Reissner-Mindlin板的非协调稳定化组合有限元法

基于Reissner-Mindlin板的组合变分格式,提出了一种非协调稳定化组合有限元方法.若有限元空间满足能量协调条件,该方法收敛,并有误差估计.作为应用,讨论了3种有限元空间,并和MITC4和DKQ方法比较.数值结果表明该方法对网格畸变不敏感,若选取适当的参数,在粗网格上就有高精度.     

对流扩散问题Crank-Nicolson差分-流线扩散法的高精度分析

讨论了对流扩散问题C rank-N ico lson差分流线扩散格式,利用插值后处理技术提高了特殊网格下该格式在双线性元空间解的精度,从而按Lα(L2(Ω))模达到最优.     

一类非定常对流占优扩散问题差分-流线扩散法的后处理

讨论了一类非定常对流占优扩散方程的差分-流线扩散格式(FDSD),利用插值后处理技术,提高了特殊网格下该FDSD格式在双线性元空间的精度,从而按L∞(L2(Ω) 模达到最优．     

三角形单元协调与非协调位移的能量正交关系

基于组合稳定化变分原理,周天孝提出的组合杂交法是绝对收敛和稳定的,它给出了一种系统化的增强应力/应变方法,并建立了一簇低阶仿射等价的n-cube(n=2,3)单元。本文论证了单元上应力插值为线性,位移插值为协调线性部分和非协调二次部分之和的三角形组合杂交单元其协调部分与非协调部分的能量正交关系,进而得到此三角形单元刚度矩阵等同于协调的三角形线性元刚度矩阵,即非协调部分无应变增强特性。     

线性抛物方程的变网格各向异性双线性有限元方法

通过利用各向异性双线性元矩形剖分,结合变网格有限元思想,导出了线性抛物方程的全离散变网格各向异性双线性元有限元格式,并给出其L2模误差估计.     

一个改进的Reissner-Mindlin矩形元

本文提出了一个改进的Reissner-Mindlin矩形非协调元方法：旋度用连续双线性元逼近，横向位移用旋转矩形非协调元逼近，而作为中间变量的剪切力用增广的分片常数元逼近，我们证明：该方法具有关于板厚一致稳定性和一致最优收敛性。     

基于杂交应力元法的颗粒增强复合材料Monte-Carlo模拟

杂交应力元假设的高阶应力场可以用较疏的网格获得较高的计算精度.采用四叉树网格离散非均质计算域,四叉树杂交应力单元悬挂节点的位移协调条件自动满足,且得益于单元类型数量有限,单元刚度矩阵可以预计算,以便在实际计算时直接读取调用,大幅提高了计算效率.考虑夹杂的随机性对颗粒增强复合材料力学性能的影响,采用均匀化方法和Monte-Carlo方法,研究了随机夹杂的体积比、数量、长宽比对材料均质等效模量的影响,结果表明,复合材料的等效弹性模量随夹杂体积比、数量、长宽比的增大而增大,且对体积比最敏感.     

双曲积分微分方程类Wilson非协调元的超收敛和外推

将类Wilson非协调元方法应用于半离散格式下双曲积分微分方程的逼近.当问题的精确解u∈H3(Ω)/H4(Ω)时,利用该单元相容误差在能量范数意义下可达到O(h2)/O(h3)阶(比其插值误差高一阶/两阶)的特殊性质,并结合双线性元的高精度分析和插值后处理技巧,得到了与以往文献中双线性元完全相同的O(h2)阶的超逼近性质和整体超收敛结果.进而,通过构造一个新的外推格式导出了具有三阶精度的外推解.     

节点应力连续的四边形单元

节点应力连续的四边形单元Q4-CNS是一种基于单位分解理论的混合的有限元无网格法.Q4-CNS可以视作FE-LSPIM QUAD4的发展.Q4-CNS形函数的导数在节点处是连续的,因此可以自然的得到节点应力,而不需要使用节点应力磨平算法.数值实验表明,与传统四边形单元(QUAD4)相比,Q4-CNS具有更好的计算精度和更高的收敛速度.在扭曲网格下,Q4-CNS也能取得满意的数值精度.然而,QUAD4的数值精度则会随着网格的扭曲明显的变差.基于Kirchhoff-Love假设的非协调板单元计算中,不仅要求形函数在单元的交界面上要保持C0连续性,而且要求形函数在节点处具有C1连续性,所以在任意的四边形单元上构造满足插值条件的非协调板单元形函数较为困难.Q4-CNS形函数的导数在节点处是连续的,所以Q4-CNS在求解基于Kirchhoff-Love假设的板单元问题中具有潜在的应用价值.     

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.     

High Accuracy for Mixes Finite Element Methods in Raviart-Thomas Element

1.IntroductionWeconsiderthemixedmethodsoftheNeumannboundaryvaJueproblemp+7u=oinfl,divp=jinfl,(1)p'n=Oonofl,whereflCR2isaboundeddomainwithboundariesparaJleltoaxes,nistheouterunitnormaJtoOfl.DenoteHo(div)={qEH(div),q'n=oonofl},thenwecanwritetheweakformulationof(1)asfollows:Find(u,p)EL'(n)xHo(div)suchthat(p,q)-(u,divq)+(v,divp)=(f,v),V(v,q)eL'(fl)xHo(div).(2)LetVhxPhCL'(fl)xHo(div)beapairoffiniteelementspaceswithrespecttoTh,auinformrectangularmeshwiththesize2h.Thenthemiredfiniteelementa…     

关于非协调位移元与杂交应力元的对应性

本文阐明了E.L.Wilson[3]等的非协调移位元与卞学鐄的杂交应力元之间所存在的对应性.     

有限元多尺度小波

利用有限元插值和多尺度分析理论构造出了有限元多尺度小波.这些小波函数集许多优良性质于一身,如固定的短支集、高阶的消失矩、半正交性及正则性等.     

A New Finite Element Space for Expanded Mixed Finite Element Method

In this article, we propose a new finite element space Λ$_h$ for the expanded mixed finite element method (EMFEM) for second-order elliptic problems to guarantee its computing capability and reduce the computation cost. The new finite element space Λ$_h$ is designed in such a way that the strong requirement V$_h\subset$Λ$_h$ in [9] is weakened to {v$_h\in$V$_h$; divv$_h$=0}$\subset$Λ$_h$ so that it needs fewer degrees of freedom than its classical counterpart. Furthermore, the new Λ$_h$ coupled with the Raviart-Thomas space satisfies the inf-sup condition, which is crucial to the computation of mixed methods for its close relation to the behavior of the smallest nonzero eigenvalue of the stiff matrix, and thus the existence, uniqueness and optimal approximate capability of the EMFEM solution are proved for rectangular partitions in $\mathbb{R}^d, d=2,3$ and for triangular partitions in $\mathbb{R}^2$. Also, the solvability of the EMFEM for triangular partition in $\mathbb{R}^3$ can be directly proved without the inf-sup condition. Numerical experiments are conducted to confirm these theoretical findings.     

Vector Equilibrium Problems,Minimal Element Problems and Least Element Problems

In this paper we introduce some concepts of feasible sets for vector equilibrium problems and some classes of Z-maps for vectorial bifunctions. Under strict pseudomonotonicity assumptions, we investigate the relationship between minimal element problems of feasible sets and vector equilibrium problems. By using Z-maps, we further study the least element problems of feasible sets for vector equilibrium problems. Finally, we prove a generalized sublattice property of feasible sets for vector equilibrium problems associated with Z-maps. This work was supported by the National Natural Science Foundation of China and the Applied Research Project of Sichuan Province (05JY029-009-1). The authors thank Professor Charalambos D. Aliprantis and the referees for valuable comments and suggestions leading to improvements of this paper.     

精确有限元法

本文提出构造有限单元的新方法——精确有限元法.它可以求解在任意边界条件下任意变系数正定或非正定偏微分方程。文中给出它的收敛性证明和计算偏微分方程的一般格式。用精确元法所得到的单元是一个非协调元,单元之间的相容条件容易处理.与相同自由度普通有限元相比,由精确元法所得到的解的高阶导数具有较高的收敛精度.文末给出数值算例,所得到的结果均收敛于精确解,并有较好的数值精度.     

Fourteen-Node Mixed Stiffness Element and Its Computational Comparisons with Twenty-Node Isoparametric Element

In this paper, a family of 3-dimensional elements different from isoparametric serendipity is developed according to the variational principle and the convergence criteria of the mixed stiffness finite element method. For the new family, which is named mixed stiffness elements, the number of nodes on the quadratic element is not 20 but 14. Theoretical analysis and various computational comparisons have found the mixed stiffness element superior over the isoparametric serendipity element, especially a substantial improvement in computational efficiency can be achieved by replacing the 20 node-isoparametric element with the 14-node mixed stiffness element.     

Non-linear Stochastic Finite Element

This paper investigates the uncertainty of physically non-linear problems by modeling the elastic random material parameters as stochastic fields. For its stochastic discretization a polynomial chaos (PC) is used to expand the coefficients into deterministic and stochastic parts. Then, from experimental data for an adhesive material the distribution of the random variables, i.e. Young's modulus E(θ), the static yield point Y₀ and the nonlinear hardening parameters q and b, are known. In the numerical example the distribution of the stresses obtained by the PC based SFEM and Monte Carlo simulation is compared. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)