四节点元和八节点元h—收敛的比较

本文从理论上比较了四边形四节点元和四边形八节点元的ｈ－收敛性，得出八节点元较四节点元有较快收敛率的结论，并通过算例进行了验证。     

三维Poisson方程特征值的四种有限元解及比较

应用三维EQ1rot元、三维Crouzeix-Raviart元、八节点等参数元、四面体线性元计算三维Poisson方程的近似特征值.计算结果表明:三维EQ1rot元和三维Crouzeix-Raviart元特征值下逼近准确特征值,八节点等参数元、四面体线性元特征值上逼近准确特征值,三维EQr1ot元和三维Crouzeix-Raviart元外推特征值下逼近准确特征值.计算结果还表明三维Crouzeix-Raviart元是一种计算效率较高的非协调元.     

CSM玻璃钢复合型断裂的有限元分析

对切短玻璃纤维毡增强聚脂层板的复合型断裂进行了有限元分析。采用八节点四边形等参元的正规型式计算应力分布与损伤区扩展;而用坍塌(collapsed)三角形四分之一点(quarter-point)奇异元计算应力强度因子K_Ⅰ与K_Ⅱ。用节点位移约束与释放技术计算了裂纹扩展过程。对决定应力强度因子K_Ⅰ与K_Ⅱ的三种方法进行了对比。对施加于裂纹顶点节点约束条件的影响进行了评价。最后基于实验测得的断裂载荷与临界裂纹长度,估算了材料在这种受力条件下的复合型临界应力强度因子K_ⅠC和K_ⅡC。     

双参数13参四边形板元

本文提出了一个双参数13参四边形板元, 其中一套参数按照广义分片检验要求选取, 另一套真正节点参数按照使离散系统更易解的要求选取,通过数值方法将一套节点参数线性过渡到另一套, 并且证明了该元的收敛性, 给出算例加以验证.     

一类改进的Wilson任意四边形单元

Wilson元是工程计算中数值效果很好的一种非协调元,但对任意四边形网格却不能收敛。石钟慈要求四边形单元满足对角线中点距离d_k=O(h_k~2),[2]、[3]提出了一个六参数非协调四边形单元。它对任意四边形网格收敛,但其单元上的形状函数非常依赖单元本     

一类六参数非协调任意凸四边形单元

本文构造了一类六参数非协调四边形单元,证明由此产生的有限元对任意四边形网格通过Irons分片检查,其收敛效果同Wilson元相当且形状函数的选择不依赖于单元本身。类Wilson元及改进的Wilson任意四边形单元是其中的特例。     

二阶问题的一个类Wilson非协调元

§1.引言 Wilson元是工程计算中常用的一种非协调元,数值计算效果很好,但是Wilson元对于任意四边形网格却不能收敛.石钟慈在[1]中限制四边形单元剖分,要求四边形单元满足对角线中点距离d_K=o(h_K~2),而[2]—[3]则修改了双线性形式,即在刚度矩阵元素的计算中采用某种数值积分,这两种方法均使得Wilson元达到收敛.另外,通过改变形状函数,[4]—[5]提出了一个六参数非协调四边形单元QP6,它是推广的Wilson元.此元对任意四边形网格能够收敛,但其单元上的形状函数非常依赖单元本身.     

构造任意非协调四边形单元的新模式

通过对Q4元增加一个非协调高阶项．构造了一类新的非协调四边形单元，并证明由此产生的单元对任意四边形网格通过Irons分片检查和广义分片检查，且形状函敷不依赖于单元本身．QM5是其中的一个特例．数值结果表明，该类单元有很好的收敛效果．     

双参数任意四边形非协调板元的构造及收敛性分析

本文利用双参数有限元方法[1]构造出十二参和十三参任意四边形板元，并对其收敛性进行分析证明．     

关于几种三角形板元等价性的注记

1．引言求解薄板弯曲问题的广义协调元法近年来有了发展,本文讨论几种三角形板元之间的等价关系．我们证明,[2]中构造的GCⅢ－T9元等价于Specht元问．同一作者在[4]中构造的GCⅡ－T9元实际上也等价于Specht元,因此,它们彼此等价．另外,[7]中用对称列式构造的一个广义协调元是和作者在问中所引进的单元等价．例已指出,[7]中的那个元等价于问中的VZ1元,所以[7]和[6]中的两个广义协调元均等价于已知的VZ1元．2．广义协调GCⅢ－T9单元设三角形单元K的三个顶点依反时针方向分别为p i（xi,yi）,节点参数是pi点处的函数值及其一阶导…     

采用三角形面积坐标的四边形17节点样条单元

利用二元4次样条插值基和三角形面积坐标构造17节点四边形单元．这个新单元具有4次完备阶,通过一些算例测试表明了该单元有较高精度并对网格畸变不敏感．     

Geometrically nonlinear analysis with a 4-node membrane element formulated by the quadrilateral area coordinate method

Recently, a 4-node quadrilateral membrane element AGQ6-I, has been successfully developed for analysis of linear plane problems. Since this model is formulated by the quadrilateral area coordinate method (QACM), a new natural coordinate system for developing quadrilateral finite element models, it is much less sensitive to mesh distortion than other 4-node isoparametric elements and free of various locking problems that arise from irregular mesh geometries. In order to extend these advantages of QACM to nonlinear applications, the total Lagrangian (TL) formulations of element AGQ6-I was established in this paper, which is also the first time that a plane QACM element being applied in the implicit geometrically nonlinear analysis. Numerical examples of geometrically nonlinear analysis show that the presented formulations can prevent loss of accuracy in severely distorted meshes, and therefore, are superior to those of other 4-node isoparametric elements. The efficiency of QACM for developing simple, effective and reliable serendipity plane membrane elements in geometrically nonlinear analysis is demonstrated clearly.     

Stokes流动的罚-杂交有限元分析*

本文建议了一种用于分析Stokes流动的罚-杂交变分原理,其中,偏应力张量和静水压力事先满足线动量平衡.建立了相应的有限元模型.由此,压力可在列式过程中消去,使得有限元矩阵方程仅以节点速度作为唯一的求解未知量.推导了几种4-节点和8-节点四边形单元.通过数值算例,显示了单元性能.     

QUADRILATERAL MESH

Several quadrilateral shape regular mesh conditions commonly used in the finite element method are proven to be equivalent. Their influence on the finite element interpolation error and the consistency error committed by nonconforming finite elements are investigated. The effect of the Bi-Section Condition and its extended version $(1+\al)$-Section Condition on the degenerate mesh conditions is also checked. The necessity of the Bi-Section Condition in finite elements is underpinned by means of counterexamples.     

QUADRILATERAL MESH

IntroductionQuadrilateral mesh Is widely used In the finite eleme     

用于平板和圆柱壳分析的势能—杂交／混合分离位移有限元格式

本文基于势能～杂交/混合有限元格式,导出了具有分离转动变量的4节点四边形Reissner-Mindlin板元MP4、MP4a和圆柱壳元MCS4.所有这些单元都显示了良好的收敛性;不含有多余机动模式;当趋于薄板/壳极限时,不存在“自锁”现象.本文还指明了在C~0和C~1连续的单元列式中使用的修正泛函,存在相互联系.本文的方法可导出Prathap的一致场列式,也可导出RIT/SRIT的位移协调模型.     

p-version hybrid/mixed finite element method

In this paper, the p-version hybrid/mixed finite element formulation using the Hu–Washizu principle is presented. The shape functions are assumed to be hierarchical for the displacement variables. The stresses and the strains are interpolated using Legendre polynomials so that the computation of the stiffness matrix will be simplified. For 2-D problems, the higher-order hierarchical shape functions start following the 8-node, quadrilateral shape functions. The geometry mapping of each element is also performed using an 8-node parametric mapping. Numerical examples for a plate with a circular hole and circular inclusion are included.     

Numerical integration over polygons using an eight-node quadrilateral spline finite element

In this paper, a cubature formula over polygons is proposed and analysed. It is based on an eight-node quadrilateral spline finite element [C.-J. Li, R.-H. Wang, A new 8-node quadrilateral spline finite element, J. Comp. Appl. Math. 195 (2006) 54–65] and is exact for quadratic polynomials on arbitrary convex quadrangulations and for cubic polynomials on rectangular partitions. The convergence of sequences of the above cubatures is proved for continuous integrand functions and error bounds are derived. Some numerical examples are given, by comparisons with other known cubatures.     

四边形单元h－收敛误差估计的探讨*

本文证明了四边形单元的h-收敛性,给出了相应的引理和定理,讨论了误差估计问题,为四边形单元h-收敛自适应有限元分析准备了基础。     

定常Satokes方程的窄边四边形有限元法

本文提出了一个试探函数不满足divν＝0的定常Stokes方程的窄边四边形有限元法，利用窄边四边形等参有限元插值定理和Falk的思想，得到了H^1(Ω）模误差的最优收敛估计阶O（h）。