扩展有限元法及与其它数值方法的联系

对扩展有限元方法(XFEM)的发展及其与其他数值方法的联系进行了综述。该文主要包括以下内容:首先对无网格法的发展背景和历程进行了介绍,并从近似位移场构造的角度对众多的无网格法进行了比较分析;从单位分解理论的形式出发,阐述了XFEM的特点及其与传统有限元法、无网格方法的联系;归纳了关于XFEM的应用研究及其自身理论发展的主要研究方向,并对XFEM的发展进行了展望。     

The Effect of Steel Plates with Shear Studs for Weak Column–Strong Beam Connections in the Reinforced Concrete Structures under Earthquake Effect

Abstract: In this study, the effect of steel plates with shear studs used in the weak column–strong beam connections was investigated both experimentally and analytically. Five RC specimens were tested under cyclic loading in the experimental programme. Steel plates with shear studs in the column were used along the connection area. The specimens were derived from the exterior joint of a frame. As the main parameters, the width of shear stud heads and their spacing on the steel plates were changed to investigate their effects on the weak column. The test results confirmed that shear studs improved the strength and stiffness of the specimens. The control specimen collapsed because of joint failure, while the other four specimens collapsed because of bending at the bottom of the beam showing ductile behaviour. The comparison of experimental results with the analytical results obtained from ANSYS finite element programme showed similar outputs from the aspects of behaviour.     

Fracture mechanics analysis using the wavelet Galerkin method and extended finite element method

This paper presents fracture mechanics analysis using the wavelet Galerkin method and extended finite element method. The wavelet Galerkin method is a new methodology to solve partial differential equations where scaling/wavelet functions are used as basis functions. In solid/structural analyses, the analysis domain is divided into equally spaced structured cells and scaling functions are periodically placed throughout the domain. To improve accuracy, wavelet functions are superposed on the scaling functions within a region having a high stress concentration, such as near a hole or notch. Thus, the method can be considered a refinement technique in fixed‐grid approaches. However, because the basis functions are assumed to be continuous in applications of the wavelet Galerkin method, there are difficulties in treating displacement discontinuities across the crack surface. In the present research, we introduce enrichment functions in the wavelet Galerkin formulation to take into account the discontinuous displacements and high stress concentration around the crack tip by applying the concept of the extended finite element method. This paper presents the mathematical formulation and numerical implementation of the proposed technique. As numerical examples, stress intensity factor evaluations and crack propagation analyses for two‐dimensional cracks are presented. Copyright © 2012 John Wiley & Sons, Ltd.     

土坡中剪切带形成过程的数值模拟

为实现对土坡中剪切带扩展过程的模拟,该文将区域控制扩展分析方法嵌入改进的扩展有限元（XFEM）程序中构建了可追踪土中剪切带扩展过程的模拟系统,并利用此系统对两个土坡中剪切带形成过程的算例进行了模拟研究,验证了其合理性。结果表明,区域控制扩展分析方法可较好地描述剪切带尖端应力集中和重分布对剪切带扩展方向的影响,同时为土中剪切带扩展方向的判断提供了更合理的区域占优假定,从而使得基于区域控制扩展分析方法的XFEM程序能够合理地描述和追踪土坡中剪切带的扩展过程和路径。     

A combined space–time extended finite element method

The Newmark method for the numerical integration of second order equations has been extensively used and studied along the past fifty years for structural dynamics and various fields of mechanical engineering. Easy implementation and nice properties of this method and its derivatives for linear problems are appreciated but the main drawback is the treatment of discontinuities. Zienkiewicz proposed an approach using finite element concept in time, which allows a new look at the Newmark method. The idea of this paper is to propose, thanks to this approach, the use of a time partition of the unity method denoted Time Extended Finite Element Method (TX‐FEM) for improved numerical simulations of time discontinuities. An enriched basis of shape functions in time is used to capture with a good accuracy the non‐polynomial part of the solution. This formulation allows a suitable form of the time‐stepping formulae to study stability and energy conservation. The case of an enrichment with the Heaviside function is developed and can be seen as an alternative approach to time discontinuous Galerkin method (T‐DGM), stability and accuracy properties of which can be derived from those of the TX‐FEM. Then Space and Time X‐FEM (STX‐FEM) are combined to obtain a unified space–time discretization. This combined STX‐FEM appears to be a suitable technique for space–time discontinuous problems like dynamic crack propagation or other applications involving moving discontinuities. Copyright © 2005 John Wiley & Sons, Ltd.     

The perturbation method and the extended finite element method. An application to fracture mechanics problems

The extended finite element method has been successful in the numerical simulation of fracture mechanics problems. With this methodology, different to the conventional finite element method, discretization of the domain with a mesh adapted to the geometry of the discontinuity is not required. On the other hand, in traditional fracture mechanics all variables have been considered to be deterministic (uniquely defined by a given numerical value). However, the uncertainty associated with these variables (external loads, geometry and material properties, among others) it is well known. This paper presents a novel application of the perturbation method along with the extended finite element method to treat these uncertainties. The methodology has been implemented in a commercial software and results are compared with those obtained by means of a Monte Carlo simulation.