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On group-theoretic computation of natural frequencies for spring–mass dynamic systems with rectilinear motion 直线运动弹簧-质量动力系统固有频率的群理论计算
Pub Date : 2007-04-20 DOI: 10.1002/CNM.1003
A. Zingoni
In this article, group theory is employed to simplify the computation of natural circular frequencies for spring–mass dynamic systems with rectilinear motion. The systems are by themselves not physically symmetric (or they exhibit only very weak symmetry properties), but they can be transformed into graphs that preserve all the connectivities between masses and springs, while featuring the maximum possible symmetry. For physical dynamic systems exhibiting symmetry, a well-known group-theoretic approach involves the computation of the full stiffness matrix of the system first, followed by transformation of this matrix in order to cast it into block-diagonal form. The present approach involves the direct assembly of much smaller stiffness matrices within the decomposed subspaces of the problem, and is therefore computationally more efficient. Of particular focus in this study are transformed configurations belonging to ‘triangular’ symmetry groups, whose symmetries are difficult to exploit using conventional methods. It is shown how the repeating eigenvalues associated with the degenerate subspaces of such symmetry groups can easily be obtained. Copyright © 2007 John Wiley & Sons, Ltd.
本文利用群理论简化了直线运动的弹簧-质量动力系统的固有圆频率的计算。这些系统本身不是物理对称的(或者它们只表现出非常弱的对称性),但它们可以转换成保留质量和弹簧之间所有连通性的图,同时具有最大可能的对称性。对于具有对称性的物理动力系统,众所周知的群论方法包括首先计算系统的全刚度矩阵,然后对该矩阵进行变换,以将其转换为块对角线形式。目前的方法涉及在问题的分解子空间内直接组装更小的刚度矩阵,因此计算效率更高。本研究特别关注的是属于“三角形”对称群的变换构型,其对称性很难用传统方法来利用。证明了如何容易地得到与这类对称群的简并子空间相关的重复特征值。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 33
Upper bound limit analysis using discontinuous quadratic displacement fields 不连续二次位移场的上限分析
Pub Date : 2007-03-27 DOI: 10.1002/CNM.998
A. Makrodimopoulos, C. Martin
The classical lower and upper bound theorems allow the exact limit load for a perfectly plastic structure to be bracketed in a rigorous manner. When the bound theorems are implemented numerically in combination with the finite element method, the ability to obtain tight bracketing depends not only on the efficient solution of the arising optimization problem, but also on the effectiveness of the elements employed. Elements for (strict) upper bound analysis pose a particular difficulty since the flow rule is required to hold throughout each element, yet it can only be enforced at a finite number of points. For over 30 years, the standard choice for this type of analysis has been the constant strain element combined with discontinuities in the displacement field. Here we show that, provided certain conditions are observed, conventional linear strain triangles and tetrahedra can also be used to obtain strict upper bounds for a general convex yield function, even when the displacement field is discontinuous. A specific formulation for the Mohr-Coulomb criterion in plane strain is given in terms of second-order cone programming, and example problems are solved using both continuous and discontinuous quadratic displacement fields.
经典的下界定理和上界定理允许以严格的方式将理想塑性结构的精确极限载荷括起来。当边界定理与有限元方法结合在数值上实现时,获得紧包络的能力不仅取决于所产生的优化问题的有效解,而且取决于所采用的单元的有效性。(严格)上界分析的元素带来了特别的困难,因为流规则需要贯穿每个元素,但它只能在有限数量的点上执行。30多年来,这类分析的标准选择一直是恒定应变单元结合位移场中的不连续面。本文证明,在一定条件下,即使位移场是不连续的,也可以使用传统的线性应变三角形和四面体来获得一般凸屈服函数的严格上界。用二阶锥规划给出了平面应变下的Mohr-Coulomb判据的具体表达式,并用连续和不连续二次位移场求解了算例问题。
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引用次数: 83
A simple error estimator for extended finite elements 扩展有限元的简单误差估计
Pub Date : 2007-03-26 DOI: 10.1002/CNM.1001
S. Bordas, M. Duflot, Phong Le
This short communication presents the idea of an a posteriori error estimate for enriched (extended) finite elements (XFEM). The enhanced strain field against which the XFEM strains are compared, is computed through extended moving least-squares smoothing constructed using the diffraction method to preserve the discontinuity. The error estimator is the L2 norm of the difference of the XFEM strain with the enhanced strain. We prove the concept of the proposed method on a 1D example with a singular solution and a 2D fracture mechanics example and conclude with some future work based on our paradigm.
这种简短的交流提出了富(扩展)有限元(XFEM)的后验误差估计的思想。利用衍射法构造的扩展移动最小二乘平滑来计算XFEM应变对比的增强应变场,以保持不连续性。误差估计量为XFEM应变与增强应变之差的L2范数。我们用一维奇异解实例和二维断裂力学实例证明了所提出方法的概念,并总结了基于我们的范式的一些未来工作。
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引用次数: 99
Topology and graph products; eigenproblems in optimal structural analysis 拓扑与图积;结构最优分析中的特征问题
Pub Date : 2007-03-14 DOI: 10.1002/CNM.1000
A. Kaveh, H. Rahami
In this paper, a topological method is presented to obtain the eigensolution of a cylindrical-shaped grid from those of a plane grid. Similarly, the eigenproperty of a torus-shaped grid is calculated from those of a cylindrical-shaped grid. These transformations are performed using an identification approach employed in topology for the formation of different surfaces. The proven theorems simplify the evaluation of the eigenvectors to be employed in the ordering and graph partitioning of regular structures for optimal analysis. Copyright © 2007 John Wiley & Sons, Ltd.
本文提出了一种由平面网格特征解得到圆柱网格特征解的拓扑方法。同样,环形网格的本征性质是由圆柱网格的本征性质计算出来的。这些转换是使用拓扑中用于形成不同表面的识别方法来执行的。所证明的定理简化了正则结构的排序和图划分中特征向量的求值。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 15
A new approach to avoid excessive numerical diffusion in Eulerian–Lagrangian methods 欧拉-拉格朗日方法中避免过多数值扩散的新方法
Pub Date : 2007-03-05 DOI: 10.1002/CNM.996
A. Younes, M. Fahs, P. Ackerer
Lumping is often used to avoid non-physical oscillations for advection–dispersion equations but is known to add numerical diffusion. A new approach is detailed in order to avoid excessive numerical diffusion in Eulerian–Lagrangian methods when several time steps are used. The basic idea of this approach is to keep the same characteristics during all time steps and to interpolate only the concentration variations due to the dispersion process. In this way, numerical diffusion due to the lumping is removed at the end of each time step. The method is combined with the Eulerian–Lagrangian localized adjoint method (ELLAM) which is a mass conservative characteristic method for solving the advection–dispersion equation. Two test problems are modelled to compare the proposed method to the consistent, the full and the selective lumping approaches for linear and non-linear transport equations. Copyright © 2007 John Wiley & Sons, Ltd.
集总通常用于避免平流-色散方程的非物理振荡,但已知会增加数值扩散。为了避免欧拉-拉格朗日方法在使用多个时间步长的情况下产生过多的数值扩散,提出了一种新的方法。这种方法的基本思想是在所有时间步长中保持相同的特性,并且只插值由于分散过程引起的浓度变化。通过这种方法,在每个时间步长结束时消除了由于集总引起的数值扩散。该方法与求解平流色散方程的质量保守特征方法欧拉-拉格朗日局部伴随法(ELLAM)相结合。通过模拟两个测试问题,将该方法与线性和非线性输运方程的一致集总、完全集总和选择性集总方法进行了比较。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 18
Note on the determination of the ignition point in forest fires propagation using a control algorithm 关于用控制算法确定森林火灾传播中着火点的注意事项
Pub Date : 2007-02-09 DOI: 10.1002/CNM.990
M. Bergmann, O. Séro-Guillaume, S. Ramezani
This paper is devoted to the determination of the origin point in forest fires propagation using a control algorithm. The forest fires propagation are mathematically modelled starting from a reaction diffusion model. A volume of fluid (V.O.F.) formulation is also used to determine the fraction of the area which is burnt. After having developed the objective functional and its derivative, results from an optimization process based on the simplex method is presented. It is shown that the ignition point and the final time of the fire propagation are precisely recovered, even for a realistic, non-horizontal, terrain
本文研究了用控制算法确定森林火灾传播的原点。从反应扩散模型出发,建立了森林火灾传播的数学模型。流体体积(vo.f.)公式也用于确定燃烧面积的比例。在建立了目标泛函及其导数之后,给出了基于单纯形法的优化过程的结果。结果表明,即使在真实的非水平地形下,也能精确地恢复火灾的着火点和最终传播时间
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引用次数: 3
An interpolation‐based local differential quadrature method to solve partial differential equations using irregularly distributed nodes 基于插值的局部微分正交法求解不规则分布节点的偏微分方程
Pub Date : 2007-01-12 DOI: 10.1002/CNM.978
Hang Ma, Q. Qin
To circumvent the constraint in application of the conventional differential quadrature (DQ) method that the solution domain has to be a regular region, an interpolation-based local differential quadrature (LDQ) method is proposed in this paper. Instead of using regular nodes placed on mesh lines in the DQ method (DQM), irregularly distributed nodes are employed in the LDQ method. That is, any spatial derivative at a nodal point is approximated by a linear weighted sum of the functional values of irregularly distributed nodes in the local physical domain. The feature of the new approach lies in the fact that the weighting coefficients are determined by the quadrature rule over the irregularly distributed local supporting nodes with the aid of nodal interpolation techniques developed in the paper. Because of this distinctive feature, the LDQ method can be consistently applied to linear and nonlinear problems and is really a mesh-free method without the limitation in the solution domain of the conventional DQM. The effectiveness and efficiency of the method are validated by two simple numerical examples by solving boundary-value problems of a linear and a nonlinear partial differential equation. Copyright © 2007 John Wiley & Sons, Ltd.
针对传统微分正交法在应用时解域必须是正则区域的限制,提出了一种基于插值的局部微分正交法。在DQ方法(DQM)中,不使用放置在网格线上的规则节点,而在LDQ方法中使用了不规则分布的节点。也就是说,节点上的任何空间导数都近似为局部物理域中不规则分布节点的功能值的线性加权和。该方法的特点是借助于本文提出的节点插值技术,通过对不规则分布的局部支撑节点的正交规则来确定权重系数。由于这种独特的特点,LDQ方法可以一致地应用于线性和非线性问题,并且是一种真正的无网格方法,而不受传统DQM在解域中的限制。通过求解线性和非线性偏微分方程的边值问题,验证了该方法的有效性和高效性。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 4
A simple way to introduce fibers into FEM models 将纤维引入有限元模型的一种简单方法
Pub Date : 2007-01-11 DOI: 10.1002/CNM.983
L. Vanalli, R. R. Paccola, H. B. Coda
This communication proposes a simple way to introduce fibers into finite element modelling. This is a promising formulation to deal with fiber-reinforced composites by the finite element method (FEM), as it allows the consideration of short or long fibers placed arbitrarily inside a continuum domain (matrix). The most important feature of the formulation is that no additional degree of freedom is introduced into the pre-existent finite element numerical system to consider any distribution of fiber inclusions. In other words, the size of the system of equations used to solve a non-reinforced medium is the same as the one used to solve the reinforced counterpart. Another important characteristic is the reduced work required by the user to introduce fibers, avoiding ‘rebar’ elements, node-by-node geometrical definitions or even complex mesh generation. An additional characteristic of the technique is the possibility of representing unbounded stresses at the end of fibers using a finite number of degrees of freedom. Further studies are required for non-linear applications in which localization may occur. Along the text the linear formulation is presented and the bounded connection between fibers and continuum is considered. Four examples are presented, including non-linear analysis, to validate and show the capabilities of the formulation. Copyright © 2007 John Wiley & Sons, Ltd.
本文提出了一种将纤维引入有限元建模的简单方法。这是一个很有前途的公式处理纤维增强复合材料的有限元方法(FEM),因为它允许考虑短或长纤维任意放置在一个连续域(矩阵)内。该公式最重要的特点是没有在先前存在的有限元数值系统中引入额外的自由度来考虑纤维夹杂物的任何分布。换句话说,用于求解非增强介质的方程组的大小与用于求解增强介质的方程组的大小相同。另一个重要的特点是减少了用户引入纤维所需的工作,避免了“螺纹钢”元素,节点逐节点的几何定义甚至复杂的网格生成。该技术的另一个特点是可以使用有限数量的自由度来表示纤维末端的无界应力。对于可能发生局部化的非线性应用,需要进一步的研究。本文提出了线性公式,并考虑了纤维与连续体之间的有界连接。给出了四个例子,包括非线性分析,以验证和展示该公式的能力。版权所有©2007 John Wiley & Sons, Ltd
{"title":"A simple way to introduce fibers into FEM models","authors":"L. Vanalli, R. R. Paccola, H. B. Coda","doi":"10.1002/CNM.983","DOIUrl":"https://doi.org/10.1002/CNM.983","url":null,"abstract":"This communication proposes a simple way to introduce fibers into finite element modelling. This is a promising formulation to deal with fiber-reinforced composites by the finite element method (FEM), as it allows the consideration of short or long fibers placed arbitrarily inside a continuum domain (matrix). The most important feature of the formulation is that no additional degree of freedom is introduced into the pre-existent finite element numerical system to consider any distribution of fiber inclusions. In other words, the size of the system of equations used to solve a non-reinforced medium is the same as the one used to solve the reinforced counterpart. Another important characteristic is the reduced work required by the user to introduce fibers, avoiding ‘rebar’ elements, node-by-node geometrical definitions or even complex mesh generation. An additional characteristic of the technique is the possibility of representing unbounded stresses at the end of fibers using a finite number of degrees of freedom. Further studies are required for non-linear applications in which localization may occur. Along the text the linear formulation is presented and the bounded connection between fibers and continuum is considered. Four examples are presented, including non-linear analysis, to validate and show the capabilities of the formulation. Copyright © 2007 John Wiley & Sons, Ltd.","PeriodicalId":51245,"journal":{"name":"Communications in Numerical Methods in Engineering","volume":"24 1","pages":"585-603"},"PeriodicalIF":0.0,"publicationDate":"2007-01-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1002/CNM.983","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51603670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 31
Comments on: Efficient placement of rigid supports using finite element models 评论:使用有限元模型有效地放置刚性支撑
Pub Date : 2007-01-01 DOI: 10.1002/cnm.898
M. Friswell
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引用次数: 1
Boundary-value recovery by the Trefftz approach in structural inverse problems 结构逆问题的Trefftz方法边值恢复
Pub Date : 2006-12-29 DOI: 10.1002/CNM.974
M. Karaś, A. Zieliński
The main idea of the Trefftz approach to numerical modelling consists in the application of trial functions identically fulfilling governing partial differential equations of a considered problem. When boundary conditions of the problem are defined a priori (direct formulation), they can be used to calculate the unknown solution coefficients. In structural inverse problems, the above conditions can be partly unknown (its shape is assumed to be unchanged). Instead, we can measure certain quantities inside the investigated structure and then approximately define the whole boundary-value problem. Usually, solutions of inverse problems are connected with minimization of certain functionals, which results in optimization procedures. This kind of formulation is presented in detail and illustrated by numerical examples. The properties of the Trefftz approach allow to formulate alternative, much more effective, simple direct algorithms, which considerably shorten the time of computer calculations. This is clearly shown in several computational benchmarks for 2D elastic inverse problems. The proposed algorithms can be applied to any inverse boundary-value problem, for which the complete T-function sets are known. Copyright © 2006 John Wiley & Sons, Ltd.
用Trefftz方法进行数值模拟的主要思想是应用试验函数来满足所考虑问题的控制偏微分方程。当问题的边界条件被先验地定义(直接公式)时,它们可以用来计算未知解系数。在结构逆问题中,上述条件可以是部分未知的(假设其形状不变)。相反,我们可以测量所研究结构内部的某些量,然后近似地定义整个边值问题。通常,反问题的解与某些函数的最小化有关,这导致了优化过程。文中详细介绍了这种公式,并用数值算例进行了说明。Trefftz方法的性质允许制定替代的,更有效的,简单的直接算法,这大大缩短了计算机计算的时间。这在二维弹性反问题的几个计算基准中清楚地显示出来。所提出的算法可以应用于任何已知完整t函数集的反边值问题。版权所有©2006约翰威利父子有限公司
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引用次数: 8
期刊
Communications in Numerical Methods in Engineering
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