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。     

欠驱动系统控制方法实现导弹时间与角度协同

首先,给出弹目距离与视线角控制的二阶欠驱动系统的标准形式,选取这两个相关的系统状态分别构造滑模平面,滑模面能够保证系统状态的跟踪;然后,选取李雅普诺夫函数,采用李雅普诺夫稳定定理求取最终的控制量,保证两个滑模面渐近稳定,实现对撞击时间与撞击角度的同时控制;最后,在时间控制基本完成后,切换为角度精确控制。     

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.     

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。     

纤维增强复合材料币状I型裂纹桥联问题

利用平面等效方法，将轴对称币状裂纹问题转化平面裂纹问题，由此给出复合材料内币状Ⅰ型裂纹的桥联积分控制方程。对权函数法应用于求解币状裂纹问题的可行性提出质疑，并给出修正的建议。然后对币状Ⅰ型裂纹桥联问题给予了断裂力学分析。利用一种新的分段插值方法求解了桥联积分控制方程。针对该积分程提出了一种近似分析解法，其结果与数值结果符合得相当好。     

运载火箭推力故障下基于智能决策的在线轨迹重规划方法

为了提高运载火箭上升段飞行中推力故障下轨迹重规划的计算效率,提出了一种基于智能决策的在线轨迹重规划方法,将原问题转化为最优救援轨道的在线智能决策和成熟的燃料最优轨迹规划问题进行求解。通过离线求解不同故障状态对应的轨迹重规划问题,建立"故障状态-救援轨道"样本集,基于径向基神经网络建立最优救援轨道的决策模型,并将决策模型装订箭上。在实际飞行中以当前故障状态作为输入,利用决策模型可在线快速决策出最优救援轨道根数,进而求解以救援轨道为目标轨道的燃料最优轨迹规划问题,从而完成推力故障下的在线轨迹重规划。数值仿真表明,与直接求解轨迹重规划问题相比,该方法的计算效率提高了两个数量级以上,同时给出一致的最优救援轨迹。