任意旋成面叶栅杂交型气动命题的变分原理与广义变分原理

本文建立了任意旋成面叶栅一种杂交型命题——在叶型周线的某段上给定叶型形状,而在其余段上则给定流速分布——的两族气动变分原理与广义变分原理,从而使正命题与反命题的处理完全统一起来,并加以推广.文中充分发挥了“自然边界条件”和“人工分界面”的有力作用,以简化各种复杂边界条件的处理,并提出了一个新的短函数.本文为在叶轮机叶栅的气动问题中引进和推广有限元法、变分-差分解法以及变分直接解法,提供一个更广泛、更完密的理论基础.     

有叶顶间隙的涡轮弯叶栅拓扑与旋涡结构(Ⅱ)——横截面流场拓扑结构与叶栅旋涡结构

根据具有叶顶间隙的直叶栅和正、反弯叶栅壁面流动的墨迹显示以及横截面内气动参数测量,应用拓扑学原理,分析了叶栅流道横截面内的拓扑结构。与直叶栅比较,叶片正弯消除了上通道涡分离线,并使二次涡由闭式分离转变为开式分离,而叶片反弯仅影响奇点位置、旋涡强度与尺度。     

有叶顶间隙的涡轮弯叶栅拓扑与旋涡结构(Ⅰ)——试验模型、端壁与叶片表面拓扑结构

根据具有叶顶间隙的直叶栅和正、反弯叶栅壁面流动的墨迹显示以及横截面内气动参数测量,应用拓扑学原理,分析了端壁与叶片表面拓扑结构。与直叶栅比较,叶片正弯消除了上通道涡分离线,并使二次涡由闭式分离转变为开式分离,而叶片反弯仅影响奇点位置、旋涡强度与尺度。     

有叶顶间隙的涡轮弯叶栅拓扑与旋涡结构（I）—试验模型、端壁与叶片表面拓扑结构

根据具有叶顶间隙的直叶栅和正、反弯叶栅壁面流动的墨迹显示以及横截面内气动参数测量，应用拓扑学原理，分析了端壁与叶片表面拓扑结构，与直叶栅比较，叶片正弯消除了上通道涡分离线，并使二次涡由闭式分离转变为开式分离，而叶片反弯仅影响奇点位置、旋涡强度与尺度。     

三维振荡机翼含激波跨声速非定常绕流广义变分原理的普遍形式及其派生族

本文在文献[1,2]基础上,建立了作任意周期性振荡的三维机翼含激波非定常跨声速绕流的广义变分原理普遍形式及其派生族。为了便于数值处理及捕获未知间断面,文中运用变域变分工具将振荡的激波及自由尾涡面上的间断条件(包括Rankine-Hugoniot激波关系)以及几乎全部边界条件都转化成自然界面条件,并兼顾了翼面吸(喷)气的作用。本文为引进有限元法等变分解法提供一更普遍、完善的理论基础,并可再推广到三维机翼-机身组合体和三维旋转叶栅上去。     

固体的离散型变分原理——有限元离散分析的变分原理

本文提出一类新的固体的离散型变分原理.它是从有限元离散分析的实际出发,考虑到元素的边界为可动边界,并且由于分片构造待解函数,使待解函数在元素的交界处具有各种间断性.由此,我们利用数学中的具有各种间断性的可动边界的变分方法,基于一阶变分为零的驻值条件上,建立了固体的离散型变分原理.离散型变分原理消除了元素交界处所导入的误差.它概括了古典与非古典变分原理.本文得到的待解函数应满足的交界方程,是有限元的收敛性(包括非保形元素在内)的必要条件,它开拓了待解函数应满足协调性的收敛性要求.     

变可信度模型在气动优化中的应用

在气动外形优化中, 采用近似模型管理结构（AMF）方法,对变可信度模型进行组织和管理．这样能够充分利用低可信度模型,将主要计算量集中在低可信度模型的优化迭代过程中．同时,采用高可信度模型监控优化过程,使最终的优化解收敛到高可信度模型上．最后,设计了零阶变可信度气动特性优化管理结构与搜索算法,对某飞翼型无人机的翼型进行了气动优化．优化外形的气动性能与初始外形比有所提高．实际结果表明所提出的方法具有良好的可行性和适用性．     

气动、结构、载荷相协调的大型风电叶片自主研发进展

从叶片设计的3个关键环节（气动设计、结构设计和载荷评估）出发,对叶片自主研发进展进行了总结分析．在气动设计方面,概述了计算流体动力学（computational fluid dynamics, CFD）方法、涡方法和叶素动量（blade element momentum, BEM）方法,并依据工程中广泛应用的BEM方法,指出了低风速区风电叶片的解决思路;在结构设计方面,简要概述了基于梁模型的传统设计分析方法,分析了其在大型复合材料叶片薄壳结构上的不足,并对有限元方法（finite element method, FEM）在叶片结构分析中的应用进展进行了介绍;在载荷评估方面,介绍了其对叶片和整机其它部件的影响,阐述了载荷预估方面的工作进展．然后,通过分析3个关键环节之间的相互关系,得到如下结论:建立气动、结构和载荷相协调的叶片优化设计体系,才能真正满足高效低成本的需要．最后,指明了需要进一步研究的主要方向,即高效低载翼型研究,结构非线性有限元分析,气动-结构耦合研究,设计标准制定．最终目标是建立适合中国风资源特点的叶片研发体系,推动我国风电产业发展.     

非线性弹性动力学率型广义变分原理及子域原理

本文基于拖带坐标描述和S-R分解定理,建立了包含速度梯度、动量、速度、应力和应变率等五类独立场变量的非线性弹性动力学率型广义变分原理和广义子域混合杂交变分原理.     

功率型变分原理和功能型拟变分原理及其应用

自从钱伟长建立了功率型变分原理以来,功率型变分原理和功能型变分原理在理论方面和应用方面有什么区别和联系,成为学术界关注的课题.应用变积方法,根据Jourdain原理和d’Alembert原理,建立了不可压缩黏性流体力学的功率型变分原理和功能型拟变分原理,推导了不可压缩黏性流体力学的功率型变分原理的驻值条件和功能型拟变分原理的拟驻值条件.研究了不可压缩黏性流体力学的功率型变分原理在有限元素法中的应用.研究表明,功率型变分原理与Jourdain原理相吻合,功能型变分原理与d’Alembert原理相吻合.功率型变分原理直接在状态空间中研究问题,不仅在建立变分原理的过程中可以省略在时域空间中的一些变换,而且给动力学问题有限元素法的数值建模带来方便.     

Anisotropic ring stretched by rigid half-disks

A theoretical basis is provided for the experimental method of determining the elastic and strength properties of materials by stretching ring specimens with a pair of rigid half-disks. The equilibrium equations of the plane problem for an anisotropic ring with mixed boundary conditions are solved by means of an expansion in Fourier series with respect to the circumferential coordinate. Numerical results obtained on a computer are analyzed. The dependence of the circumferential stress concentration coefficient on various parameters is investigated.Moscow Power Engineering Institute. Translated from Mekhanika Polimerov, No. 6, pp. 1113–1116, November–December, 1970.     

RBF Neural Network Based Prediction on Blade Surface Pressure Fields in Compressors北大核心CSCD

The airflow characteristics of the internal flow path of an aero-engine compressor are complex, and the vortex flow field around the blade is characterized by high pressure, high speed, rotation, and unsteadiness. Therefore, there is an urgent need to calculate and predict the aerodynamic characteristics of the complex flow field around the compressor blade efficiently and accurately. The computational fluid dynamics (CFD) method was used to generate the aerodynamic load distribution on the blade surface under different operating conditions for the study of the complex flow fields around aero-engine blades. The radial based function (RBF) neural network was applied to establish the pressure surface aerodynamic load prediction model, and the neural network modeling method was combined with the flow field calculation. The neural network method can learn and train the CFD-based data set to properly compensate the errors from the CFD, which provides a reference for the effective prediction of the complex flow fields around aero-engine compressor blades. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Optimality conditions in multiobjective differentiable programming

Necessary conditions not requiring convexity are based on the convergence of a vector at a point and on Motzkin's theorem of the alternative. A constraint qualification is also involved in the establishment of necessary conditions. Three theorems on sufficiency require various levels of convexity on the component of the functions involved, and the equality constraints are not necessarily linear. Scalarization of the objective function is used only in the last sufficiency theorem.The author is thankful to the unknown referce whose comments improved the quality of the paper.     

A Coordinate Gradient Descent Method for Nonsmooth Nonseparable Minimization

This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex function. We find a search direction by solving a subproblem obtained by a second-order approximation of the smooth function and adding a separable convex function. Under a local Lipschitzian error bound assumption, we show that the algorithm possesses global and local linear convergence properties. We also give some numerical tests (including image recovery examples) to illustrate the efficiency of the proposed method.     

Airfoil design optimization using the Navier-Stokes equations

A design optimization technique is presented which couples a computationally efficient Navier-Stokes code with a numerical optimization algorithm. The design method improves the aerodynamic performance of an airfoil subject to specified design objectives and constraints. Recent advances in computers and compputational fluid dynamics have permitted the use of the Navier-Stokes equations in the design procedure to include the nonlinear, rotational, viscous physics of transonic flows. Using numerical optimization guarantees that a better design will be produced even with strict design constraints. The method is demonstrated with several examples at transonic flow conditions.     

An algorithm for maximizing entropy subject to simple bounds

An unusual form of the maximum entropy problem is considered, that includes simple bound constraints on the Fourier coefficients of the required image, as well as nonnegativity conditions on the image intensities. The algorithm avoids mixing these constraints by introducing a parameter into the objective function that is adjusted by an outer iteration. For each parameter value an inner iteration solves a large optimization calculation, whose constraints are just the simple bounds, by a combination of the conjugate gradient procedure and an active set method. An important feature is the ability to make many changes to the active set at once. The outer iteration includes a test for inconsistency of all the given constraints. The algorithm is described, a proof of convergence is given, and there are some second-hand remarks on numerical results.     

An optimization procedure for the design of prop-rotors in high speed cruise including the coupling of performance,aeroelastic stability,and structures

An optimization procedure is developed to address the complex problem of designing prop-rotors in high speed cruise. The objectives are maximization of the aerodynamic efficiency in high speed cruise and minimization of the total rotor weight. Constraints are imposed on aeroelastic stability in cruise and rotor thrust. An isotropic box beam is used to model the principal load carrying member in the blade. Design variables include blade sweep and twist distributions, rotational velocity in cruise, and the box beam wall thickness. Since the optimization problem is associated with multiple design objectives, the problem is formulated using a multiobjective formulation technique known as the Kreisselmeier-Steinhauser function approach. The optimization algorithm is based on the method of feasible directions. A hybrid approximate analysis technique is used to reduce the computational expense of using exact analyses for every function evaluation within the optimizer. The results are compared to two reference rotors, unswept and swept. The optimum result shows significant improvements in the propulsive efficiency in cruise and reductions in the rotor weight without loss of aeroelastic stability or thrust, when compared to the reference unswept rotor. The swept reference rotor is initially unstable and the optimization procedure has been successful in producing a blade design which is fully stable with significant improvements in efficiency and blade weight. Off-design studies performed indicate that the optimum rotor maintains high propulsive efficiency over a wide range of operating conditions.     

数码相机定位研究

讨论了数码相机的定位问题,假设针孔镜头成像,根据射影几何的理论建立数学模型．首先,对靶标的像图形进行处理,求出其中每个图形的外切点,通过交比不变性和点的共线理论对所求的外切点进行约束从而得到最优的外切点,最后求出各个圆圆心在像平面的坐标．然后,考虑图形在成像过程中发生的“畸变”,通过空间坐标变换把在像平面局部坐标的分析...     

On-line optimization design of sliding mode guidance law with multiple constraints

The design of terminal guidance law with impact angle constraint is required for air-to-ground guided weapons to increase their warhead effect. The variable structure guidance law that consists of diving plane guidance and turning plane guidance equations with impact angle constraint is derived, and the saturation function is introduced into the design of reaching law control to weaken the chattering of the guidance system. The influence of four guidance parameters (i.e., reaching law factor, switching item gain, angle error item factor, and boundary layer thickness) on guidance performance is studied and three typical constraints (i.e., heating rate, normal load factor, and dynamic pressure) are analyzed. An optimization model is established for this problem and the feasibility of on-line optimization on guidance law parameters by the Sequential Quadratic Programming (SQP) algorithm is discussed as well. Simulation results show that the on-line optimization of the derived guidance law not only satisfies specified constraints, but also minimizes the fuel cost during the flying course. Moreover, the optimization process can be completed in a few seconds so that it is suitable for on-board applications.