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姜磊 《数学的实践与认识》1989,(1)
本文给出高维欧氏空间中具有旋转对称性的所有的极小超曲面,它们是三维欧氏空间中悬链面的自然推广.但是,与古典的悬链面有很大不同之处是,每一个广义的悬链面都被夹在两个平行的超平面之间,并渐近于这两个平面. 相似文献
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给出针对一类可降阶高阶微分方程的一种教学设计.以趣味故事作为实例引入,得出悬链线所满足的一类高阶微分方程,找出通用的求解方法对其求解.使学生对求解方法印象深刻,并对微分方程的应用有一个初步的了解.在教学过程中,步步引导,全程既具有趣味性又具有启发性. 相似文献
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拋物线和悬链线是工程技术中常用的曲线(比如桥梁的拱轴线),这两种曲线的长度可用定积分求得,但计算较为复杂。本文根据工程技术的已知条件推导计算它们长度的近似公式。 (一)求抛物綫长度的近似公式图1所示为一拋物线,端点A及B关于O_y轴对称。已知f为拋物线拱高,L为拋物线拱跨径。由解析几何可知,拋物线方程为:x~2=2P_y。当x=L/2时, 相似文献
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Rail-bridge coupling element of unequal lengths for analysing train-track-bridge interaction systems
This paper presents a rail-bridge coupling element of unequal lengths, in which the length of a bridge element is longer than that of a rail element, to investigate the dynamic problem of train-track-bridge interaction systems. The equation of motion in matrix form is given for a train-track-bridge interaction system with the proposed element. The first two numerical examples with two types of bridge models are chosen to illustrate the application of the proposed element. The results show that, for the same length of rail element, (1) the dynamic responses of train, track and bridge obtained by the proposed element are almost identical to those obtained by the rail-bridge coupling element of equal length, and (2) compared with the rail-bridge coupling element of equal length, the proposed element can help to save computer time. Furthermore, the influence of the length of rail element on the dynamic responses of rail is significant. However, the influence of the length of rail element on the dynamic responses of bridge is insignificant. Therefore, the proposed element with a shorter rail element and a longer bridge element may be adopted to study the dynamic responses of a train-track-bridge interaction system. The last numerical example is to investigate the effects of two types of track models on the dynamic responses of vehicle, rail and bridge. The results show that: (1) there are differences of the dynamic responses of vehicle, rail and bridge based on the single-layer and double-layer track models, (2) the maximum differences increase with the increase of the mass of sleeper, (3) the double-layer track model is more accurate. 相似文献
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半导体器件瞬态模拟的对称正定混合元方法 总被引:3,自引:3,他引:0
提出具有对称正定特性的混合元格式求解非稳态半导体器件瞬态模拟问题。提出一个最小二乘混合元方法、一个新的具有分裂和对称正定性质的混合元格式和一个解经典混合元方程的对称正定失窃工格式求解电场位势和电场强度方程;提出一个最小二乘混合元格式求解关于电子与空穴浓度的非稳态对流扩散方程,浓度函数和流函数被同时求解;采用标准的有限元方法求解热传导方程。建立了误差分析理论。 相似文献
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Let $R$ be a ring with involution. It is well-known that an EP
element in $R$ is a core invertible element, but the question when a
core invertible element is an EP element, the authors answer in this
paper. Several new characterizations of star-core, normal and
Hermitian elements in $R$ are also presented. 相似文献
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非定常对流扩散问题的非协调局部投影有限元方法 总被引:1,自引:1,他引:0
本文将近年来基于协调有限元逼近提出的涡旋粘性法推广应用到非协调有限元逼近,对非定常的对流占优扩散问题,空间采用非协调Crouzeix-Raviart元逼近,时间用Crank-Nicolson差分离散格式,提出了Crank-Nicolson差分-局部投影法稳定化有限元格式,我们对稳定性和误差估计给出了详细的分析,得出了最... 相似文献
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Kıvanç Ersoy 《代数通讯》2013,41(12):4627-4638
An element of a group is called anticentral if the conjugacy class of that element is equal to the coset of the commutator subgroup containing that element. A group is called Camina group if every element outside the commutator subgroup is anticentral. In this paper, we investigate the structure of locally finite groups with an anticentral element. Moreover, we construct some non-periodic examples of Camina groups, which are not locally solvable. 相似文献
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A stabilized mixed formulation for finite strain deformation for low-order tetrahedral solid elements 总被引:1,自引:0,他引:1
A stabilized mixed finite element formulation for four-noded tetrahedral elements is introduced for robustly solving small and large deformation problems. The uniqueness of the formulation lies within the fact that it is general in that it can be applied to any type of material model without requiring specialized geometric or material parameters. To overcome the problem of volumetric locking, a mixed element formulation that utilizes linear displacement and pressure fields was implemented. The stabilization is provided by enhancing the rate of deformation tensor with a term derived using a bubble function approach. The element was implemented through a user-programmable element of the commercial finite element software ANSYS. Using the ANSYS platform, the performance of the element was evaluated by comparing the predicted results with those obtained using mixed quadratic tetrahedral elements and hexahedral elements with a B-bar formulation. Based on the quality of the results, the new element formulation shows significant potential for use in simulating complex engineering processes. 相似文献
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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. 相似文献
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A wavelet-based stochastic finite element method is presented for the bending analysis of thin plates. The wavelet scaling functions of spline wavelets are selected to construct the displacement interpolation functions of a rectangular thin plate element and the displacement shape functions are expressed by the spline wavelets. A new wavelet-based finite element formulation of thin plate bending is developed by using the virtual work principle. A wavelet-based stochastic finite element method that combines the proposed wavelet-based finite element method with Monte Carlo method is further formulated. With the aid of the wavelet-based stochastic finite element method, the present paper can deal with the problem of thin plate response variability resulting from the spatial variability of the material properties when it is subjected to static loads of uncertain nature. Numerical examples of thin plate bending have demonstrated that the proposed wavelet-based stochastic finite element method can achieve a high numerical accuracy and converges fast. 相似文献
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The approach of nonconforming finite element method admits users to solve the partial differential equations with lower complexity,but the accuracy is usually low.In this paper,we present a family of highaccuracy nonconforming finite element methods for fourth order problems in arbitrary dimensions.The finite element methods are given in a unified way with respect to the dimension.This is an effort to reveal the balance between the accuracy and the complexity of finite element methods. 相似文献