复变量移动最小二乘法及其应用

提出了复变量移动最小二乘法，并详细讨论了基于正交基函数的复变量移动最小二乘 法. 然后，将复变量移动最小二乘法和弹性力学的边界无单元法结合，提出了弹性力学的复 变量边界无单元法，推导了相应的公式，并给出了数值算例. 基于正交基函数的复变量移动 最小二乘法的优点是不形成病态方程组、精度高，所形成的无网格方法计算量小. 复变量边 界无单元法是边界积分方程的无网格方法的直接列式法，容易引入边界条件，且具有更高的 精度.     

A Constrained Control Approach for the Automated Choice of an Optimal Progress Variable for Chemistry Tabulation

Flame structure look-up table generating strategies, e.g. the flamelet-progress variable approach, are based on the definition of a suitable progress variable. This variable is usually obtained from a linear combination of the species’ mass fractions contained in the system. The most important issue is the unique mapping between the progress variable and the independent variable, e.g. space or time. This is ensured by claiming the monotonicity of the progress variable. For simple fuel-oxidiser compositions, this can be performed by analysing the flame structure. However, in the case of complex chemical systems, finding such a progress variable is a non-trivial task, since a lack of monotonicity in the main species mass fractions often exists. In this article it is investigated how a valid progress variable can be found by an automated procedure. Some recent investigations use the fact that finding a monotonous progress variable is equivalent to solving a constrained optimisation problem. The new approach is to construct an algorithm to find a valid progress variable, which is also optimal in the sense that the gradients of the tabulated quantities are minimized. This leads to smoother data and reduces the interpolation effort when reading from the table. The method solves a nonlinear optimal control problem, where the monotonicity of the progress variable is ensured as an inequality constraint by using a genetic algorithm. Finally the performance of the new algorithm is evaluated for homogeneous reactor calculations and laminar diffusion flamelet look-up tables.     

MIKUSINSKI＇S OPERATORS SOLUTION OF THREE－ORDER LINEAR DIFFERENCE EQUATION WITH VARIABLE COEFFICIENTS

ＭＩＫＵＳＩＮＳＫＩ＇ＳＯＰＥＲＡＴＯＲＳＳＯＬＵＴＩＯＮＯＦＴＨＲＥＥ－ＯＲＤＥＲＬＩＮＥＡＲＤＩＦＦＥＲＥＮＣＥＥＱＵＡＴＩＯＮＷＩＴＨＶＡＲＩＡＢＬＥＣＯＥＦＦＩＣＩＥＮＴＳＺｈｏｕＺｈｉ－ｈｕ（周之虎）（ＡｎｈｕｉＡｒｃｈｉｔｅｃｔｕｒａｌＩ...     

Variational principles of fluid full-filled elastic solids

IntroductionManypracticalproblemsinengineeringinvolveanalysisoffluidfijll-filledelasticsolids.Energyexplorationand"utilizationaretwoexamples.ThefieldequationsofBlot'sstaticalanddynamicaltheoryoffluidfijll-filledelasticsolidswereestablishedinRefs.[1,Zj.BecausetheitisdifficulttogetexactanswersInumericalmethodsareadopted,especiallythet'initCelementmethod.Theelementmethodbasedonvariationalprinciplesisappliedextensively.GhaboussiandWilsonderivedvariationalprinciplesonthebasisofBlot'sequationsan…     

RELATIVISTIC VARIATION PRINCIPLES AND EQUATION OF MOTION FOR VARIABLE MASS CONTROLLABLE MECHANICAL SYSTEM

ＲＥＬＡＴＩＶＩＳＴＩＣＶＡＲＩＡＴＩＯＮＰＲＩＮＣＩＰＬＥＳＡＮＤＥＱＵＡＴＩＯＮＯＦＭＯＴＩＯＮＦＯＲＶＡＲＩＡＢＬＥＭＡＳＳＣＯＮＴＲＯＬＬＡＢＬＥＭＥＣＨＡＮＩＣＡＬＳＹＳＴＥＭ￥(罗绍凯)ＬｕｏＳｈａｏｋａｉ（ＳｈａｎｇｑｉｕＴｅａｃｈｅｒｓ...     

Solutions of the generaln-th order variable coefficients linear difference equation

In this paper.variable operator and its product with shifting operator are studied.The product of power series of shifting operator with variable coefficient is defined andits convergence is proved under Mikusinski’s sequence convergence.After turning ageneral variable coefficient linear difference equation of order n into a set of operatorequations.we can obtain the solutions of the general n-th order variable coefficientlinear difference equation.     

Elastic interactions between multi-valued foldons and anti-foldons for the (2+1)-dimensional variable coefficient Broer–Kaup system in water waves

With the help of the improved tanh-function method, some exact variable separation solutions for a (2+1)-dimensional variable coefficient Broer–Kaup system in water waves are found. The detailed investigation indicates that these seemly independent variable separation solutions actually depend on each other. Based on the exact variable separation solution, completely and noncompletely elastic interactions between multi-valued foldons and anti-foldons are studied analytically and graphically.     

关于可变区域问题的变分法以及广义数学规划问题

本文具体研究了定义在可变区域上或可变边界表面上的泛函的一阶、二阶变分问题，得到了与经典变分法相对应的关于可变区域问题的变分法。并用该变分法讨论了具有可变区域的弹性系统的势能原理。另一方面，与传统的数学规划相对应，研究了可变区域上泛函的约束极值问题——广义数学规划问题，给出了相应的广义Ｋｕｈｎ－Ｔｕｃｋｅｒ条件。     

Mikusinski’s operators solution of three-order linear difference equation with variable coefficients

This paper proceeds the papers [3] [4], we make use of the idea of the variable number operators and some concepts and conclusions of the shifting operators series with variable coefficients in the operational field of Mikusinski, it is devoted to the solution of the general three-order linear difference equation with variable coefficients, and it is also devoted to the better solution formula for the some special three-order linear difference equations with variable coefficients: in addition, we try to provide the idea and method for realizing solution of the more than three-order linear difference equation with variable coefficients. Project Supported by the Science Foundation of Anhui Province     

On a network method for unsteady incompressible fluid flow on triangular grids

The dual variable method for Delaunay triangulations is a network-theoretic method that transforms a set of primitive variable finite difference or finite element equations for incompressible flow into an equivalent system which is one-fifth the size of the original. Additionally, it eliminates the pressures from the system and produces velocities that are exactly discretely divergence-free. In this paper new discretizations of the convection term are presented for Delaunay triangulations, the dual variable method is extended to tessellations that contain obstacles, and an efficient algorithm for the solution of the dual variable system is described.     

弹性与断裂力学复变方法研究进展——纪念弹性与断裂力学复变函数法提出100周年

1909年,俄国数学力学家哥洛索夫首先将复变函数方法应用于二维弹性力学问题,揭开了弹性力学复变方法研究的序幕.100年来,复变方法在求解弹性与断裂力学问题中取得了很大发展,特别在断裂力学中的应用尤为成功.2009年恰逢弹性力学复变方法提出100周年,该文试图总结100年来复变方法在经典断裂力学、复合材料断裂力学、新型材料断裂力学以及三维空间断裂问题中的发展与应用,以作纪念.     

基于无网格法的非均匀弹性地基上变厚度加筋板弯曲与固有频率分析

采用基于移动最小二乘近似的无网格方法并结合一阶剪切变形理论,分析了非均匀弹性地基上变厚度加筋板的弯曲和固有频率问题.首先,用节点对变厚度板和筋条分别进行离散,导出变厚度板和筋条的势能;其次,利用筋条与变厚度板之间的位移协调条件将筋条的节点参数转换为板的节点参数,再将两者的势能进行叠加得到变厚度加筋板的总势能,并根据能量...     

中性线修正型变截面梁类构件压电控制

传统绝对节点坐标法(absolute nodal coordinate formulation,ANCF)在变截面梁类构件建模过程中常以几何中位线等效构造单元中性线,难以对变截面单元位移场状态进行精确描述.为解决此类问题,本文以中细型变截面梁类构件为研究对象,深入考虑变截面结构几何因素及复合材料属性对变截面梁类构件中性...     

Nonlinear natural frequency of shallow conical shells with variable thickness

IntroductionTheplatesandtheshellswithvariablethicknessarewidelyusedinengineering .Theproblemaboutstaticshasbeenstudiedbymanyscholars;therearemanyRefs .[1 -4 ]inthisfield .Papersaboutnonlineardynamicsaremuchless[5 ,6 ].Inthispaper,selectingthemaximumamplitudeinthecenterofshallowconicalshellswithvariablethicknessasperturbationparameter,thenonlinearnaturalfrequencyofshallowconicalshellswithvariablethicknessisobtainedbymethodgiveninRef.[7] .Thenonlinearnaturalfrequencyisnotonlyconnectedwiththeva…     

内压作用下弯管的塑性极限载荷分析

在变壁厚椭圆截面弯管应力分析的基础上,运用Tresca 和von Mises 屈服准则,对承受内压作用的钢制弯管进行了极限载荷分析,推导出考虑弯管截面壁厚变化和弯管椭圆度的变壁厚椭圆弯管的塑性极限压力计算式. 弯管的极限载荷随着弯管的壁厚和弯管的椭圆度的不同而变化.     

Establishment of several differential equations for the case of variable solid thermal conductivity

In this paper we propose that the solid thermal conductivity varies first with the space coordinate according to a linear law and then with an exponential one. In this way we have set up six differential equations successfully; and for variable density, variable specific heat as well as variable conductivity, another six differential equations have also been deduced.     

结构拓扑优化中变量连接算法研究与软件实现Research and software implementation of variable connection algorithm for structural topology optimization

结构拓扑优化的变量连接,是通过对设计变量之间添加约束关系,从而得到特定的拓扑优化构型,使得优化结果能够满足工程上的特殊要求和工艺制造技术的限制。针对拓扑优化中的几类过滤形式及灵敏度分析,给出了考虑变量连接的计算公式;基于自主研发的SiPESC软件集成化平台,在SiPESC ．TOPO拓扑优化模块上进行二次开发,构建了拓扑优化的变量连接算法框架,其核心思想是基于面向对象设计方法和软件设计模式,实现算法与数据分离。详细阐述了变量连接的作用方式,以及软件框架通用接口设计方案,并通过数值算例验证了其在静力问题、动力问题和热传导问题上的可行性。     

The Conley Index for Fast-Slow Systems I. One-Dimensional Slow Variable

We develop a qualitative theory for fast-slow systems with a one-dimensional slow variable. Using Conley index theory for singularity perturbed systems, conditions are given which imply that if one can construct heteroclinic connections and periodic orbits in systems with the derivative of the slow variable set to 0, these orbits persist when the derivative of the slow variable is small and nonzero.     

Basic equations of turbulent flow for variable density and variable viscosity Newtonian fluid in open channel

I.Intr0ducti0nManyscholarshaveresearchedtheturbulenceproblemsofnon-compressiblefluidll'2l,e.g.inRef[1],DouGu0renhaspresentedtheturbulentmotionaldifferentialequationsofconstantdensityandconstantvisc0sityfluidin0penchannel;inRef[3],XiaoTianduohasstudiedthet…     

Optimization of one-dimensional multistage linear processes

Summary A multistage process which can be completely characterized by a state variable and a control variable is called a one-dimensional multistage process with a control variable. It is shown that the optimal policy for controlling or operating such a process is to apply an equal control action at each stage when the process is linear in state variables.