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Computation of the J‐integral for large strains 大应变J积分的计算
Pub Date : 2007-11-09 DOI: 10.1002/CNM.1069
Á. Horváth
The phenomenon of failure by catastrophic crack propagation in structural materials poses problems of design and analysis in many fields of engineering. Cracks are present to some degree in all structures. They may exist as basic defects in the constituent materials or they may be induced in construction or during service life. Using the finite element method, a lot of papers deal with the calculation of stress intensity factors for two- and three-dimensional geometries containing cracks of different shapes under various loadings to elastic bodies. In order to increase the accuracy of the results, special elements have been used. They are described together with methods for calculating the stress intensity factors from the computed results. At the vicinity of a crack tip, the strains are not always small, but they may also be large. In this case, the J-integral can also be applied to characterize the cracks in elastic or elastic–plastic bodies. This paper describes the computation of the two-dimensional J-integral for large strains to elastic and elastic–plastic bodies and represents some numerical examples. Copyright © 2007 John Wiley & Sons, Ltd.
结构材料的突变裂纹扩展破坏现象在许多工程领域提出了设计和分析问题。所有的结构都有不同程度的裂缝。它们可能作为组成材料的基本缺陷存在,也可能在施工或使用寿命期间产生。许多论文用有限元法计算了含不同形状裂纹的二维和三维几何弹性体在各种载荷作用下的应力强度因子。为了提高结果的准确性,采用了特殊的元素。并叙述了它们以及根据计算结果计算应力强度因子的方法。在裂纹尖端附近,应变并不总是很小,但也可能很大。在这种情况下,j积分也可以用来表征弹性体或弹塑性体的裂纹。本文介绍了弹性体和弹塑性体大应变时二维j积分的计算方法,并给出了一些数值算例。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 1
A fast method for numerical simulation of casting solidification 一种快速铸造凝固数值模拟方法
Pub Date : 2007-10-29 DOI: 10.1002/CNM.1062
R. Tavakoli, P. Davami
An efficient numerical method for simulation of casting solidification is presented. The presented method is based on a stable explicit finite difference solution of the heat equation in conjunction with the temperature recovery method to incorporate latent heat effect. The computational cost of the presented method is approximately the same as an explicit method (per time step), while it is free from the time step limitation due to the stability criterion. A simple domain decomposition method is included to improve the computational performance of the presented method. The efficiency, stability and accuracy of the presented method are supported with illustrative examples. Copyright © 2007 John Wiley & Sons, Ltd.
提出了一种有效的铸件凝固过程数值模拟方法。该方法基于热方程的稳定显式有限差分解,并结合考虑潜热效应的温度恢复方法。该方法的计算量与显式方法的计算量(每时间步长)大致相同,但由于稳定性判据的存在,该方法不受时间步长的限制。为了提高该方法的计算性能,引入了一种简单的区域分解方法。通过算例验证了该方法的有效性、稳定性和准确性。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 14
Boundary contour method fracture analysis of bimaterial interface cracks 双材料界面裂纹的边界轮廓法断裂分析
Pub Date : 2007-10-11 DOI: 10.1002/CNM.1060
A. Phan, S. Mukherjee
A variant of the boundary element method, called the boundary contour method (BCM), offers a further reduction in dimensionality. Consequently, boundary contour analysis of two-dimensional (2-D) problems does not require any numerical integration at all. The method is thus very computationally effective and accurate as shown in previous related studies. This paper presents a further development of the BCM for multi-region problems in 2-D elasticity, and an application of this development, coupled with the displacement correlation technique, to evaluating the stress intensity factors K1 and K2 for bimaterial interface cracks. Some preliminary tests conducted within this work suggest that the proposed technique is robust and able to provide highly accurate results of both K1 and K2 for this challenging class of fracture problems. Copyright © 2007 John Wiley & Sons, Ltd.
边界元法的一种变体,称为边界轮廓法(BCM),进一步降低了维数。因此,二维(2-D)问题的边界轮廓分析不需要任何数值积分。因此,在以往的相关研究中表明,该方法具有很高的计算效率和准确性。本文介绍了二维弹性多区域问题的BCM的进一步发展,并结合位移相关技术,应用于双材料界面裂纹的应力强度因子K1和K2的评估。在这项工作中进行的一些初步测试表明,所提出的技术是可靠的,能够为这类具有挑战性的压裂问题提供高度精确的K1和K2结果。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 2
Advantages of a semi-analytical approach for the analysis of an evolving structure with contacts 半解析法分析带接触的演化结构的优点
Pub Date : 2007-10-08 DOI: 10.1002/CNM.1059
V. Denoël
This paper presents a semi-analytical approach for the evolution analysis of a beam into given boundaries. The analytical description of contact locations, contact forces and beam deflections results in an exact modelling of the phenomenon (no penetration allowed). Despite the apparent complexity of the problem, the analytical relations leading to two-point boundary and integro-restrained differential equations are formally written. An iterative resolution of these equations is adopted by converting the problem into a single-point boundary value one. Due to a proper selection of the global unknowns, namely the contact forces and their locations, the proposed method is particularly efficient in the context of evolving structures. The resolution is illustrated on a simple example, and comparisons with the finite element method are given as persuasive arguments. Copyright © 2007 John Wiley & Sons, Ltd.
本文提出了一种半解析方法,用于梁在给定边界内的演化分析。对接触位置、接触力和光束挠度的分析描述可以精确地模拟这种现象(不允许穿透)。尽管问题看起来很复杂,但两点边界和积分约束微分方程的解析关系被形式化地写了出来。将问题转化为单点边值问题,采用迭代法求解。由于正确选择了全局未知量,即接触力及其位置,所提出的方法在不断变化的结构中特别有效。通过一个简单的实例说明了该方法的解法,并与有限元法进行了比较,作为有说服力的论据。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 17
On the 'most normal' normal 关于“最正常”的正常
Pub Date : 2007-10-03 DOI: 10.1002/CNM.1056
R. Aubry, R. Löhner
Given a set of normals in ℛ3, two algorithms are presented to compute the ‘most normal’ normal. The ‘most normal’ normal is the normal that minimizes the maximal angle with the given set of normals. A direct application is provided supposing a surface triangulation is available. The set of normals may represent either the face normals of the faces surrounding a point or the point normals of the points surrounding a point. The first algorithm is iterative and straightforward, and is inspired by the one proposed by Pirzadeh (AIAA Paper 94-0417, 1994). The second gives more insight into the complete problem as it provides the unique solution explicitly. It would correspond to the general extension of the algorithm presented by Kallinderis (AIAA-92-2721, 1992). Copyright © 2007 John Wiley & Sons, Ltd.
给定一组法线,给出两种算法来计算“最正规”的法线。“最法线”法线是与给定法线集合的最大角度最小的法线。假设曲面三角测量是可用的,提供了一种直接应用。法线集合可以表示围绕一个点的面的法线,也可以表示围绕一个点的点的点法线。第一个算法是迭代和直接的,灵感来自于Pirzadeh (AIAA Paper 94-0417, 1994)提出的算法。第二种方法可以更深入地了解完整的问题,因为它明确地提供了唯一的解决方案。它将对应于Kallinderis (aiaa -92- 2721,1992)提出的算法的一般扩展。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 31
Parabolic recovery of boundary gradients 边界梯度的抛物线恢复
Pub Date : 2007-09-28 DOI: 10.1002/CNM.1054
R. Löhner, J. Cebral, Sunil Appanaboyina
A parabolic recovery procedure suited for shear stress and heat flux recovery on surfaces from linear element data is proposed. The information required consists of the usual unknowns at points, as well as gradients recovered at the points that are one layer away from the wall. The procedure has been in use for some time and has consistently delivered superior results as compared with the usual wall shear stress and heat flux obtained from linear finite element method shape functions. Copyright © 2007 John Wiley & Sons, Ltd.
提出了一种适用于从线性元数据中恢复表面剪应力和热流的抛物线恢复方法。所需的信息包括点上通常的未知数,以及在距离墙一层的点上恢复的梯度。该方法已经使用了一段时间,并且与线性有限元法形状函数获得的通常的壁面剪切应力和热流密度相比,始终提供了更好的结果。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 14
A numerical approach for efficient and accurate modeling of spot-welding connection in automotive crash analysis 汽车碰撞分析中点焊连接高效准确建模的数值方法
Pub Date : 2007-09-28 DOI: 10.1002/CNM.1058
He Wen, Zhang Weigang, Zhong Zhi-hua
Modeling of spot-welding connection is very important in automotive crash analysis, as spot welding is the main approach to assemble the automobile body from hundreds of press-formed components. Although alternative methods are available for modeling the spot welding, new methods are desirable for better efficiency and accuracy. In this paper, a new approach is proposed for the modeling in an explicit analysis environment. Virtual welding nodes are introduced and constructed from actual nodes of the associated finite element. Given constraints are then imposed on the welding nodes using the Lagrange approach. Good accuracy may be obtained while compatibility with the explicit approach is achieved and numerical stability is unaffected for general mesh layout. The approach is implemented in an explicit code and validated with numerical examples. Copyright © 2007 John Wiley & Sons, Ltd.
汽车碰撞分析中,点焊连接的建模是非常重要的,因为点焊是由数百个冲压成形零件组装车身的主要方式。虽然现有的点焊建模方法可供选择,但为了提高效率和精度,需要新的方法。本文提出了一种新的显式分析环境下的建模方法。引入了虚拟焊接节点,并以关联有限元的实际节点为基础构建虚拟焊接节点。然后使用拉格朗日方法对焊接节点施加给定的约束。在与显式方法兼容的同时,可以获得较好的精度,并且对一般网格布局不影响数值稳定性。该方法在显式代码中实现,并通过数值算例进行了验证。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 0
An integrated parameter identification method combined with sensor placement design 结合传感器布置设计的综合参数辨识方法
Pub Date : 2007-09-19 DOI: 10.1002/CNM.1052
Yiqian Li, Z. Xiang, M. Zhou, Z. Cen
Material parameter identification based on in situ measurements plays a very important role in engineering. Since noises are inevitable in measurements and the parameter identification is inherently ill posed, it is necessary to consider some methods to stabilize the identification procedure. One choice is properly designing the sensor placement, which has attracted much attention over the past 30 years. Most existing sensor placement design methods are based on certain sensitivity analysis, which commonly requires evaluating Jacobian matrix for given parameters. However, the ‘true’ values of parameters are unknown at that moment, because sensor placement design is carried out before the parameter identification. Consequently, roughly estimated ‘true’ parameters have to be used and less optimal sensor placement could be obtained. To solve this problem, this paper presents an integrated method in which the parameter identification and sensor placement design are carried out alternatively. The validity of the proposed method is illustrated by two simple academic examples. Then it is implemented to detect damages in a real highway bridge. Copyright © 2007 John Wiley & Sons, Ltd.
基于现场测量的材料参数识别在工程中具有十分重要的意义。由于测量过程中不可避免地存在噪声,且参数辨识本身就存在病态,因此有必要考虑一些方法来稳定辨识过程。一种选择是合理设计传感器的位置,这在过去的30年里引起了人们的广泛关注。现有的传感器布局设计方法大多基于一定的灵敏度分析,通常需要对给定参数求雅可比矩阵。然而,此时参数的“真实”值是未知的,因为传感器放置设计是在参数识别之前进行的。因此,必须使用粗略估计的“真实”参数,并且可以获得较少的最优传感器放置。为了解决这一问题,本文提出了一种参数辨识与传感器放置设计交替进行的集成方法。通过两个简单的理论算例说明了该方法的有效性。并将其应用于实际公路桥梁的损伤检测中。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 11
High dimensional model representation for piece‐wise continuous function approximation 分段连续函数近似的高维模型表示
Pub Date : 2007-09-19 DOI: 10.1002/CNM.1053
R. Chowdhury, B. N. Rao, A. M. Prasad
High dimensional model representation (HDMR) approximates multivariate functions in such a way that the component functions of the approximation are ordered starting from a constant and gradually approaching to multivariance as we proceed along the terms like first-order, second-order and so on. Until now HDMR applications include construction of a computational model directly from laboratory/field data, creating an efficient fully equivalent operational model to replace an existing time-consuming mathematical model, identification of key model variables, global uncertainty assessments, efficient quantitative risk assessments, etc. In this paper, the potential of HDMR for tackling univariate and multivariate piece-wise continuous functions is explored. Eight numerical examples are presented to illustrate the performance of HDMR for approximating a univariate or a multivariate piece-wise continuous function with an equivalent continuous function. Copyright © 2007 John Wiley & Sons, Ltd.
高维模型表示(HDMR)以这样一种方式逼近多元函数,即近似值的分量函数从常数开始排序,随着我们继续进行一阶,二阶等项,逐渐接近多方差。到目前为止,HDMR的应用包括直接从实验室/现场数据构建计算模型,创建高效的全等效操作模型以取代现有耗时的数学模型,识别关键模型变量,全局不确定性评估,高效的定量风险评估等。本文探讨了HDMR在处理单变量和多变量分段连续函数方面的潜力。给出了八个数值例子来说明HDMR用等价连续函数逼近单变量或多变量分段连续函数的性能。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 54
Charge distribution on narrow MEMS beams of nearly square cross-section 近方截面窄MEMS光束上的电荷分布
Pub Date : 2007-06-25 DOI: 10.1002/CNM.1021
Hui Chen, S. Mukherjee
The subject of this paper is the calculation of charge distribution on the surfaces of thin conducting microelectromechanical systems beams, of nearly square cross-section, in electrostatic problems, by the boundary element method (BEM). A line model of a beam is proposed here. This model overcomes the problem of dealing with nearly singular matrices that occur when the standard BEM is applied to very thin features (objects or gaps). This new approach is also very efficient. Numerical results are presented for selected examples. Copyright © 2007 John Wiley & Sons, Ltd.
本文的主题是用边界元法计算静电问题中近方截面薄导电微机电系统光束表面的电荷分布。本文提出了一种梁的直线模型。该模型克服了在标准边界元应用于非常薄的特征(对象或间隙)时处理近乎奇异矩阵的问题。这种新方法也非常有效。对选定的算例给出了数值计算结果。版权所有©2007 John Wiley & Sons, Ltd
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引用次数: 4
期刊
Communications in Numerical Methods in Engineering
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