余能积分提取法计算应力强度因子

本文利用最小余能原理导出了一种计算应力强度因子的积分提取法，本方法的特点是只要已知位移场就可切口尖端附近的任意围线区域内进行应力强度因子的积分提取，对不同的问题及对任意张切口和任意多材料问题具通用性，文中给出基于有限元线法（ＦｉｎｉｔｅＥｌｅｍｅｎｔＭｅｔｈｏｄｏｆＬｎｅ，简称ＦＥＭＯＬ）求解的单材料和双材料反平面切口问题及平面切口问题初步实施方案，给出了数值算例表明，本法原理简单，行之有效，为计     

求解双材料界面裂纹应力强度因子的扩展有限元法

基于双材料界面裂纹尖端的基本解,构造扩展有限元法(eXtended Finite Element Methods, XFEM)裂尖单元结点的改进函数。有限元网格剖分不遵从材料界面,考虑3种类型的结点改进函数：弱不连续改进函数、Heaviside改进函数和裂尖改进函数,建立XFEM的位移模式,给出计算双材料界面裂纹应力强度因子(Stress Intensity Factors, SIFs)的相互作用积分方法。数值结果表明：XFEM无需遵从材料界面剖分网格,该文的方法能够准确评价双材料界面裂纹尖端的SIFs。     

压电材料中孔边径向裂纹的动应力强度因子

采用Green函数法研究含圆孔边界径向有限长度裂纹的无限压电材料对SH波的散射和裂纹尖端动应力强度因子问题。首先构造出具有半圆型凹陷半无限压电介质的弹性位移Green函数和电场Green函数,然后采用裂纹切割方法构造孔边裂纹,并根据契合思想和界面上的连接条件建立起求解问题的定解积分方程组。得到孔边动应力强度因子的解析表达式。最后作为算例,给出了裂纹尖端动应力强度因子的计算结果图并进行了讨论。部分计算结果与相应的弹性材料进行了比较。     

含裂纹压电材料的Cell-Based光滑扩展有限元法

为精确而有效地求解机电耦合作用下含裂纹压电材料的断裂参数,首先,通过将复势函数法、扩展有限元法和光滑梯度技术引入到含裂纹压电材料的断裂机理问题中,提出了含裂纹压电材料的Cell-Based光滑扩展有限元法;然后,对含中心裂纹的压电材料强度因子进行了模拟,并将模拟结果与扩展有限元法和有限元法的计算结果进行了对比。数值算例结果表明:Cell-Based光滑扩展有限元法兼具扩展有限元法和光滑有限元法的特点,不仅单元网格与裂纹面相互独立,且裂尖处单元不需精密划分,与此同时,Cell-Based光滑扩展有限元法还具有形函数简单且不需求导、对网格质量要求低且求解精度高等优点。所得结论表明Cell-Based光滑扩展有限元法是压电材料断裂分析的有效数值方法。      

Cymbal压电发电换能器有限元分析

通过建立Cymbal压电发电换能器的机电耦合有限元分析模型,计算分析了换能器结构参数对输出电压和谐振频率的影响以及外接负载对Cymbal换能器输出电压和输出功率的影响。研究表明,为了降低换能器的工作频率和提高换能器的输出电压,应增大换能器的空腔底部直径和减小换能器的空腔高度;在选择金属端冒和压电陶瓷厚度等参数时,应综合考虑换能器系统的刚度和外界振动源的频率特性和加速度特性;在任意一个频率点上,Cymbal换能器均存在一个最佳的外接负载,使得换能器的输出功率最大,而这个最佳的负载阻抗就等于Cymbal换能器在这个工作频率点上的输出阻抗。文中还提出并分析了基于外加预应力的多振子级联方式Cymbal压电发电换能器系统的结构。     

压电材料渗透型反平面界面裂纹的奇异因子

本文用复变函数解析延展原理,研究了集中载荷作用下的不同压电材料反平面应变 状态的电渗透型界面裂纹的耦合场:对单个裂纹,给出了封闭形式的复函数解和场强度因子。 结果表明,在裂尖处耦合场有(1/2)阶的奇异性。     

梯度复合材料应力强度因子计算的梯度扩展单元法

推导了一种适用于梯度复合材料断裂特性分析的梯度扩展单元,采用细观力学方法描述材料变化的物理属性,通过线性插值位移场给出了4节点梯度扩展元随空间位置变化的刚度矩阵,并建立了结构的连续梯度有限元模型.通过将梯度单元的计算结果与均匀单元以及已有文献结果进行对比,证明了梯度扩展有限元(XFEM)的优越性,并进一步讨论了材料参数对裂纹尖端应力强度因子(SIF)的影响规律.研究结果表明:随着网格密度的增加,梯度单元的计算结果能够迅速收敛于准确解,均匀单元的计算误差不会随着网格细化而消失,且随着裂纹长度和属性梯度的增大而增大;属性梯度和涂层基体厚度比的增大导致涂覆型梯度材料的SIF增大;裂纹长度的增加和连接层基体厚度比的减小均导致连接型梯度材料的SIF增大.     

梯度复合材料应力强度因子计算的梯度扩展单元法

推导了一种适用于梯度复合材料断裂特性分析的梯度扩展单元, 采用细观力学方法描述材料变化的物理属性, 通过线性插值位移场给出了4节点梯度扩展元随空间位置变化的刚度矩阵, 并建立了结构的连续梯度有限元模型。通过将梯度单元的计算结果与均匀单元以及已有文献结果进行对比, 证明了梯度扩展有限元(XFEM)的优越性, 并进一步讨论了材料参数对裂纹尖端应力强度因子(SIF)的影响规律。研究结果表明: 随着网格密度的增加, 梯度单元的计算结果能够迅速收敛于准确解, 均匀单元的计算误差不会随着网格细化而消失, 且随着裂纹长度和属性梯度的增大而增大; 属性梯度和涂层基体厚度比的增大导致涂覆型梯度材料的SIF增大; 裂纹长度的增加和连接层基体厚度比的减小均导致连接型梯度材料的SIF增大。     

基于有限单元法对动态应力强度因子进行数值计算的研究*

运用ANSYS 商用有限元软件,采用非奇异单元和Newmark 积分算法,通过最小二乘法拟合,准确的获得了多个模型动态应力强度因子的解。所使用的方法适用范围广,这对于运用线弹性断裂动力学解决工程中的实际问题是有益的和必要的。     

扩展有限元法在裂纹扩展问题中的应用

扩展有限元法(Extended finite element method,XFEM)是近几年发展起来的数值方法,属于传统有限元法的扩展,具有区别于传统有限元法的优点,在求解不连续断裂问题上具有更高的精度及效率。本文针对影响裂纹扩展的主要因素进行探讨,继而介绍扩展有限元的基本原理,并对其在裂纹扩展中的应用进行综述,同时对该方法的下一步研究进行了展望。     

3D J‐integral evaluation using the computation of line and surface integrals

In the analysis of fracture mechanics of structures using three‐dimensional (3D) J‐integral, an integral evaluation of line and surface is required. However, because surface integral evaluation requires the calculation of the second derivative of displacement field and commercial finite element codes cannot calculate it, then this portion of the integral is neglected in some research. In this paper, a method for computing 3D J‐integral is presented using finite element analysis. In the analysis, the second derivative evaluation of displacement field is employed. The method is implemented in calculating the J‐integral of some 3D cracks and results are compared to well‐known reference values. The results show that the method is reliable and is suitable for applications in engineering. The portion of 3D J‐integral, namely the surface integral value is investigated and it is shown that neglecting this portion can introduce considerable error in the final results.     

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.     

Robust and direct evaluation of J2 in linear elastic fracture mechanics with the X‐FEM

The aim of the present paper is to study the accuracy and the robustness of the evaluation of J_k‐integrals in linear elastic fracture mechanics using the extended finite element method (X‐FEM) approach. X‐FEM is a numerical method based on the partition of unity framework that allows the representation of discontinuity surfaces such as cracks, material inclusions or holes without meshing them explicitly. The main focus in this contribution is to compare various approaches for the numerical evaluation of the J₂‐integral. These approaches have been proposed in the context of both classical and enriched finite elements. However, their convergence and the robustness have not yet been studied, which are the goals of this contribution. It is shown that the approaches that were used previously within the enriched finite element context do not converge numerically and that this convergence can be recovered with an improved strategy that is proposed in this paper. Copyright © 2008 John Wiley & Sons, Ltd.