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Parallel Delaunay triangulation for particle finite element methods 粒子有限元方法的平行Delaunay三角剖分
Pub Date : 2007-06-11 DOI: 10.1002/CNM.1007
Y. Fragakis, E. Oñate
Delaunay triangulation is a geometric problem that is relatively difficult to parallelize. Parallel algorithms are usually characterized by considerable interprocessor communication or important serialized parts. In this paper, we propose a method that achieves high speed-ups, but needs information regarding locally maximum element circumspheres prior to the beginning of the algorithm. Such information is directly available in iterative methods, like the particle finite element methods. The developed parallel Delaunay triangulation method, has minimum communication requirements, is quite simple and achieves high parallel efficiency. Copyright © 2007 John Wiley & Sons, Ltd.
德劳内三角剖分是一个比较难并行化的几何问题。并行算法通常具有相当大的处理器间通信或重要的序列化部分。在本文中,我们提出了一种实现高速加速的方法,但在算法开始之前需要有关局部最大元圆的信息。这些信息可以在迭代方法中直接获得,如粒子有限元方法。所开发的并行Delaunay三角剖分方法具有通信需求最小、结构简单、并行效率高的特点。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 3
On volumetric locking‐free behaviour of p‐version finite elements under finite deformations 有限变形下p型有限元的无体积锁紧特性
Pub Date : 2007-06-05 DOI: 10.1002/CNM.1008
U. Heisserer, S. Hartmann, A. Düster, Z. Yosibash
We demonstrate the locking-free properties of the displacement formulation of p-finite elements when applied to nearly incompressible Neo-Hookean material under finite deformations. For an axisymmetric model problem we provide semi-analytical solutions for a nearly incompressible Neo-Hookean material exploited to investigate the robustness of p-FEM with respect to volumetric locking. An analytical solution for the incompressible case is also derived to demonstrate the convergence of the compressible numerical solution towards the incompressible case when the compression modulus is increased.
我们证明了p-有限元位移公式在有限变形下几乎不可压缩的Neo-Hookean材料的无锁性。对于轴对称模型问题,我们提供了近乎不可压缩的Neo-Hookean材料的半解析解,用于研究p-FEM在体积锁定方面的鲁棒性。导出了不可压缩情况的解析解,证明了当压缩模量增大时,可压缩数值解向不可压缩情况收敛。
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引用次数: 2
Three-dimensional Mohr-Coulomb limit analysis using semidefinite programming 半定规划的三维莫尔库仑极限分析
Pub Date : 2007-06-05 DOI: 10.1002/CNM.1018
K. Krabbenhøft, A. Lyamin, S. Sloan
Recently, Krabbenhoft et al. (Int. J. Solids Struct. 2007; 44:1533–1549) have presented a formulation of the three-dimensional Mohr–Coulomb criterion in terms of positive-definite cones. The capabilities of this formulation when applied to large-scale three-dimensional problems of limit analysis are investigated. Following a brief discussion on a number of theoretical and algorithmic issues, three common, but traditionally difficult, geomechanics problems are solved and the performance of a common primal–dual interior-point algorithm (SeDuMi (Appl. Numer. Math. 1999; 29:301–315)) is documented in detail. Although generally encouraging, the results also reveal several difficulties which support the idea of constructing a conic programming algorithm specifically dedicated to plasticity problems. Copyright © 2007 John Wiley & Sons, Ltd.
最近,Krabbenhoft等人。J.固体结构。2007;(44:1533-1549)提出了一个正定锥的三维莫尔-库仑判据的公式。研究了该公式应用于大尺度三维极限分析问题时的能力。在对一些理论和算法问题进行了简短的讨论之后,解决了三个常见但传统上很困难的地质力学问题,并提出了一种常见的原对偶内点算法(SeDuMi)。号码。数学。1999;(29:301-315))有详细的记录。尽管总体上令人鼓舞,但结果也揭示了一些困难,这些困难支持构建专门用于塑性问题的二次规划算法的想法。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 127
Ibero-Latin American Conference on Computational Methods in Engineering CILAMCE 2005 伊比利亚-拉丁美洲工程计算方法会议
Pub Date : 2007-06-01 DOI: 10.1002/CNM.994
A. Valli, A. Coutinho
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引用次数: 0
A stabilized finite element model for the hydrothermodynamical simulation of the Rio de Janeiro coastal ocean 里约热内卢海岸海洋水热力学模拟的稳定有限元模型
Pub Date : 2007-06-01 DOI: 10.1002/CNM.935
C. Carbonel, A. Galeão
In this paper, a stabilized space-time Petrov-Galerkin finite element model of coastal ocean circulation is derived. Continuous linear interpolation in space and time is employed and a spatial unstructured mesh of triangular elements is used. To simulate the hydro-thermodynamical ocean behaviour a gravity reduced model is proposed. This model solves the motion and continuity hydrodynamic equations coupled with the advection-diffusion transport equation for temperature which governs the heat exchanges in the upper layer. The model is used to evaluate the main dynamical features of the coastal waters of the Rio de Janeiro State, namely: cold plumes, coastal jets and the influence of the warmer water bays. Numerical experiments are performed to highlight the typical observed events of coastal upwelling phenomena and their interaction with the existing coastal bays and the offshore conditions. Such experiments deal with a series of idealized northeast wind field forcing patterns, showing the solutions dependence on the horizontal structure of the wind fields in relation to the coastline configuration.
本文建立了沿海海洋环流的稳定时空Petrov-Galerkin有限元模型。在空间和时间上采用连续线性插值,并采用三角形单元的空间非结构化网格。为了模拟海洋的水热动力学行为,提出了一个重力简化模型。该模型求解了运动和连续流体动力学方程以及控制上层热交换的温度平流-扩散输运方程。该模式用于评价巴西里约热内卢州沿海水域的主要动力特征,即:冷羽流、沿海喷流和暖水湾的影响。通过数值实验,重点分析了海岸上升流现象的典型观测事件及其与现有海岸海湾和近海条件的相互作用。这些实验处理了一系列理想化的东北风场强迫模式,显示了与海岸线配置相关的风场水平结构的解依赖。
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引用次数: 7
Multiresolution analysis for finite element method using interpolating wavelet and lifting scheme 基于插值小波和提升方案的有限元多分辨率分析
Pub Date : 2007-05-24 DOI: 10.1002/CNM.1011
Yumin He, Xuefeng Chen, J. Xiang, Zhengjia He
Based on interpolating wavelet transform and lifting scheme, a multiresolution analysis for finite element method is developed. By designing appropriate finite element interpolation functions using interpolating wavelet and lifted interpolating wavelet on the interval, the finite element equation may be scale decoupled via eliminating all coupling in the stiffness matrix of element across scales, and then resolved in different spaces independently. The coarse solution can be obtained by solving the equation in the coarse approximation space, and refined by adding details, which can be obtained by solving the equations in the corresponding detail spaces, respectively. The method is well suited to the construction of adaptive algorithm and is powerful in analysing the field problems with changes in gradients and singularities. The numerical examples are given to verify the effectiveness of such a method. Copyright © 2007 John Wiley & Sons, Ltd.
基于插值小波变换和提升格式,提出了有限元法的多分辨率分析方法。通过在区间上采用插值小波和提升插值小波设计合适的有限元插值函数,消除单元跨尺度刚度矩阵中的所有耦合,实现有限元方程的尺度解耦,在不同空间内独立求解。通过在粗近似空间中求解方程得到粗解,通过添加细节进行细化,分别在相应的细节空间中求解方程得到粗解。该方法适用于自适应算法的构造,对于分析具有梯度和奇异性变化的野外问题具有较强的实用价值。数值算例验证了该方法的有效性。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 7
Modelling unsaturated flow by using Mathematica 利用Mathematica模拟非饱和流动
Pub Date : 2007-05-15 DOI: 10.1002/CNM.1005
M. Mikhailov
The built-in Mathematica function NDSolve is extended to solve nonlinear boundary-value problems and a second-order partial differential equation subjected to inconsistent boundary and initial conditions. This communication demonstrates the ability of the extended NDSolve to find steady-state and transient solutions of unsaturated flow described by the one-dimensional Richards equation. Only first kind boundary conditions are considered, but the extended NDSolve is applicable for first, second, and third kind boundary conditions. To verify the steady-state numerical results, an original analytical solution is derived. The results given by numerical and analytical steady-state solutions coincide. The residuum of transient solution is plotted to show that the numerical results satisfy the transient problem except in a singular point, where the boundary and initial conditions are inconsistent. The transient pressure head and soil moisture content are plotted for typical soil properties, starting from different initial steady-state distribution up to the time needed to reach the final steady-state distribution. Copyright © 2007 John Wiley & Sons, Ltd.
扩展了内置的Mathematica函数NDSolve,用于求解非线性边值问题和边界和初始条件不一致的二阶偏微分方程。该通信证明了扩展NDSolve找到一维Richards方程所描述的非饱和流动的稳态和瞬态解的能力。本文只考虑第一类边界条件,扩展NDSolve适用于第一类、第二类和第三类边界条件。为了验证稳态数值结果,导出了一个原始的解析解。数值解和解析解的结果是一致的。绘制了瞬态解的残差,表明数值结果除边界和初始条件不一致的奇点外,均满足瞬态问题。从不同的初始稳态分布开始,直到达到最终稳态分布所需的时间,绘制了典型土壤性质的瞬态压头和土壤含水量。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 2
A Chebyshev expansion method for solving the time‐dependent partial differential equations 求解时变偏微分方程的切比雪夫展开法
Pub Date : 2007-05-15 DOI: 10.1002/CNM.1010
E. Elbarbary
A Chebyshev expansion method for the parabolic and Burgers equations is developed. The spatial derivatives are approximated by the Chebyshev polynomials and the time derivative is treated by a finite-difference scheme. The accuracy of the resultant is modified by using suitable extrapolation scheme in the time direction. The Chebyshev expansion method is based on using an explicit formula for the Chebyshev polynomials in terms of arbitrary order of their derivatives. In addition, this formula is used in equating the order of derivatives appearing in the differential equation to the order of differential equation. The successive integration is used to obtain an algebraic system in the expansion coefficients. Finally, numerical examples are studied to demonstrate the viability of this method. Copyright © 2007 John Wiley & Sons, Ltd.
提出了求解抛物型方程和Burgers方程的Chebyshev展开方法。空间导数用切比雪夫多项式逼近,时间导数用有限差分格式处理。在时间方向上采用合适的外推方案,提高了结果的精度。切比雪夫展开法是基于对其任意阶导数的切比雪夫多项式使用显式公式。此外,这个公式还用于将微分方程中出现的导数的阶数等同于微分方程的阶数。采用逐次积分的方法,得到了展开式系数的代数系统。最后,通过数值算例验证了该方法的可行性。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 0
Numerical study of hemodynamics comparison between small and large femoral bypass grafts 小股与大股旁路血流动力学比较的数值研究
Pub Date : 2007-05-15 DOI: 10.1002/CNM.1012
A. Qiao, Youjun Liu
The geometry factors have prominent impacts on the flow patterns of bypass graft. In order to clarify the influence of graft diameter on the hemodynamics of femoral bypass graft, the pulsatile blood flows in three bypassing models with different graft diameters were simulated with finite-element method. The temporal–spatial distributions of flow patterns, pressure drops, and wall shear stresses were depicted and compared. The results indicated that femoral artery bypassed with a large graft demonstrates relatively better and more profitable hemodynamic phenomena with large longitudinal velocity, uniform wall shear stress, and small wall shear stress gradient. The large model may be effective in decreasing the probability of the initiation and development of postoperative intimal hyperplasia and restenosis. Copyright © 2007 John Wiley & Sons, Ltd.
几何因素对搭桥桥的流动形态有显著影响。为了阐明移植物直径对股动脉搭桥血流动力学的影响,采用有限元方法模拟了3种不同移植物直径的搭桥模型的脉动血流。描述并比较了流态、压降和壁面剪应力的时空分布。结果表明,大移植物旁路股动脉具有纵流速大、壁剪应力均匀、壁剪应力梯度小等较好、较有利的血流动力学现象。大模型可能有效降低术后内膜增生和再狭窄发生和发展的可能性。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 10
Finite-element model for creep buckling analysis of beam-type structures 梁型结构蠕变屈曲分析的有限元模型
Pub Date : 2007-05-02 DOI: 10.1002/CNM.1004
D. Lanc, G. Turkalj, J. Brnić
This paper presents a one-dimensional finite element for creep buckling analysis of structures comprised of straight and prismatic beam members. Spatial displacements and rotations are allowed to be large while strains are assumed to be small. Material is assumed to be homogenous and isotropic. The corresponding equilibrium equations are formulated in the framework of co-rotational description, using the virtual work principle. In contrast to conventional co-rotational formulation, which is linear on element level and unable to model Wagner effect, in this paper an additional nonlinear part of stiffness matrix is evaluated and added to standard elastic stiffness. Implementation of developed numerical algorithm is demonstrated through few test problems.
本文提出了一种用于直梁和棱柱梁结构蠕变屈曲分析的一维有限元方法。空间位移和旋转允许很大,而应变假设很小。假定材料是均匀的和各向同性的。利用虚功原理,在共旋转描述的框架下,建立了相应的平衡方程。传统的共旋转公式在单元水平上是线性的,无法模拟瓦格纳效应,与之相反,本文评估了刚度矩阵的额外非线性部分,并将其添加到标准弹性刚度中。通过几个测试问题证明了所开发的数值算法的实现。
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引用次数: 6
期刊
Communications in Numerical Methods in Engineering
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