样条配点法在厚板动力分析中的应用

本文运用样条配点法对厚板进行动力分析。基本方程系采用由本文作者推演得到的改进的Donnell厚板振动方程。对广义坐标运用三次B样条求解。对任意荷载作用下厚板弹性响应给出解的一般表达式。文中以矩形板为例给出了数值结果,对按改进理论和经典理论所预示的结果进行了比较。本文方法可以推广用于厚板弹塑性动力分析和厚板与连续介质共同作用的场合。     

二维拉氏辐射流体力学人为解构造方法

人为构造解方法是复杂多物理过程耦合程序正确性验证的重要方法之一,适用于二维拉氏大变形网格的流体、辐射耦合人为解模型较为少见。针对拉氏辐射流体力学程序正确性验证的需要,从二维拉氏辐射流体力学方程组出发,基于坐标变换技术,给出了拉氏空间到欧氏空间的物理变量导数关系式,开展了辐射流体耦合的人为解构造方法研究,构造了一类质量方程无源项的二维人为解模型,并应用于非结构拉氏程序LAD2D辐射流体力学计算的正确性考核,为流体运动网格上的辐射扩散计算提供了一种有效手段。数值结果显示观测到的数值模拟收敛阶与理论分析一致。     

高维周期解支的数值延续算法

本文提出了描述动力系统周期解的一个定解问题，给出其的充要条件，并基于样条函数在Ｇａｕｓｓ点的配置法和伪弧长算法，发展了适合高维、复杂构形、具有极值分侧周期解支的数延续算法。计算了若干非线性常微和偏微分方程组的周期解支，以说明本文数值方法在解题规模，精度上的有效性。     

基于余弦样条函数的有限点阵法

应用节点影响域的概念,提出了基于余弦样条函数的有限点阵方法.利用余弦样条函数的性质,通过张量积的形式构造余弦样条函数正则解空间,用于逼近场函数,余弦样条基的线性组合使得边界条件处理如同有限元法一样方便.余弦样条与边界型方法结合,可用于求解不规则域问题.数值实例的计算结果表明,文中方法避免了高阶多项式构造形函数所带来的数值振荡,解的连续性不受限制,为改进计算精度而加密点阵所导致的计算量增加量较少,计算收敛快.     

重力作用下液体自由面的数值解

给出一种重力作用下静止液体自由面的数值解方法。根据流体力学Young-Laplace公式和微分几何学主曲率方程,并利用液体自由面的对称性质,导出重力作用下静止液体自由面母线的常微分控制方程。为了使该方程便于利用现有的Runge-Kutta法,根据问题的物理背景,将体积边界条件转化为固-液接触面半径条件;采用一种坐标变换,避免了该方程数值计算中刚性问题的出现。最后给出了算例。     

一种区间B样条小波平板壳单元及应用

基于二维张量积区间B样条小波,构造了一种件能良好的小波平板壳单元．在小波单元的构造过程中,用二维区间B样条小波尺度函数取代传统多项式插值,在所构造的区间B样条平面弹性单元和平面Mindlin板单元的基础上组合而成．区间B样条小波单元同时具有B样条函数数值逼近精度高和多种用于结构分析的基函数的特点．数值算例表明：与传统有限元和解析解相比,构造的小波平板壳单元具有求解精度高,单元数量和自由度少等优点．     

计算流体选讲(一)

计算流体是对描述流体运动的偏微分方程(或方程组)给出数值解的一门科学.目的在于进一步理解物理现象从而改进工程设计,实用性十分明确.计算流体的内容十分丰富并涉及多种学科:流体力学,偏微分方程,数值分析,计算几何,计算机科学等等.它需要书本文献中的理论和技巧,也需要实际工作中的经验和见解.在多年工作中我们深刻体会到从一般偏微分方程数值解的基本课程到从事计算流体的研究工作还有相     

一种准确度高的土工测试数据拟合新方法

针对目前岩土工程土工测试数据处理方法的不足,给出了一种能够减少端点导数误差的三次样条拟合方法.三次样条函数拟合是曲线拟合的一个公认的较好方法,它具有很好的分段光滑性.但当端点的导数值无法精确得到时,会给样条拟合的准确性带来较大的影响.为了尽量减少这种误差的出现,本文提出先用多项式函数对前、后各一小部分测量数据点进行拟合后,再对函数求导,得到所需端点导数带入三次样条函数,最终得到更加准确的拟合结果.采用文中建立的拟合方法,对地基沉降实测数据进行分析,拟合结果表明本文方法的工程适用性强、拟合准确度高.     

区间B样条小波平面弹性及Mindlin板单元构造研究

基于二维张量积区间B样条小波及小波有限元理论,构造了一类用于分析弹性力学平面问题和中厚板问题的C0型区间B样条小波板单元。在二维小波单元的构造过程中,传统多项式插值被二维区间B样条小波尺度函数取代,进而构造形状函数和单元。与小波Galerkin方法不同,本文构造的区间B样条小波单元通过转换矩阵将无明确物理意义的小波插值系数转换到物理空间。区间B样条小波单元同时具有传统有限元和B样条函数数值逼近精度高及多种用于结构分析的基函数的优点。数值算例表明:与传统有限元和解析解相比,本文构造的二维小波单元具有求解精度高,单元数量和自由度少等优点。     

计算流体选讲(一)

<正> 计算流体是对描述流体运动的偏微分方程(或方程组)给出数值解的一门科学.目的在于进一步理解物理现象从而改进工程设计,实用性十分明确.计算流体的内容十分丰富并涉及多种学科:流体力学,偏微分方程,数值分析,计算几何,计算机科学等等.它需要书本文献中的理论和技巧,也需要实际工作中的经验和见解.在多年工作中我们深刻体会到从一般偏微分方程数值解的基本课程到从事计算流体的研究工作还有相     

Convergence and exact solutions of spline finite strip method using unitary transformation approach

The spline finite strip method(PSM) is one of the most popular numerical methods for analyzing prismatic structures.Efficacy and convergence of the method have been demonstrated in previous studies by comparing only numerical results with analytical results of some benchmark problems.To date,no exact solutions of the method or its explicit forms of error terms have been derived to show its convergence analytically. As such,in this paper,the mathematical exact solutions of spline finite strips in the plat...     

Modelling of two‐dimensional laminar flow using finite element method

In this paper, a Galerkin weighted residual finite element numerical solution method, with velocity material time derivative discretisation, is applied to solve for a classical fluid mechanics system of partial differential equations modelling two‐dimensional stationary incompressible Newtonian fluid flow. Classical examples of driven cavity laminar flow and laminar flow past a cylinder are presented. Numerical results are compared with data found in the literature. Copyright © 1999 John Wiley & Sons, Ltd.     

Mathematical programming analysis of bilinear rheological lubrication mechanics

Bilinear rheological lubrication mechanics provides an important basis for the designs of recently developed electrorheological (ER) “smart”journal bearings and those lubricated by mixed fluid-solid lubricants. But there is not yet a reliable and efficient numerical method for such a problem of non-Newtonian fluid mechanics. In the present paper, a finite element method (FEM) together with mat hematical programming solution is successfully used to solve such a problem. A reliable and generalized numerical method for the designs of electrorheological “smart” journal bearings and the bearings lubricated by mixed fluid-solid lubricant is presented.     

A high‐order mass‐lumping procedure for B‐spline collocation method with application to incompressible flow simulations

This paper presents new developments of the staggered spline collocation method for cost‐effective solution to the incompressible Navier–Stokes equations. Maximal decoupling of the velocity and the pressure is obtained by using the fractional step method of Gresho and Chan, allowing the solution to sparse elliptic problems only. In order to preserve the high‐accuracy of the B‐spline method, this fractional step scheme is used in association with a sparse approximation to the inverse of the consistent mass matrix. Such an approximation is constructed from local spline interpolation method, and represents a high‐order generalization of the mass‐lumping technique of the finite‐element method. A numerical investigation of the accuracy and the computational efficiency of the resulting semi‐consistent spline collocation schemes is presented. These schemes generate a stable and accurate unsteady Navier–Stokes solver, as assessed by benchmark computations. Copyright © 2003 John Wiley & Sons, Ltd.     

结构动力方程的样条精细积分法

结合精细积分法和样条函数拟合技术的优点,提出了求解结构动力方程的一种有效方法.首先对非齐次项用三次正规化B样条函数进行拟合,然后利用正规化B样条函数形状相同、仅相差一个平移量的特点,构造了一个高效的特解求解方法.按此方法只需求出一个标准B样条项所对应的特解,然后通过时间坐标的平移并结合叠加原理,即可求出任意时刻的特解值.由于特解计算中采用数值积分的方法,避免了矩阵求逆,因而本方法具有较大的适用范围.算例结果证明了该方法的有效性.     

Efficient ADI and spline ADI methods for the steady-state Navier-Stokes equations

The present paper provides an improved alternating direction implicit (ADI) technique as well as high-order-accurate spline ADI method for the numerical solution of steady two-dimensional incompressible viscous flow problems. The vorticity-stream function Navier-Stokes equations are considered in a general curvilinear coordinate system, which maps an arbitrary two-dimensional flow domain in the physical plane into a rectangle in the computational plane. The stream function equation is parabolized in time by means of a relaxation-like time derivative and the steady state solution is obtained by a time-marching ADI method requiring to solve only 2 × 2 block-tridiagonal linear systems. The difference equations are written in incremental form; upwind differences are used for the incremental variables, for stability, whereas central differences approximate the non-incremental terms, for accuracy, so that, at convergence, the solution is free of numerical viscosity and second-order accurate. The high-order-accurate spline ADI technique proceeds in the same manner; in addition, at the end of each two-sweep ADI cycle, the solution is corrected by means of a fifth-order spline interpolating polynomial along each row and column of the computational grid, explicitly. The validity and the efficiency of the present methods are demonstrated by means of three test problems.     

基于离散元法的干湿颗粒系统仿真

介绍了基于离散元法的干湿颗粒系统仿真软件DEMSIM。对于干颗粒系统,DEMSIM可以分析二维和三维颗粒系统的弹性和塑性接触碰撞过程;对于湿颗粒系统,DEMSIM采用传统的液桥模型;对于颗粒-流体系统,DEMSIM采用CFD-DEM细观耦合模型模拟。一系列典型算例的模拟分析,验证了干湿颗粒系统仿真软件DEMSIM的精度和有效性。     

An improved approximation technique to obtain numerical solution of a class of two-point boundary value similarity problems in fluid mechanics

A simple and efficient approximate numerical technique is presented to obtain solutions to a wide class of two-point boundary value similarity problems in fluid mechanics. This technique is based on the common finite difference method with central differencing, a tridiagonal matrix manipulation and an iterative procedure. The technique described in this paper has been successfully applied to three different representative similarity problems of fluid mechanics. Each one of these problems is described by a coupled, non-linear system of three ordinary differential equations and has already been solved elsewhere using a different numerical method. So, the obtained numerical results, by our efficient numerical technique, permit a comparative study and show the accuracy and the effectiveness of this technique.     

Dynamic response of elastic rectangular plates by spline state variable method

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