Method of initial functions in the analysis of thick circular plates

The method of initial functions has been used for the analysis of thick circular plates. In this method, the governing equations are derived from the three-dimensional elasticity equations in cylindrical polar coordinates using a Maclaurin series expansion in thickness coordinate for the unknowns. The formulation is in a form which is particularly amenable to consistent reduction to obtain approximate theories of any desired order. Numerical results obtained using this method are compared with those of elasticity solution for the case of a simply supported plate and for a plate subjected to self-equilibrating normal loads. Results are also given for clamped plates subjected to a uniformly distributed load.     

Influence of thermal gradient on natural frequency of rectangular plate vibration

Dynamic free response of thin rectangular plates subjected to steady state one dimensional and two dimensional temperature distributions satisfying the Laplace equation is analysed in this paper by using the finite difference method and finite element method. The governing equations of motion derived by the finite difference method are solved by a simultaneous iteration technique to obtain eigenvalues and eigenvectors. The results of both the methods compare well with those of classical methods in some typical cases. An attempt is made to correlate the non-dimensional frequency parameter and the temperature parameter. Plates of different boundary conditions with at least one edge simply supported are studied.     

Transient heat conduction problems in inhomogeneous media discretized by means of boundary-volume element

An integral equation formulation is presented for the transient heat conduction problems in inhomogeneous media. The material constants are assumed to be prescribed as arbitrary, continuous and differentiable functions of position vector. The governing integral equations are derived from the weighted residual statement of the problems in which the fundamental solution to the corresponding heat conduction problems in homogeneous media is used as the weight function. The whole domain of interest is discretized into a series of boundary-volume-time elements, and then a set of linear simultaneous equations are obtained. Their solutions yield the temperature in the whole domain as well as the heat flux on the boundary.     

Analysis of moderately thick flanged reactor vessels

A computer method is presented for the analysis of moderately thick flanged shells of revolution such as are used for reactor pressure vessels. The shell may be subjected to symmetrical or unsymmetrical loads and a thermal environment. The method employs a finite element discretization for modelling the flange portions, and a theory appropriate to moderately thick shells for the remainder of the pressure vessel. The governing differential equations for the shell portions are put in the Goldberg-Bogdanoff first-order form and integrated numerically using a scheme such as a Runge-Kutta process. The finite element stiffness matrix for a flange region is used to form a superelement influence coefficient matrix, permitting the flange region to be treated as a giant step in the numerical integration process.     

Hybrid method for vibration analysis of rectangular plates

This paper presents a semi-analytical approach for the dynamic analysis of rectangular plates. The mathematical model is developed using a hybrid combination of the finite element method and Sanders’ shell theory. The in-plane, membrane displacement components are modelled by bilinear polynomials and the out-of-plane, normal to mid-surface displacement component is modelled by an exponential function that represents a general form of the exact solution of the equations of motion. The displacement functions are obtained by exact solution of the equilibrium equations of the rectangular plates. The mass and stiffness matrices are then determined by exact analytical integration to establish the plate's dynamic equations. The effect of various geometrical parameters and boundary conditions on the dynamic responses of the rectangular plates has been explored in this work. The results are in satisfactory agreement with those of experiments and other theories.     

A high precision triangular plate bending element for the analysis of thick plates

A high precision triangular plate bending element for the analysis of thick plates is developed in thin paper. The element has three nodes and 12 degrees of freedom per node. Explicit expressions for stiffness coefficients are derived. The superiority of the element is demonstrated by the accuracy of the results obtained by applying it to some typical thick plate problems.     

Boundary conditions for the solution of Boltzmann's equation in periodic lattices

A generalization is made of the methodological approach to the solution of the tramport equations in heterogeneous periodic lattices, which was presented in the diffusion approximation in [1], The boundary conditions at the outside surface of the cell are derived for making an accurate solution of the one velocity Boltzmann kinetic equations, which permits considering a single cell of the heterogeneons medium. A short discussion is given of methods of solving the problem with these boundary conditions and of the question of eigenvalues.A general solution for the whole heterogeneous medium in accurate and macroscopic (averaged) form is made up of the special solutions found for a single celt, using the same principle as in [1].The boundary conditions formulated for a plane one dimensional lattice may be extended to a two dimensional lattice.Translated from Atomnaya Énergiya, Vol. 14, No. 4, pp. 371–374, April, 1963.     

New algorithm for the numerical simulation of two-phase stratified gas–liquid flow and its application for analyzing the Kelvin–Helmholtz instability criterion with respect to wavelength effect

In this article, the transient condition of two-phase stratified gas–liquid flow was investigated using numerical simulation. The basis of the method involves the one-space dimensional transient solution of the governing equations using the two-fluid model. In this paper, an analogy between the SIMPLE algorithm in two-space dimensional single-phase flow and one-space dimensional two-phase stratified flow is established through the application of a special algorithm created to solve the conservation equations. After the modeling was established and justified, wave growth was examined in two-phase stratified flow in a horizontal duct. The results were then compared with the results of the previously published articles. The results show that the classical criterion for the Kelvin–Helmholtz (K–H) instability is consistent when the long wavelength with small amplitude is considered. In this case (of the K–H instability criterion), the wavelength effect on this instability and pressure variation on the two phases interface was consistent with prior researchers’ correlations. However, as the wavelengths decreased, the results indicated that the K–H instability criterion is over-predicted and must be modified. The application of the present numerical simulation method improved the results, and the consistency with the analytical solution is higher in comparison with other well-known computer codes.     

Thermal bending of thick rectangular plates

An analysis with a shear deformation capability for the thermal bending of thick rectangular plates is presented. Formulation of the problem, with appropriate thermal terms incorporated and applicable to the bending of moderately thick plates, has been carried out by using Reissner's plate bending theory. Representative plate bending problems have been considered for illustrating the procedure. Numerical results obtained indicate that thick plate solutions to thermal problems deviate from those of the classical theory in practically the same manner as with mechanical loading cases.     

Integral boundary layer heat transfer modeling for Tehran Research Reactor

In the present work the validity of applying the Boussinesq approximation in the analysis of natural convection heat transfer along nuclear fuel plates with large coolant channel aspect ratios is evaluated. The Boussinesq approximation is introduced into the integral boundary layer equations governing the system to describe the velocity and temperature distributions of the coolant in the cooling channels. The fuel plate temperature is related to the adjacent coolant fluid temperature by a fundamental law in conduction heat transfer. Air and water are considered as fluids. The coolant flow is assumed to be fully developed which is a convenient assumption for coolant channels having large aspect ratios. Obtained results indicate that the Boussinesq approximation is merely applicable over a limited range of coolant channel outlet fluid temperatures. The use of this approximation produces conservative estimation of the critical plate power for air flow and non-conservative estimation of the critical plate power for water flow.     

Structurally compatible fluid finite element for solid fluid interaction studies

This study develops a fluid finite element compatible with existing structural finite elements with the ultimate objective of analysing solid-fluid interaction problems. This type of problem is of interest in the design of nuclear components involving geometric complexities and nonlinearities. Employing the weighted residual method, the differential equations governing the pressure distribution in a two-dimensional viscous flow subjected to small amplitude oscillations are discretized on finite element subdivisions of the fluid region. The elemental inertia, damping and volumetric fluidity matrices are computed for plane, axisymmetric, triangular and quadrilateral fluid elements. These matrices are then assembled for all the system elements and the final differential equations are integrated numerically in time to obtain the pressure and velocity distribution in the flow region. The analysis is verified analytically by solving a wave propagation flow problem consisting of fluid between two flat plates initially at rest and accelerated suddenly by applying a step pressure at one end.     

A comparison of closed-form and finite-element solutions of thick laminated anisotropic rectangular plates

In this study the effects of reduced integration, mesh size, and element type (i.e. linear or quadratic) on the accuracy of a penalty-finite element based on the theory governing thick, laminated, anisotropic composite plates are investigated. In order to assess the accuracy of the present finite element, exact closed-form solutions are developed for cross-ply and antisymmetric angle-ply rectangular plates simply supported and subjected to sinusoidally distributed mechanical and/or thermal loadings, and free vibration.     

一个高效核反应堆热工水力分析方法

提供了一个高效率的核反应堆堆芯热工水力分析方法。以子通道概念为基础，给出了描述堆芯流体流动与传热特性的数学模型和控制方程。文中采用了两相流的滑移流模型，并考虑了过冷沸腾的影响。引入若干补充关系式，用以确定空泡份额、湍流掺混、阻力系数及热力学参数等的大小，与广泛应用的ＣＯＢＲＡ系列程序不同，本文求解的是压力梯度方程而不是关于速度的方程，大大提高了数值求解的稳定性和计算收敛速度。初步的数值结果与实验结果的比较表明。本文提供的方法和程序是令人满意的。     

Limit loads of variable thickness circular plates in bending

This paper presents the results of an investigation of rigid-plastic collapse of simply supported circular plates of variable thickness. The plates are loaded with a uniformly distributed transverse pressure and the material is assumed to yield according to the von Mises criterion. Numerical results for collapse loads and stress fields are given in graphs and the solution for the resulting velocity fields is indicated.     

基于先进节块法的六边形三维中子物理程序的开发与验证

六边形燃料组件在液态金属冷却快堆尤其是钠冷快堆中被广泛应用,针对这类堆型的设计与安全分析需要对堆芯中子通量与中子流进行三维全堆芯耦合计算。经过多年发展,目前已有多种解析节块法、积分节块法、节块展开法等先进节块法能在笛卡尔坐标系下较为精确求解多维中子扩散方程。本文通过径向半解析节块法耦合轴向高阶节块展开法的综合节块方法开发了反应堆三维中子物理计算软件SA HNHEX,并对VVER 440二维、三维基准题进行建模与仿真计算。计算结果与参考值符合较好,初步验证了使用该方法进行反应堆堆芯中子扩散计算的正确性。     

Effect of chemical reaction, heat and mass transfer on nonlinear boundary layer past a porous shrinking sheet in the presence of suction

This work is concerned with the viscous flow due to a shrinking sheet in the presence of suction with variable stream conditions. The cases of two-dimensional and axisymmetric shrinking have been discussed. The governing partial differential equations of the problem, subjected to their boundary conditions, are solved numerically by applying an efficient solution scheme for local nonsimilarity boundary layer analysis. Favorable comparison with previously published work is performed. Numerical results for the dimensionless velocity, temperature and concentration profiles as well as for the skin friction, heat and mass transfer and deposition rate are obtained and displayed graphically for pertinent parameters to show interesting aspects of the solution.     

两相自然循环稳定性无量纲频域分析研究

基于一维均相平衡模型，导出系统无量纲特征方程，采用频域分析方法，开发了一个通用性程序，研究两相自然循环中流动不稳定特性。程序能直接求解自然循环回路的无量纲稳定边界，计算结果与所得到的实验数据吻合良好，并讨论了各参数对系统稳定性的影响。     

Application of cellular neural network (CNN) method to the nuclear reactor dynamics equations

This paper describes the application of a multilayer cellular neural network (CNN) to model and solve the nuclear reactor dynamic equations. An equivalent electrical circuit is analyzed and the governing equations of a bare, homogeneous reactor core are modeled via CNN. The validity of the CNN result is compared with numerical solution of the system of nonlinear governing partial differential equations (PDE) using MATLAB. Steady state as well as transient simulations, show very good comparison between the two methods. We used our CNN model to simulate space-time response of different reactivity excursions in a typical nuclear reactor.     

PWS: an efficient code system for solving space-independent nuclear reactor dynamics

The reactor kinetics equations are reduced to a differential equation in matrix form convenient for explicit power series solution involving no approximations beyond the usual space-independent assumption. The coefficients of the series have been obtained from a straightforward recurrence relation. Numerical evaluation is performed by PWS (power series solution) code, written in Visual FORTRAN for a personal computer. The results are applied to the step reactivity insertion, ramp input, zigzag input, and oscillatory reactivity changes. When the reactivity is given, including the case in which the feedback reactivity is a function of neutron density, the developed method can provide a straightforward procedure for computing reactor dynamics problems. The solution of this method was compared to some other analytical and numerical solutions of the point reactor kinetics equations; the results proved that the approach is both efficient and accurate to several significant figures.     

Solution of the transport equation by the BIF method

A research code and applications code are described for the numerical solution of the three dimensional linearized and stationary transport equation over a finite domain which is subdivided into a finite number of parallelepipeds. The main program uses only flux densities at the boundaries and interfaces but at no other interior points. This minimizes the order of the associated matrix equations needed for the numerical solution, but requires a good knowledge of the analytic behaviour of the mathematical solution of the problem. Because only Boundary and Interface Functions are used, this approach is called the BIF method.