压电材料平面裂纹尖端场的杂交应力有限元分析

基于复势理论和杂交变分原理建立了一种适用于力电耦合分析的杂交应力有限元模 型. 给出了建立刚度矩阵的主要公式和推导过程，单元内的位移场和应力场采用满足平 衡方程的复变函数级数解，假设的复变函数级数解事先精确满足裂纹的无应力和电位移法向 分量为零的条件，单元外边界的位移场假设按抛物线变化, 单元的刚度矩阵采用Gauss积分的方法得出. 通过对力电耦合裂尖场的数值计算验证了程序 的正确性和单元的有效性，同时也用所得结果校验了理论解.     

On the influence of singular-type finite elements on the critical force in studying the buckling of a circular plate with a crack

The axisymmetric buckling (delamination) of a circular disk (plate) with a penny-shaped crack is analyzed using a continuum model, piecewise-homogeneous model, and the three-dimensional linearized theory of stability. The FEM is used. The analysis is carried out using various singular and ordinary finite elements. The numerical results obtained indicate that it is not necessary to use singular finite elements to solve the problem Published in Prikladnaya Mekhanika, Vol. 43, No. 9, pp. 120–129, September 2007.     

面向对象的无单元法

介绍了一种用C 进行的面向对象无单元方法程序设计;定义了一些关键的类并将有些类设计成类等级,从而建立了包含权函数、基函数和形函数在内的面向对象无单元法程序类库,在此过程中考虑了无单元法与有限元法的某些联系,保留并重用了面向对象有限元法程序中的一些类。本文提供了一种无单元法大型分析软件开发新途径。     

Pole placement controllers for linear time-delay systems with commensurate point delays

This paper investigates the exact and approximate spectrum assignment properties associated with realizable output-feedback pole-placement type controllers for single-input single-output linear time-invariant time-delay systems with commensurate point delays. The controller synthesis problem is discussed through the solvability of a set of coupled diophantine equations of polynomials. An extra complexity is incorporated to the above design to cancel extra unsuitable dynamics being generated when solving the above diophantine equations. Thus, the complete controller tracks any arbitrary prefixed (either finite or delaydependent) closed-loop spectrum. However, if the controller is simplified by deleting the above mentioned extra complexity, then the robust stability and approximated spectrum assignment are still achievable for a certain sufficiently small amount of delayed dynamics. Finally, the approximate spectrum assignment and robust stability problems are revisited under plant disturbances if the nominal controller is maintained. In the current approach, the finite spectrum assignment is only considered as a particular case to the designer‘s choice of a (delay-dependent) arbitrary spectrum assignment objective.     

激光切割脆性材料的温度场模拟

激光切割脆性材料是一个复杂的光致热过程。在综合考虑材料的热物性参数、初始条件及边界条件的情况下,运用Ansys软件建立了激光切割脆性材料温度场的三维有限元模型。采用APDL语言实现了对热流密度的高斯分布和强制对流换热及移动激光热源的模拟。通过设置不同的激光切割参数,对温度场的变化进行了模拟分析。所建立的温度场模拟系统可以对实际激光切割脆性材料的热过程进行前期预测,并能对激光切割参数的选择进行一定的优化,以减少实际切割的盲目性。     

计算流管声场的三维有限元数值模型

发展了一种三维有限元数值模型和计算方法来对矩形流管声场进行整体的计算.与以往的二维方法相比,此种数值方法不仅全面反映了矩形流管内声波的传播情况,而且提高了网格精度,从而大大扩展了对铺设有声衬的流管的计算领域.结果表明,该数值模型是有效和准确的,与其它方法和文献的计算结果吻合得非常好.同时,在大大增加计算量的同时,也对程序代码进行了优化工作,提高了计算效率.     

一维瞬态辐射传输的有限元法模拟

随着超短脉冲激光的快速发展,吸收散射性介质内的瞬态辐射传输引起了人们的广泛关注.本文基于离散坐标法和最小二乘有限元法(LSFEM),提出了模拟多维吸收散射性介质内瞬态辐射传输的数值模型.该模型有效地克服了在标准Galerkin有限元法(GFEM)中发生的伪振荡现象,在时间步长较大的情况下仍然可以得到光滑无振荡的解.而且,最小二乘法产生的求解系数矩阵是对称正定的,与GFEM中的系数矩阵相比,仅需要存储一半的非零系数,可以应用许多高效的迭代求解方法进行求解.为了检验模型,本文研究了一维吸收散射性介质内瞬态辐射传输问题,其结果与蒙特卡洛法(MCM)和积分模型法(IE)的结果进行了比较,结果证实:本文的方法可以精确、高效地模拟参与性介质内的瞬态辐射传输.     

非线性对流扩散问题的交替方向差分流线扩散法

1引言Peaceman,Douglas等人于1955年提出了差分格式的交替方向法。随后,Douglas,Dupont于1972年又提出了有限元格式的交替方向法[1]。其基本思想是:对两个或三个空间变量的二阶抛物型和双曲型问题,将交替方向法与Galerkin方法相结合,通过算子分裂技术,把高维问题转化为一系列低维问题,交替地沿各空间变量的方向求解。[2]、[3]和[4]给出了对更一般扩散问题(带对流项的抛物方程)的数值求解和误差分析。     

Finite Difference Method for Reaction-Diffusion Equation with Nonlocal Boundary Conditions

In this paper, we present a numerical approach to a class of nonlinear reaction-diffusion equations with nonlocal Robin type boundary conditions by finite difference methods. A second-order accurate difference scheme is derived by the method of reduction of order. Moreover, we prove that the scheme is uniquely solvable and convergent with the convergence rate of order two in a discrete L2-norm. A simple numerical example is given to illustrate the efficiency of the proposed method.