对应不同类型变分原理的旋转薄壳轴对称单元

本文在一定范围内,统一考察基于不同变分原理建立的有限元模型中,泛函约束条件的不同对单元性态的影响.文中以旋转薄壳轴对称单元(简称TSR单元)为例,采用相同的曲边单元几何描述,推导了七种TSR杂交单元和二种TSR位移协调元,它们分别对应于三类杂交变分原理及最小势能原理.通过单刚列式分析和波纹壳等数值算例比较,分析了不同模型的性态异同和应用上的适应性与局限性;讨论了两类模型间的相互关系;指出了TSR杂交位移元的—个发散条件,并推荐了二种性态较理想的TSR单元.     

Mindlin板几何非线性分析的附加内部剪应变法

本文在几何非线性分析的Ｍｉｎｄｌｉｎ板元中引入单元附加内部剪应变，有效地解决了薄板情况下的剪切自锁问题．文中导出了相应的能量相容条件，给出了有限元非线性列式的全过程及有关簿板及中厚板大挠度问题的数值结果．     

Wilson元插值误差渐近估计

Wilson元是工程界常用的一种有限元计算方法,但在理论分析中插值误差估计的常数只知道存在,不知道具体值.本文给出了在L~2、H~1范数意义下Wilson元在参考单元和一般单元上插值误差渐近估计,导出了主要常数.这种精确的估计为有限元后验误差估计和自适应计算提供保障.     

对偶变量块体混合元及其位移元的收敛性和精度分析

弹性力学Hamilton正则方程和Hamilton混合元的等效刚度系数矩阵,均具有直观的辛特性.基于H R变分原理和弹性力学保辛理论建立的对偶变量块体混合元,其等效刚度系数矩阵同样具有直观的辛特性.根据对偶变量块体混合元列式,可直接建立问题的控制方程,进行混合法求解.同时,通过对偶变量块体混合元列式可以导出对偶变量块体位移元列式,建立问题的控制方程后,可先求位移的解.数值实例表明:线性8结点对偶变量块体位移减缩积分元的各力学量的收敛速度均衡、收敛过程稳定、结果精度高,其应力变量的收敛速度与传统的20结点位移协调减缩积分元接近.对偶变量块体位移元具有普适性.     

四阶抛物方程H1-Galerkin混合有限元方法的超逼近及最优误差估计

 本文基于双线性元及零阶Raviart-Thomas元 (R-T)对四阶抛物方程建立了半离散和向后欧拉全离散H¹-Galerkin混合有限元格式. 利用积分恒等式技巧和单元的特殊构造, 证明了关于上述两元的两个新的重要性质. 进而导出了这两种格式下相关变量的最优误差估计和超逼近性质.     

杂交应力元增量分析非线性橡胶类材料

本文基于增量Reissner变分原理,对不可压缩的Mooney型橡胶类材料,进行了非线性的有限元分析,给出了杂交应力元的计算列式.列式中考虑了不平衡力和不可压缩性偏差的修正项.算例计算与精确解符合得很好.     

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.     

迹分解秩(英文)

首先引入迹分解秩的概念,具有这个结构的稳定有限的顺从C~*-代数非常多.这个概念和Elliott的用K-理论来分类顺从C~*-代数的分类计划有重要的联系.然后研究C~*-代数扩张.设0→I→A-→A/I→0是C~*-代数的一个短正合序列,其中A有单位元.假设I有分解秩k,A/I有迹分解秩k,那么如果扩张是拟对角的,本文将证明A的迹分解秩不超过k.     

具有不等厚表层的夹层旋转壳问题

本文探讨了具有各向同性夹心及不等厚表层组成的三层旋转壳的小挠度问题,采用广义变分法,在考虑表层抗弯刚度的情况下,导出了基本方程,其特例即为文献[3],[4]的结果. 根据所导出的基本方程,本文求解对称加载的夹层旋转壳问题,将其归结为只含一个广义位移的六阶微分方程. 本文的理论可应用于复合装甲及其它工程设计.     

一种有效的边界元/有限元混合法迭代算法及其在回转体自由扭振分析中的应用*

本文给出一种新的边界元/有限元混合法迭代算法,基本做法是将近似的固有频率值代入自由振动问题的基本解,按一般混合法列式,通过迭代逐步修正近似解的值.这种算法避开了一般边界元法需要求解非代数特征值问题的困难,同时数值结果的精度基本上不依赖于区域内单元网格的疏密程度,这都给实际计算带来很多方便.应用于回转体自由扭振问题的分析,得到令人满意的数值结果.     

Analysis of reinforced concrete structures subjected to dynamic loads with a viscoplastic Drucker–Prager model

The behavior of reinforced concrete structures subjected to dynamic loads is analyzed. The concrete material is modelled by an elasto-viscoplastic law, whose inviscid counterpart is the Drucker–Prager model. A viscous regularization is introduced in order to avoid the mesh dependency effects that usually appear when strain softening occurs. The model is implemented in a general finite element computer code for fast transient analysis of fluid-structure systems, based on an explicit central difference scheme. The model is activated to both continuum elements and layered shell elements. So, realistic numerical analyses of complex 3-D engineering problems are simple and efficient. Three examples, two of which are modelled with layered shell elements, are presented below.     

Comments on Membrane Locking

Membrane locking is a severe issue frequently neglected in the context of low-order (four node isoparametric) shell elements. From a theoretical point of view, the present contribution illustrates the underlying mechanism by means of shallow shell theory. From a numerical point of view, different element formulations based on standard enhanced assumed membrane strains and reduced integration methods have been compared to each other applying standard as well as modified benchmark examples. A modified integration scheme is proposed. According to preliminary results it behaves virtually optimal within the limits of finite element perfectibility. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Partial hybrid finite elements for composite laminates

Three types of partial hybrid finite elements are presented in order to set up a global/local finite element model for analysis of composite laminates. In the global/local model, a composite laminate is divided into three different regions: global, local, and transition regions. These are modeled using three different elements. In the global region, a 4-node degenerated plate/shell element is used to model the overall response of the composite laminate. In the local region, a multilayer element is used to predict detailed stress distribution. In the transition region, a multilayer transition element is used to smoothly connect the two previous elements. The global/local finite element model satisfies the compatibility of displacement at the boundary between the global region and the local region. It also satisfies the continuity of transverse stresses at interlaminar surfaces and traction conditions on the top and bottom surfaces of composite laminates. The global/local finite element model has high accuracy and efficiency for stress analysis of composite laminates. A numerical example of analysis of a laminated strip with free edge is presented to illustrate the accuracy and efficiency of the model.     

关于Ciarlet-Raviart混合有限元法的一个注记

本文推广解双调合方程的Ciarlet-Raviart混合有限元方案：用二次元逼近流函数φ．一次元逼近涡度-Δφ．在拟一致三角形剖分的条件下,证明了推广方案具有φ和-Δφ都用二次元逼近的标准Ciarlet－Raviart方案同样的精度阶．     

A spatial shear deformable beam finite element based on the absolute nodal coordinate formulation

In the present paper a three-dimensional beam finite element undergoing large deformations is proposed. Since the definition of the proposed finite element is based on the absolute nodal coordinate formulation (ANCF), no rotational coordinates occur in the formulation. In the current approach, the orientation of the cross section is parameterized by means of slope vectors. Since those are no unit vectors, the cross-section can deform, similar to existing thick beam and shell elements. The nodal displacements and the directional derivatives of the displacements are chosen as nodal coordinates, but in contrast to standard ANCF elements, the proposed formulation is based on the two transversal slope vectors per node only. Different approaches for the virtual work of elastic forces are presented: a continuum mechanics based formulation, as well as a structural mechanics based formulation, which is in accordance with classical nonlinear beam finite elements. Since different interpolation functions as in standard ANCF elements are used, a much better convergence rate (up to order four) can be obtained. Therefore, the present element has high potential for application in geometrically nonlinear problems. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

CONVERGENCE OF THE CRANK-NICOLSON/NEWTON SCHEME FOR NONLINEAR PARABOLIC PROBLEM

In this paper, the Crank-Nicolson/Newton scheme for solving numerically secondorder nonlinear parabolic problem is proposed. The standard Galerkin finite element method based on P2 conforming elements is used to the spatial discretization of the problem and the Crank-Nicolson/Newton scheme is applied to the time discretization of the resulted finite element equations. Moreover, assuming the appropriate regularity of the exact solution and the finite element solution, we obtain optimal error estimates of the fully discrete CrankNicolson/Newton scheme of nonlinear parabolic problem. Finally, numerical experiments are presented to show the efficient performance of the proposed scheme.     

A NEW STABILIZED FINITE ELEMENT METHOD FOR SOLVING TRANSIENT NAVIER-STOKES EQUATIONS WITH HIGH REYNOLDS NUMBER

In this paper, we present a new stabilized finite element method for transient Navier-Stokes equations with high Reynolds number based on the projection of the velocity and pressure. We use Taylor-Hood elements and the equal order elements in space and second order difference in time to get the fully discrete scheme. The scheme is proven to possess the absolute stability and the optimal error estimates. Numerical experiments show that our method is effective for transient Navier-Stokes equations with high Reynolds number and the results are in good agreement with the value of subgrid-scale eddy viscosity methods, Petro-Galerkin finite element method and streamline diffusion method.     

THE FULL DISCRETE DISCONTINUOUS FINITE ELEMENTANALYSIS FOR FIRST-ORDER LINEAR HYPERBOLICEQUATION

1.IntroductionLetfibeaboundeddomaininRZwithpiecewisesmoothboundaryOff,[0,T]beatimeinterval.Considerthefirst-orderhyperbolicproblemasfollowingwhereac~(%,%),p(x,t)~(gi(x,t),pZ(x,t)),Off--(t)~{xEOff:fi(x,t)'ac<0},700istheoutwardunitnormaltoOff;fi(t)~fi\Ofl--(t).Asusual,Off--(t)isreferedtoasinflowboundaryattimet,andOff (t)~Off\Ofl--(t)iscalledoutflowboundaryattimet.FOrsimplicityinfiniteelementanalysis,supposethatboundaryOff--(t)isindependentoft.ThusforalltE(0,T]wecanwriteandproblem(1.0)can…