模态参数.最后对1个三维空间结构模型进行算法验证,得到相应的各阶模态参数,证明了将随机减量技术和复模态指示因子函数法相结合的方法识别大型结构模态参数的有效性和合理性.     

基于遗传算法的平流层飞艇航迹规划方法研究

文章针对平流层飞艇驻空阶段航迹规划问题进行研究和仿真分析.考虑平流层飞艇自身飞行的特点,建立其运动学方程和风场模型,并在适当假设基础上,构造能够反映其飞行能耗的代价函数.最后采用遗传算法进行算例计算,求解平流层飞艇最优轨迹.仿真结果表明,遗传算法能够有效、快速地收敛并稳定至问题的最优解;其所构造的代价函数能够反映飞艇自...     

单纯形法在飞机平尾大轴结构设计中的应用

为了研究歼击机水平尾翼大轴的结构设计，本文采用工程梁理论进行结构建模，将尺寸变量与坐标变量作为两个设计空间中的设计变量，其中，利用近似函数与黄金分割法相结合进行尺寸优化．再使用Nelder-Mead单纯形方法进行几何优化，分别进行交替优化，直至迭代收敛。实际箅例的优化结果表明：与传统的经验设计相比，本方法对大轴结构减重效果明显，在工程上是可行的。     

利用协方差分析法合理评价高数教学效果

本文利用协方差分析法合理评价高数教学效果。     

自然写生与工业设计

本文论述了自然界中生命存在的基本规律，进而指出这些基本规律对提高设计者的创造力，从而设计出更为实用的、完美的工业产品是非常重要的。     

An efficient large-scale mesh deformation method based on MPI/OpenMP hybrid parallel radial basis function interpolation

An efficient MPI/OpenMP hybrid parallel Radial Basis Function (RBF) strategy for both continuous and discontinuous large-scale mesh deformation is proposed to reduce the computational cost and memory consumption. Unlike the conventional parallel methods in which all processors use the same surface displacement and implement the same operation, the present method employs different surface points sets and influence radius for each volume point movement, accompanied with efficient geometry searching strategy. The deformed surface points, also called Control Points (CPs), are stored in each processor. The displacement of spatial points is interpolated by using only 20–50 nearest control points, and the local influence radius is set to 5–20 times the maximum displacement of control points. To shorten the searching time for the nearest control point clouds, an Alternating Digital Tree (ADT) algorithm for 3D complex geometry is designed based on an iterative bisection technique. Besides, an MPI/OpenMP hybrid parallel approach is developed to reduce the memory cost in each High-Performance Computing (HPC) node for large-scale applications. Three 3D cases, including the ONERA-M6 wing and a commercial transport airplane standard model with up to 2.5 billion hybrid elements, are used to test the present mesh deformation method. The robustness and high parallel efficiency are demonstrated by a wing deflection case with a maximum bending angle of 45° and more than 80% parallel efficiency with 1024 MPI processors. In addition, the availability for both continuous and discontinuous surface deformation is verified by interpolating the projecting displacement with opposite directions surface points to the spatial points.     

台劳公式的新证明及其推广

中值定理及其台劳公式的证明一般采用构造辅助函数的方法。利用行列式构造了一个统一格式的辅助函数,利用该辅助函数可以证明各中值定理及台劳公式,而且很容易得出台劳公式的推广形式。