Quadrilateral isoparametric finite elements for plane elastic Cosserat bodies

4-node, 8-node and 8（4）-node quadrilateral plane isoparametric elements are used for the solution of boundary value problems in linear isotropic Cosserat elasticity. The patch test is applied to validate the finite elements. Engineering problems of stress concentration around a circular hole in plane strain condition and mechanical behaviors of heterogeneous materials with rigid inclusions and pores are computed to test the accuracy and capability of these three types of finite elements.

A second order isoparametric finite element method for elliptic interface problems

A second order isoparametric finite element method （IPFEM） is proposed for elliptic interface problems. It yields better accuracy than some existing second-order methods, when the coefficients or the flux across the immersed curved interface is discontinuous. Based on an initial Cartesian mesh, a mesh optimization strategy is presented by employing curved boundary elements at the interface, and an incomplete quadratic finite element space is constructed on the optimized mesh. It turns out that the number of curved boundary elements is far less than that of the straight one, and the total degree of freedom is almost the same as the uniform Cartesian mesh. Numerical examples with simple and complicated geometrical interfaces demonstrate the efficiency of the proposed method.

ISOPARAMETRIC HYPERSURFACES AND COMPLEX STRUCTURES

The main purpose of this note is to construct almost complex or complex structures on certain isoparametric hypersurfaces in unit spheres.As a consequence,complex structures on S^(1)×S^(7)×S^(6),and on S^(10)×S^(3)×S(2)with vanishing first Chern class,are built.

LOCKING-FREE DEGENERATED ISOPARAMETRIC SHELL ELEMENT

An 8-noded locking-free degenerated isoparametric shell element is presented. A revised interpolation for shear strain terms was constructed in natural co-ordinate system such that all necessary modes (translation, rotation and constant curvature) are preserved, which can be used to eliminate shear locking. A revised interpolation for membrane strains was produced in the local Cartesian co-ordinate system to overcome membrane locking behavior. The new 8-noded element has the proper rank, with the requisite number of zero eigenvalues each associated with a rigid mode. The element does not exhibit membrane or shear locking for large span-thickness ratio. The element does not form element mechanisms or extra spurious zero energy modes. Therefore, it can be used for both thin and thick shells.

Isoparametric Boundary Element Method Applied to the Rectangular and Delta Hydrofoils near the Free Surface

In this paper, the hydrodynamic characteristics and flow field around rectangular and delta hydrofoils, moving with a constant speed beneath the free surface are numerically studied by means of isoparametric boundary element method （IBEM）. The quantities （source and dipole strengths） and the geometry of the dements are represented by a linear distribution. Two types of three-dimensional hydrofoils （rectangular and delta） are selected with NACA4412 and symmetric Joukowski sections. Some numerical results of pressure distribution, lift, wave-making drag coefficients and velocity field around the hydrofoils are presented. Also, the wave pattern due to moving hydrofoil is predicted at different operational conditions. Comparisons are made between computational results obtained through this method and those from the experimental measurements and other numerical results which reveal good agreement.

Numerical Simulation of Mold Filling in Resin Transfer Molding Using Isoparametric Method

The mold filling of RTM was simulated based on the control volume finite element method (CV/FEM). The formulat ion using isoparametric transformation was discussed in detail and a computation al code based on isoparametric technique was developed. The simulation results w ere compared with experimental data. Different isoparametric elements, quadrilat eral and triangular, were compared in the simulation.It demonstrates that the us e of bilinear quadrilateral isoparametric elements in simulating the process can produce a higher precision and cost a less time than the use of triangular ones .

Isoparametric Surfaces in 3-dimensional De Sitter Space and Anti-de Sitter Space

A spacelike surface M in 3-dimensional de sitter space S13 or 3-dimensional anti-de Sitter space H13 is called isoparametric, if M has constant principal curvatures. A timelike surface is called isoparametric, if its minimal polynomial of the shape operator is constant. In this paper, we determine the spacelike isoparametric surfaces and the timelike isoparametric surfaces in S13 and H13.

THE IMPROVED ISOPARAMETRIC TRANSFORMATION IN BEM

The midside node sensitivity of eight-node isoparametric element in 3-D BEM is investigated. The paper points out that the suggestion, based upon which the midside nodes should be located in the middle third of distance between the adjacent corners, should be followed even more strictly for the conventional isoparametric transformation (CIT) in BEM as that in FEM. A new coordinate transformation relation has been put forward to solve the singular integral problem. The computation is carried to two cases: a cubic body subjected to tensile stress and pure bending. The numerical results show that the improved isoparametric transformation (IIT) is easier and more flexible to practice.

CLASSIFICATIONS OF DUPIN HYPERSURFACES IN LIE SPHERE GEOMETRY

This is a survey of local and global classification results concerning Dupin hypersurfaces in S^(n)(or R^(n))that have been obtained in the context of Lie sphere geometry.The emphasis is on results that relate Dupin hypersurfaces to isoparametric hypersurfaces in spheres.Along with these classification results,many important concepts from Lie sphere geometry,such as curvature spheres,Lie curvatures,and Legendre lifts of submanifolds of S^(n)(or R^(n)),are described in detail.The paper also contains several important constructions of Dupin hypersurfaces with certain special properties.

损伤开裂承压壳体泄漏率分析模型改进与验证

承压壳体发生放射性、易燃等危险气体泄漏会对环境造成重大威胁,泄漏状况评估是应急措施优化的必要前提。针对严重事故下的厚壳壁微开裂,建立了一套快速定量的泄漏率分析数值模型。基于流量守恒原理,提出了厚壁结构中多段微裂缝构成变截面通道的泄漏率计算改进模型;采用混凝土塑性损伤模型模拟极限载荷下结构的非线性破坏,通过等参函数实现几何不规则单元与规则空间之间的变换,改进了弥散型微裂缝扩展尺度的计算模型。通过数值算例对比文献中的结果,分别验证了以上两个子模型的稳定性和有效性,并由受损剪力墙的泄漏率分析进一步验证了模型的可行性。最后,将模型应用于抗高温内压损伤过程中的某预应力混凝土复杂承压壳体,结果表明:改进的模型适用于厚壁、带孔道等复杂构造承压结构的泄漏率分析,具有一定的实际工程意义。

On the Chern conjecture for isoparametric hypersurfaces

For a closed hypersurface Mn?Sn+1(1)with constant mean curvature and constant non-negative scalar curvature,we show that if tr(Ak)are constants for k=3,...,n-1 and the shape operator A,then M is isoparametric.The result generalizes the theorem of de Almeida and Brito(1990)for n=3 to any dimension n,strongly supporting the Chern conjecture.

Isoparametric Hypersurfaces Induced by Navigation in Lorentz Finsler Geometry

Using a navigation process with the datum(F,V),in which F is a Finsler metric and the smooth tangent vector field V satisfies F(−V(x))>1 everywhere,a Lorentz Finsler metric F˜can be induced.Isoparametric functions and isoparametric hypersurfaces with or without involving a smooth measure can be defined for F˜.When the vector field V in the navigation datum is homothetic,we prove the local correspondences between isoparametric functions and isoparametric hypersurfaces before and after this navigation process.Using these correspondences,we provide some examples of isoparametric functions and isoparametric hypersurfaces on a Funk space of Lorentz Randers type.

Topology and Curvature of Isoparametric Families in Spheres

An isoparametric family in the unit sphere consists of parallel isoparametric hypersurfaces and their two focal submanifolds.The present paper has two parts.The first part investigates topology of the isoparametric families,namely the homotopy,homeomorphism,or diffeomorphism types,parallelizability,as well as the Lusternik-Schnirelmann category.This part extends substantially the results of Wang(J Differ Geom 27:55-66,1988).The second part is concerned with their curvatures;more precisely,we determine when they have non-negative sectional curvatures or positive Ricci curvatures with the induced metric.

任意基础板的有限元分析

假定基础板对地基的作用为一连续分布荷载 ,采用 16节点退化实体等参元对基础板进行有限元分析。实体退化等参元不仅能够比较精确地描述基础板的平面形状 ,而且特别适合于变厚度基础板的有限元分析。Winkler地基上的板和弹性地基上的板的数值算例表明 ,本文方法适用于厚、薄基础板的分析 ,且具有精度高。

基于解析性质的等参有限元逆变换高效算法

由于等参元不存在逆变换的显式 ,所以在有限元分析的列式中都回避等参元逆变换 .但是在工程分析中 ,尤其在涉及两个物理场的耦合分析中 ,往往会遇到等参逆变换的需求 .文章从两种常见的四节点平面等参元和八节点空间等参元入手 ,通过分析等参变换的解析性质 ,提出了一种等参有限元逆变换的新算法 ,该算法具有简便、高效和高精度的特点 。

弹性地基板的等参有限元法计算

提出了弹性半空间地基板的四节点和八节点等参元计算方法。该方法适用于弹性地基上不同形状的薄板或厚板的计算。算例表明，本文方法适应性强、精度较高，用较少的单元就能获得较好的结果。

协调等参元与非协调元的对应性研究

本文据协调等参元位移模式转换式，提出了广义自由度的概念。并通过对广义自由度施加一定约束，证明了协调等参元与非协调元之间存在的对应性。从而阐明了非协调元内自由度的实质是广义自由度的退化；而非协调元是协调等参元的特列。

大型水轮发电机定子三维温度场的等参元计算

本文给出了直角坐标系下6面体8节点等参元和3棱柱单元的计算格式以及3种确定径向通风 沟表面散热系数公式。通过这两种不同有限单元和3种确定径向通风沟表面散热系数的方法 ， 计算了两台大型水轮发电机定子温度场。比较了采用这两种三维有限元方法计算所得到的结 果，并利用数值方法对影响定子温度场的相关因素进行了数值模拟。最后与实测结果进行了 对比，计算精度满足工程计算的要求。

一种基于等势场的胀形坯料反推新方法

为提高产品的质量、降低生产成本,需要合理地确定成形件的毛坯形状。而传统的方法不仅精度低,而且费时、费力,难以满足质量和效率的要求。基于已有的电模拟坯料展开方法,提出了一种新的关于胀形件的类等势场反推坯料展开方法。该方法基于能量最小原理和最小阻力原理,利用塑性变形过程中坯料的流动规律类似于静电场等势线所描述的结果这一特性,来反推胀形时的成形坯料。并将该方法应用于TC4合金板料的超塑性胀形工艺,计算了坯料的各项参数以及坯料内部的应变分布,并对应力及气压胀形力进行了简要的分析。最后将该方法计算结果与有限元计算结果相对照,结果表明,该方法避免了复杂的几何解析运算,提高了效率,结果可靠和方法可行。