Nonconforming finite elements for the equation of planar elasticity

Two new locking-free nonconforming finite elements for the pure displacement planar elasticity problem are presented. Convergence rates of the elements are uniformly optimal with respect to A. The energy norm and L2 norm errors are proved to be O（h2） and O（h3）, respectively. Numerical tests confirm the theoretical analysis.     

A class of Wilson arbitrary quadrilateral elements for an axisymmetric problem

A class of modified Wilson arbitrary quadrilateral nonconforming elements for an axisymmetric problem is proposed. Their convergence is proven by means of the strong patch test. The structure of this finite element class is investigated. Thus a general method of axisymmetric nonconforming elements with convergence properties is presented. Project supported by the Foundation of the Chinese Ministry of Machine-Building Industry     

On the problems of sandwich shells having the form of a surface of revolution and face layers of non-equal thicknesses

Fundamental equations which govern the behavior of an elasticsandwich shell having the form of a surface of revolution andface layers of non-equal thicknesses are derived,with the so-lution of Refs.[3]and[4]as special examples.The problems of the shell under the action of symmetricalloads are reduced to the solution of a displacement-function4～,where4αsatisfies a differential equation of sixth order.     

复合材料中矩形夹杂角端部力学行为分析

提出了一种分析矩形夹杂角端部奇异应力场的新型杂交有限元方法,该方法在分析矩形夹杂角端部奇异应力场时,需要在夹杂端部构造一个超级单元。超级单元的刚度矩阵可以通过夹杂端部特征问题数值解建立。我们用这种方法计算了单向载荷作用下无限大均质板中单个矩形夹杂角端部奇异应力场,并与现有的数值解进行了比较。比较结果表明:本文提出的方法是可行的、有效的,而且数值结果精度高。为说明本文方法适用范围更广,文章最后讨论了各向异性弹性材料和横观各向同性压电材料中矩形夹杂角端部电弹性场行为。     

精化直接刚度法与不协调模式

基于不协调元的收敛条件，建立了精化直接刚度法（ＲＤＳＭ）所对应的不协调位移模式，从而使ＲＤＳＭ成为建立单变量不协调元的有实用性的一般方法。     

Anisotropic nonconforming Crouzeix-Raviart type FEM for second-order elliptic problems

The nonconforming Crouzeix-Raviart type linear triangular finite elementapproximate to second-order elliptic problems is studied on anisotropic general triangularmeshes in 2D satisfying the maximal angle condition and the coordinate system condition.The optimal-order error estimates of the broken energy norm and L2-norm are obtained.     

The finite element method based on interpolating with wavelet basis function

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边界元法计算切口多重应力奇性指数

提出采用边界元法直接计算V形切口的多重应力奇性指数。首先在切口尖端挖出一微小扇形域,在该域边界列常规边界积分方程,后将扇形域内的位移场和应力场表示成关于切口尖端距离ρ的渐近级数展开式,回代入切口边界积分方程,离散后得到关于切口奇性指数的代数特征方程,从而求解获得V形切口的应力奇性指数。该法避免了常规边界元法和有限元法在切口尖端附近布置细密单元的缺陷,并可同时求得多阶应力奇性指数。     

Analytical removal of singularity and direct evaluation of singular integrals in 3-D elastoplastic finite deformation analysis by BEM

As a further development of the present authors' research work [1,2], in this paper a method of the so-called quadratic pentahedron polar co-ordinate transformation and analytical removal of singularity of Cauchy principal value singular integrals is proposed to evaluate the strongly singular integrals in the sense of Cauchy principal values and the weakly singular integrals over quadratic internal cells in 3-D elastoplastic finite deformation analysis by BEM. First, a quadratic pentahedron polar co-ordinate transformation technique is used to reduce the order of singularity of the singular integrals. Then, a form of Gauss' theorem is introduced to remove the singularity in the Cauchy principal value singular integrals analytically. Therefore, the evaluation of all those strongly and weakly singular integrals can be carried out by standard Gaussian quadrature accurately and efficiently. Numerical examples of the 3-D elastoplastic problem and 3-D finite deformation problem are given to demonstrate that the method possesses good accuracy and numerical stability, and is convenient to implement. The method in this paper can be applied extensively to evaluating the singular integrals over cubic and higher order elements.     

三维双材料结构的应力奇异性分析

应用有限单元法子模型技术,对具有不同界面角的三维双材料结构的应力奇异性进行了分析。结果表明,应用子模型技术估算三维双材料结构的应力奇异性指数是有效的。然后分析了界面端线和界面端点处附近奇异性指数,得到了一些重要而有趣的结果。最后对消除三维双材料结构应力奇异性的几何条件进行了讨论。     

非线性广义杂交元

选择新的三类变量建立了放松单元间连续性条件的用于非线性有限元分析的泛函，并由此建立了基于不协调模式的非线性广义杂交元方法。     

Superconvergence analysis of lower order anisotropic finite element

The convergence analysis of the lower order nonconforming element pro- posed by Park and Sheen is applied to the second-order elliptic problem under anisotropic meshes.The corresponding error estimation is obtained.Moreover,by using the interpo- lation postprocessing technique,a global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is derived.Numerical results are also given to verify the theoretical analysis.     

Neurocomputing theory and numerical simulation on elasticity

A new finite element analysis principle based on neural networks is propsed. It can realize the finite element analysis in real time. The neural computation of a simple structure was simulated on digital computer, the effect of input parameters on convergent speed and precision was analyzed. Before solving a certain FE problem, the linking weight matrix of the neural net, i.e., the global stiffness matrix of the structure analyzed, must be defined. In this paper, a method which uses the BP net to compute the element stiffness matrix in real time is proposed. The subject is supported by the Natural Science Foundation of China     

随机场的投影展开法

本文基于伽辽金投影方法，提出了一种新的随机场的展开方法。它是通过构造一组标准正交基，并将随机场用其在这组基上的投影表示。这种展开方法避免了求解相关函数的特征函数的困难，最后通过算例说明了本文方法的特性。     

接触问题应力分析的混合解法

接触问题是一个极其复杂的非线性问题,单独使用数值方法或实验方法求解应力都有一定的困难．有限元计算与平面光弹性实验相结合的混合法是对接触问题进行应力分析简单而有效的途径．     

Three‐dimensional simulation of planar contraction viscoelastic flow by penalty finite element method

The planar contraction flow is a benchmark problem for the numerical investigation of viscoelastic flow. The mathematical model of three‐dimensional viscoelastic fluids flow is established and the numerical simulation of its planar contraction flow is conducted by using the penalty finite element method with a differential Phan‐Thien–Tanner constitutive model. The discrete elastic viscous split stress formulation in cooperating with the inconsistent streamline upwind scheme is employed to improve the computation stability. The distributions of velocity and stress obtained by simulation are compared with that of Quinzani's experimental results detected by laser–doppler velocimetry and flow‐induced birefringence technologies. It shows that the numerical results agree well with the experimental results. The numerical methods proposed in the study can be well used to predict complex flow patterns of viscoelastic fluids. Copyright © 2009 John Wiley & Sons, Ltd.     

The near tip stress and strain fields in cracked single crystals

The numerical analyses of stationary mathematically sharp Mode I crack in FCC and BCC crystals with elastic-ideally plastic (EIP) and fast hardening saturation (FHS) law are carried out in the present paper. From the calculated results, it is shown that: for the cases of small strain, EIP crystal cracks, the features of concentrated deformation patterns and the stress state in near-crack tip deformation fields are identical to the earlier analytical solutions, but along the angular sector boundaries, there exist narrow complex stress zones. The overall characteristics of deformation patterns for the cases of EIP and FHS are similar. The behaviours of crack tip opening can be characterized by crack-tip-opening-displacement (CTOD). For the case of FHS, finite deformation BCC crystal crack, our calculations are qualitatively in agreement with recent experimental observations. The project supported by National Natural Science Foundation of China     

New nonconforming finite element method for solving transient Naiver-Stokes equations

For transient Naiver-Stokes problems, a stabilized nonconforming finite element method is presented, focusing on two pairs inf-sup unstable finite element spaces, i.e., pNC/pNC triangular and pNQ/pNQ quadrilateral finite element spaces. The semi- and full-discrete schemes of the stabilized method are studied based on the pressure projection and a variational multi-scale method. It has some attractive features： avoiding higher-order derivatives and edge-based data structures, adding a discrete velocity term only on the fine scale, being effective for high Reynolds number fluid flows, and avoiding increased computation cost. For the full-discrete scheme, it has second-order estimations of time and is unconditionally stable. The presented numerical results agree well with the theoretical results.     

On the equivalence of the Wilson element and the generalized hybrid element

In this paper the equivalence of the generalized hybrid element and the modified Wilson element, which is derived by the generalized hybrid method, is proved. The project is supported by the National Natural Science Foundation of China     

The dynamic plastic response characteristics of circular beam

In this paper the problem of a circular beam subjected to radial impact by a rigid mass at its tip in its own plane is investigated on the basis of rigid-perfectly plastic assumption. The analytical solution of the particle velocities is obtained as the function of travelling plastic hinge location. By analysing the solution, some special properties of circular beam problem are found.