FINITE ANALYTIC NUMERICAL METHOD FOR TRANSIENT HEAT DIFFUSION IN LAYERED COMPOSITE MATERIALS

The finite analytic (FA) method, which has been recently developed and used in fluid flow and heat transfer problems, is presented and extended to the solution of the problem of transient heat conduction in a one-dimensional muMlayered composite slab. The basic idea of the FA method is to incorporate a local analytic solution of the governing equation in the numerical solution of the boundary-value problem. In thii: study, the local analytic solutions are obtained by the standard integral-transformation technique and the associated eigenvalue problem is solved by the Galerkin method. Some numerical examples are computed to demonstrate the applicability of the FA method in dealing with heat diffusion in a composite material. It is shown that the FA method is accurate and provides reductions in computational costs.     

土坝二维渗流问题的有限分析法数值模拟

采用一种用于不规则边界的有限分析五点格式的方法，对稳定渗流中的非均质各向异性问题进行了计算，给出了适用于非稳定渗流计算的有限分析五点格式，对均质非稳定土坝渗流进行了计算。与其他方法相比，不规则边界的有限分析五点格式具有良好的数值性能。     

基于博弈论—有限云模型的尾矿库溃坝风险评价

针对进行尾矿库溃坝风险评价时存在的模糊性、随机性等问题,提出了博弈论-有限云模型评价方法。首先从浸顶溃坝、失稳溃决、自然因素等6个方面入手建立由17个风险因素组成的评价指标,将其分为4个风险等级,计算相对标准云数字特征值,生成有限云模型,通过博弈论思想优化模糊层次分析法及改进CRITIC法所得的主客观权重,得出最终权重,最后通过有限云模型求得综合隶属度并进行加权平均,根据最大隶属度原则确定各尾矿库所处风险等级。以河南省5个尾矿库为例,将各实测值代入博弈论-有限云模型评价溃坝风险,并将结果与传统云模型及模糊综合评价模型进行比较。结果表明,该模型所得结果更具有效性、准确性,且各尾矿库风险等级与实际情况基本相符。     

增压器涡轮叶片模态特性研究

基于有限元法，对增压器涡轮吉进行模态特性研究，从理论上探讨了材料参数，离心惯性及工作温度对涡轮叶片模态特性的影响。根据Ｈａｍｉｌｔｏｎ原理，推导了考虑离心惯性力影响的涡轮叶片振动方程。给出了材料参数，工作温度对涡轮叶片模态特性影响的解析式。在涡轮转速不十分高时，引入等效弹性模量的概念，得出涡轮转速对叶片模态特性影响的近似公式。     

基于参数化建模的转子有限元剖分

分析汽轮机转子的结构特点,将汽轮机转子结构参数化,提出了汽轮机转子参数化建模的方法,提高了转子原始几何模型的输入效率和准确性。利用有限元网格生成的Delaunay三角化方法,得到了汽轮机转了二维有限元计算模型,生成的有限元网格大小均匀,疏密过渡平滑,没有奇异单元,从而保证了转子温度场和热应力有限元分析计算的精度。     

An approximate analytic method for solving 1D dual-phase-lagging heat transport equations

In this study, we develop an approximate analytic method for solving 1D dual-phase-lagging heat conduction equations, which are derived based on the original dual-phase-lagging model without the first-order Taylor series approximation. The approximate analytic solution is obtained by employing the method of separation of variables. The coefficients of the series solution are then approximated by polynomials. The numerical method is illustrated with two simple examples.     

具有温度场的冷却叶片振动特性计算方法研究

根据稳态热传导的相关理论,建立了透平冷却叶片温度场和热应力场的四面体三维有限元分析模型和方法,并在此基础上建立了透平冷却叶片振动特性三维有限元分析方法,开发了相关计算软件。对某航空发动机透平高压第1级冷却叶片在不同工作条件下的振动特性进行了计算分析,同时研究了热应力、温度场、转速等对叶片振动特性的影响,表明本文中所建立模型和方法是科学、合理和精确的,为开展透平冷却叶片的设计和振动安全性评价奠定了基础。     

On the non-linear Maxwell–Cattaneo equation with non-constant diffusivity: Shock and discontinuity waves

A numerical study on a non-linear hyperbolic diffusion equation is proposed. The Hartree hybrid method combining finite difference techniques with the method of characteristics is used in the presence of discontinuities between initial and boundary conditions. The technique proved to be an useful tool to overcome oscillation problems and spurious solutions in case of strong non-linearities related to both attractive or repulsive interactions between diffusing species. Two different expressions for the diffusion coefficient are used in order to compare our results with the ones obtained in previous studies relying upon the Laplace transform technique and the MacCormack predictor–corrector method. Finally, an analytic approach based on the singular surface theory is proposed to motivate the numerical results and to clarify some controversial aspects concerning the penetration depth of a diffusive front in the presence of interactions.     

An approximate method for computing the temperature distribution over material thickness during hot flat rolling

An analytic solution for computing the temperature distribution over material thickness during hot flat rolling is so complex that finding the exact answer takes too much time. We approximate the analytic solution to cut significantly the run time required in calculating the temperature distribution. The proposed approach finds a finite number of eigenvalues instead of an infinite number of eigenvalues via minimizing the natural metric of definite real-valued functions. The initial condition of the cooling conditions altering sequentially is approximated using a sixth-order polynomial function so that we can perform the integral inherent in the analytic solution without numerical analysis.To substantiate the usefulness of the proposed method, we applied it to the hot rolling process where cooling conditions such as convection and radiation are activated repetitively. The run time is reduced drastically to less than 3% of that required by the analytic solution. The accuracy of the proposed method is as good as those by the finite difference method and analytic method.     

输电线动力学分析中的找形研究

输电线静态半衡位置找形是动力学分析的前提．找形精确与否对后续分析结果有很大影响。介绍了输电线找形中的解析法和有限元法,以某跨越档为例,分别对导线在自重和覆冰荷载下进行找形．着重分析了非均布荷载作用下这2种方法找形的差异。结果表明,均布荷载作用时．解析法和有限元法对导线静态平衡位置找形有相同的效果：非均布荷载作用时,有限元法得到的结果相对准确。     

APPLICATION OF THE PIECEWISE PARABOLIC FINITE ANALYTIC METHOD TO THE THREE-DIMENSIONAL CAVITY FLOW

Abstract

The three-dimensional piecewise parabolic finite analytic method (PPFAM3D), with vector potential and vorticity as dependent variables, was used to solve the steady three-dimensional (3-D) laminar cavity flow. Predictions were obtained for Reynolds numbers between 100 and 2000. Results for Re = 100, 400, and 1000 are compared with those available in the literature. The overall agreement is excellent. Results are also compared with the two-dimensional PPFAM cavity flow, showing the effect of three-dimensionality on the velocity predictions at the symmetry plane. The PPFAM3D is a robust numerical algorithm requiring no relaxation to produce physically meaningful and numerically converged solutions. It is a promising tool for solving a variety of flow phenomena governed by unsteady second-order partial differential convection-diffusion equations     

THREE-DIM ENSIONAL DIAGONAL CARTESIAN METHOD FOR INCOMPRESSIBLE FLOWS INVOLVING COMPLEX BOUNDARIES

A diagonal Cartesian method for the three-dimensional simulation of incompressible fluid flows over complex boundaries is presented in this article. The method is derived utilizing the superposition of the finite analytic solutions of a linearized two-dimensional convection-diffusion equation in Cartesian coordinates. The complex boundary is approximated with a structured grid in a series of calculation planes which are perpendicular to the x, y, and z coordinate axis. In the calculation plane, both Cartesian grid lines and diagonal line segments are used. It is observed that this geometry approximation is more accurate than the traditional sawtooth method. Mass conservation on complex boundaries is enforced with an appropriate pressure boundary condition. The method, which utilizes cell-vertex nodes on a staggered grid, uses boundary velocity information to avoid the specification of pressure values on boundaries. An enlarged control-volume method is introduced for the mass conservation and the pressure boundary condition on complex boundaries. The conservation of momentum on complex boundaries is enforced through the use of three-dimensional 19, 15, 11, or 7-point finite analytic elements. The proposed diagonal Cartesian method is verified by the solution of a rotated lid-driven cavity flow. It is shown that this diagonal Cartesian method predicts the fluid flow very well.     

Calculation of monthly average daily insolation on tilted, variously oriented surfaces using analytically weighted factors

A new, analytic method for calculating monthly average daily insolation on surfaces with various tilts and orientations is proposed. Beside the usual geometrical expressions concerning diurnal sun path, this method also takes into account changes in atmospheric transmissivity. Results are compared with those obtained by the widely accepted Klein's method also based on daily radiation data, as well as with more detailed and more accurate hourly calculations. Our results for two climatically very different locations in Yugoslavia stand in close agreement with hourly calculations for surfaces of arbitrary orientation and tilt, whereas Klein's method leads to significant error for large azimuth angles.     

预应力混凝土梁非线性有限元分析

无粘结预应力混凝土的计算并不象有粘结预应力混凝土那样,由外荷载引起预应力筋的应变不能根据相应截面的混凝土的应变求得,其应力的计算比较复杂。以有限元理论为基础,提出无粘结预应力混凝土梁的全过程分析模型,并研究编制了计算程序,分析了无粘结预应力混凝土的整个受力过程、变形发展、混凝土及无粘结筋的应力分布状态等。实例计算结果表明,该模型具有较好的精度,可用于工程结构的实际模拟分析。     

预应力混凝土梁非线性有限元分析

无粘结预应力混凝土的计算并不象有粘结预应力混凝土那样,由外荷载引起预应力筋的应变不能根据相应截面的混凝土的应变求得,其应力的计算比较复杂。本文以有限元理论为基础,提出无粘结预应力混凝土梁的全过程分析模型,并研究编制了计算程序,分析了无粘结预应力混凝土的整个受力过程、变形发展、混凝土及无粘结筋的应力分布状态等。实例计算结果表明,该模型具有较好的精度,可用于工程结构的实际模拟分析。     

钝尾缘叶片有限元模态与实验模态的对比研究

风力机叶片的模态分析是保障风力机整机稳定性及其可靠性分析的重要基础。对中国科学院工程热物理研究所研发的100kW钝尾缘实验叶片进行了有限元模态及实验模态研究,得出了叶片前几阶模态的振型及频率,探讨了对叶片稳定性影响比较显著的模态特性,通过对有限元模态及实验模态结果对比,分析了产生误差的原因及产生共振的可能性,为风力机叶片的稳定运行提供了理论依据。     

HEAT CONDUCTION THROUGH THE SUPPORT PILLARS IN VACUUM GLAZING

Vacuum glazing consists of two glass sheets with a narrow internal evacuated space. The separation of the sheets under the influence of atmospheric pressure is maintained by an array of small support pillars. The thermal resistances associated with the heat flow through individual pillars, and through the pillar array, are calculated using a simple analytic method, and by more complex finite element models. The results of both approaches are in very good agreement, and are validated by comparison with experimental data. It is shown that, for many purposes, the amount of heat which flows through the pillars can be determined without incurring significant errors by assuming that the heat flow is uniformly distributed over the area of the glass. Finite element modelling, and a superposition method, are used to determine the temperature distribution on the external surfaces of the glass sheets due to pillar conduction. Again the results obtained with both approaches are in very good agreement. An approximate method is described for calculating the magnitude of these temperature non- uniformities for all practical glazing parameters.     

GE9FA燃机压气机增强型S1静叶片固有频率分析

为了评估GE 9FA燃机压气机增强型S1静叶片的可靠性,采用有限元法对其进行了模态分析.得到了增强型S1静叶片的固有频率和振型,确定了其固有频率与其前排动叶尾迹激振频率的安全裕度.数值结果表明:增强型S1静叶片的4F型振动频率与其前级动叶尾迹所产生激振频率具有较大的安全裕度.     

Calculation of monthly average daily insolation on tilted,variously oriented surfaces using analytically weighted Rb factors

A new, analytic method for calculating monthly average daily insolation on surfaces with various tilts and orientations is proposed. Beside the usual geometrical expressions concerning diurnal sun path, this method also takes into account changes in atmospheric transmissivity. Results are compared with those obtained by the widely accepted Klein's method also based on daily radiation data, as well as with more detailed and more accurate hourly calculations. Our results for two climatically very different locations in Yugoslavia stand in close agreement with hourly calculations for surfaces of arbitrary orientation and tilt, whereas Klein's method leads to significant error for large azimuth angles.     

强度折减法在三维有限元边坡稳定分析中的应用

为研究强度折减法在边坡三维稳定分析中的适用性,选择已知滑裂面和未知滑裂面共4个经典算例,运用强度折减法求解其安全系数,并与既有的极限平衡法结果进行对比。计算结果表明,数值解与既有的极限平衡法解析解非常接近,模拟的滑动方向与理论假定亦基本一致。由此证明了强度折减法在三维有限元边坡稳定性分析中的适用价值,为解决工程计算问题提供了参考。