基于虚拟元方法的二维带源夹紧方板问题求解

应用虚拟元方法研究二维带源夹紧方板问题,推导该方板的平面瞬态温度场的数值解并讨论网格剖分的细化程度对二维带源夹紧方板的平面瞬态温度场的影响.通过二维带源夹紧功能梯度材料板的平面瞬态热方程的数值计算,证明了理论分析结果的正确性,并且步长越精细,计算结果越精确,所得的等温线图符合实际温度场分布规律,因此该方法可以为检验其它近似方法提供参考.     

带相变的连续浇铸铸坯温度场分析

本文通过适当变换，将考虑铸坯相变潜热影响的三维稳态非线性温度场问题，化成等效的二维瞬态非线性问题来求解，并用等效比热代替相变影响，给出了有限元计算公式，并对相变区作了精确仔细的处理．     

二维瞬态热传导的PDDO分析北大核心CSCD

采用近场动力学微分算子(peridynamic differential operator, PDDO)理论求解了二维瞬态热传导问题.将热传导方程和边界条件由其局部微分形式重构为非局部积分形式,引入Lagrange乘数法,采用变分原理的概念,建立了二维瞬态热传导问题的非局部分析模型.通过误差与收敛性分析,与其他数值方法计算结果进行比较,验证了本模型的准确性.在此基础上,将本模型应用于计算不规则边界板和内部含微缺陷(裂纹和圆孔)板的二维瞬态热传导问题.结果表明该方法计算精度高、适用范围广、具有较好的收敛性,为计算二维瞬态热传导问题提供了新的思路.     

基于滑动Kriging插值的MLPG法求解结构非耦合热应力问题

将基于滑动Kriging插值的无网格局部Petrov-Galerkin(MLPG)法用来求解二维结构非耦合热应力问题,首先进行瞬态热传导的求解,然后再通过顺序耦合法将不同时刻节点温度作为附加体力项施加到应力分析中.瞬态温度场和非耦合热应力分析通过加权余量法来离散,同时用Heaviside分段函数作为局部弱形式的权函数.由于滑动Kriging插值构造的形函数满足Kroneckerδ函数的性质,因此方便了本质边界条件的施加.刚度矩阵形成过程中只涉及到边界积分而没有涉及到区域积分,因此可以减少计算工作量,最后通过两个数值算例来验证本文方法的有效性.     

基于非傅里叶的有限空圆柱体的温度场解析解及其在谐波均匀的圆柱体上的应用

在有限空圆柱体的热冲击问题中引进非傅里叶分析,考虑了在极端热传递条件下的非稳态热传递过程中热量传播速度的有限性,建立了有限空圆柱体的轴对称非傅里叶温度场的数学模型,利用分离变量法和杜哈尔积分求得有限空圆柱体双曲型热传导问题的精确解析解.并将结果应用于外表面是谐波均匀的热通量的有限空圆柱体,得到其瞬态温度场及其径向、轴向温度分布规律.     

二维瞬态热传导问题的无单元Galerkin法分析

采用无单元Galerkin(element-free Galerkin,EFG)法求解具有混合边界条件的二维瞬态热传导问题.首先采用二阶向后微分公式离散热传导方程的时间变量,将该问题转化为与时间无关的混合边值问题;然后采用罚函数法处理Dirichlet边界条件,建立了二维瞬态热传导问题的无单元Galerkin法;最后基于移动最小二乘近似的误差结果,详细推导了无单元Galerkin法求解二维瞬态热传导问题的误差估计公式.给出的数值算例表明计算结果与解析解或已有数值解吻合较好,该方法具有较高的计算精度和较好的收敛性.     

轴向运动粘弹性板的横向振动特性

研究了轴向运动粘弹性矩形薄板的动力特性和稳定性问题．从二维粘弹性微分型本构关系出发,建立了轴向运动粘弹性板的运动微分方程．采用微分求积法,对四边简支、一对边简支一对边固支两种边界条件下粘弹性板的无量纲复频率进行了数值计算．分析了薄板的长宽比、无量纲运动速度及材料的无量纲延滞时间对其横向振动及稳定性的影响．     

二维热传导型半导体瞬态问题的二次元特征有限体积元方法

将特征线方法与有限体积元方法相结合,采用Lagrange型分片二次多项式空间和分片常数函数空间分别作为试探函数和检验函数空间构造了二维热传导型半导体瞬态问题的全离散二次元特征有限体积元格式,并进行误差分析,得到了次优阶L^2模误差估计结果．     

瞬态热传导的奇异边界法及其MATLAB实现

基于动力学问题时间依赖基本解的奇异边界法是一种无网格边界配点法.该方法引入源点强度因子的概念从而避免了基本解的源点奇异性,具有数学简单、编程容易、精度高等优点.将该方法用于瞬态热传导问题的数值模拟,运用MATLAB实现该问题的数值研究,并创建相应的MATLAB工具箱.针对二维和三维瞬态热传导问题,进行了基于反插值技术和经验公式的奇异边界法MATLAB算例实现.针对支撑圆坯低温瞬态温度场的模拟结果表明,瞬态热传导奇异边界法的MATLAB工具箱具有简单、方便、精确可靠的优点.研究成果有助于发展瞬态热传导的奇异边界法,并为瞬态热传导问题的数值分析和仿真提供了一种简单高效的模拟工具.     

热载荷作用下平面裂纹问题的奇异积分方程与边界无法

从边界积分方程出发,导出了二维裂纹体热传导问题及热弹性问题的积分方程组,继而使用奇异积分方程与边界元相结合的方法,为其建立了相应的数值求解方法。此外,利用奇异积分方程的主部分析法,严格地证明了裂纹尖端温度梯度场的1/√r 奇异性,并且给出了奇性温度梯度场的精确解。最后。对一些典型例子,做了数值计算。     

Analysis of the vibrations due to thermal deflection of the drum in the coiling process

The modelling of the coiling process involves a mechanical model of the dynamic system that consists of the rotating coiling drum and the axially and transversally moving strip. Due to the coiling a change of mass in the system takes place. For such a variable mass system a control volume concept has to be introduced in order to get the equations of motion of the dynamic system with variable parameters. A Runge Kutta time integration algorithm is applied to compute the solution. It is assumed that the outer radius of the coiling drum increases linear with the rotation angle. The bending deflection of the shaft results from an inhomogeneous temperature distribution within the coiled material on the coiling drum. Two different boundary conditions of the moving strip have been considered and it is demonstrated that the thermal deflection of the drum has a high influence upon the fluctuation of the strip force. For a given geometry and strip speed we obtain a critical thermal deflection where the minimum strip tension force is zero. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Can One Hear the Composition of a Drum?

This note is related to the famous question raised by Mark Kac and concerning the determination of the shape of the drum by the eigenvalues of its governing equation. Here, we allow the drum to be composed by several different types of membranes and we consider the problem of hearing the composition of the drum, starting from the eigenvalues of numerical approximations of the related equation. Some key tools, taken from asymptotic linear algebra, are reported and extended, and allow somehow to answer to the question in the positive.     

Analysis of non-deterministic drum scheduling

A non-deterministic drum scheduler reads a file of drum pages in unpredictable order because it selects, at each step, to read the first not previously read page after the reading heads. In this paper bounds are derived for the average latency time of such a scheduler when reading a file uniformly distributed over the drum circumference under the assumption that read requests are issued at uniformly and independently distributed points of the drum circumference.     

基于系统双重风险共担的多项目鼓缓冲设置研究

为了提高关键链多项目缓冲管理的效率,首次提出了一种基于多项目双重风险共担的鼓缓冲设置方法。新方法从系统角度分析了多项目不同层级的风险共担作用,以同时落在在子项目关键链和多项目系统关键链上的系统关键活动工期占比为切入点对缓冲进行分层管理,抽取部分项目缓冲集中到系统层面,同时综合考虑风险独立因子以及鼓活动有效产出影响指数对鼓缓冲进行了定量设置。仿真结果表明,本文方法在多项目按时完工率、项目缓冲平均消耗率、系统关键链上鼓活动平均延误百分比、多项目系统总工期和成本这几个绩效方面的表现更优,提高了多项目系统的风险应对能力。     

Moon patterns,sun patterns,and wave breaking in rotating granular mixtures

Granular materials, such as powders and sand, tend to segregate due to differences in particle properties. When a cylindrical drum is partially filled with particles of different sizes and rotated about its axis, this leads to radial segregation patterns in which the smaller particles concentrate in a radial core near the axis, and the larger particles near the outside walls of the drum. Under certain conditions, undulations in the radial core of smaller particles grow into radial stripes that extend toward the outer walls of the drum in a manner somewhat reminiscent of viscous fingering. The patterns are strongly dependent on the fill level and rotation speed of the drum. These observations can be explained by two spatially disjoint mechanisms: (1) a wave‐breaking mechanism that promotes the growth of the stripes and (2) a filtering mechanism that limits the growth of stripes. © 2005 Wiley Periodicals, Inc. Complexity 10: 79–86, 2005     

A storage allocation scheme for ALGOL 60

A storage allocation scheme for a machine with a 2048-instruction core store and a magnetic drum is described. The use of the drum for storing program blocks and/or data must be directed by the programmer through auxiliary information in the ALGOL program. The administrative routines controlling the storage at run time are described in full. A detailed example is given.     

“同心协力”策略研究

针对"同心协力"拓展项目中队员的协同控制问题,建立了在理想条件下的最优策略模型,以及在非精确控制条件下的鼓面倾斜模型,讨论了稳定性要求对最优策略的影响,给出当球跳动方向偏离竖直方向后,鼓的控制方法及效果.最后对2019年"高教社杯"全国大学生数学建模竞赛B题的参赛论文予以简要评述.     

Prediction of risers’ tubes temperature in water tube boilers

A dynamic model is developed which enables the prediction of risers’ tubes temperature of water tube boilers under various operating conditions. The model is composed of fluid dynamics model representing the fluid flow in the drum-downcomer-riser loop and a dynamic thermal model of the riser’s temperature. The model gives a detailed account of the two-phase heat transfer process which takes place between the risers’ inner walls and the water–steam mixture flow inside the tubes. The model is used to simulate various operational scenarios of water tube boilers. Results of the simulation provide insight into the dynamic interactions of the boiler’s main variables including the drum pressure, water volume, steam quality and risers’ temperature. Such a model is useful in checking operational scenarios before their actual plant implementation, can be a basis for developing boiler start up procedures and online temperature predictions to prevent eminent tube overheating.     

An advanced dynamic process model for industrial horizontal anode baking furnace

The global aluminum industry is facing new challenges due to new technological developments. Carbon anodes, consisting of mainly petroleum coke and coal tar pitch, are used in the electrolytic production of aluminum. High amperage utilization in the electrolytic cells with the objective of increasing production requires high quality carbon anodes. The anode quality depends both on raw material quality, anode recipe as well as forming and baking conditions of anode manufacturing process. The cost of the baking process constitutes 15 to 25% of the total aluminum production cost [1]. The industrial challenge is to produce better quality anodes consuming less energy, and reducing environmental emissions.A transient two dimensional (2D⁺) process model for horizontal anode baking furnace was developed during this study. The main objective was to develop an efficient furnace model with low computation load and time, using the transient Finite Difference Method and simplified furnace geometry. The model represents several phenomena involved during the anode baking process such as heat transfer (convection, radiation and conduction), fuel combustion, volatile matter (tar, methane and hydrogen) generation and combustion, air infiltration and energy loss to the atmosphere from the walls, the top of the furnace and the foundation. The model was developed using two coupled sub-models; the first one describes the thermal conduction through the solid materials (brick refractory wall, packing coke and anode block) as well as the volatile release, and the second one describes the gas flow, heat and mass transfer as well as the combustion of fuel and volatiles in the flue. Compared to the existing process models (where the gas flow in flue is assumed as unidirectional along the horizontal furnace direction), the present model also considers the gas flow in vertical direction and uses four vertical planes per pit section to predict the temperature of the solids. The model predicts 2D temperature distribution within the flue gas (xy plane) and the pit solid materials (yz plane) allowing then the prediction of the pseudo tridimensional distribution of the solid temperature. This model is a useful tool for the continuous monitoring of anode temperature and studying of the horizontal anode baking furnace behaviour. The effect of any change in operational parameters and the energy consumption on the furnace operation can be predicted.     

水温及其预报方法初探

本文着重利用 Matlab讨论了水温与气温之间的相关变化关系和利用气温预报水温的初步方法 .结合武汉市气象局在武汉市东西湖区养殖场气象观测站 1 982年至 1 989年的连续观测资料给出了水温与气温之间的相关系数以及水温预报方程 ,并讨论了误差及消除误差的途径 .