Using moiré interferometry and boundary integral hybrid method to determine mixed-mode stress intensity factor

The paper describes a hybrid experimental and numerical method of Moiré Interferometry and the boundary-integral-element method. The interference patterns used for the evaluation of the displacement vector are obtained by Moiré Interferometry. The boundary displacements obtained experimentally are conveniently used for the calculation of the stress intensity factor in the body by the boundary-integral-method. Some examples bear witness to the effectiveness and accuracy of the hybrid technique. Project is supported by the Science Fundation of the State Education Commission of China.     

2D dynamic analysis of cracks and interface cracks in piezoelectric composites using the SBFEM

The dynamic stress and electric displacement intensity factors of impermeable cracks in homogeneous piezoelectric materials and interface cracks in piezoelectric bimaterials are evaluated by extending the scaled boundary finite element method (SBFEM). In this method, a piezoelectric plate is divided into polygons. Each polygon is treated as a scaled boundary finite element subdomain. Only the boundaries of the subdomains need to be discretized with line elements. The dynamic properties of a subdomain are represented by the high order stiffness and mass matrices obtained from a continued fraction solution, which is able to represent the high frequency response with only 3–4 terms per wavelength. The semi-analytical solutions model singular stress and electric displacement fields in the vicinity of crack tips accurately and efficiently. The dynamic stress and electric displacement intensity factors are evaluated directly from the scaled boundary finite element solutions. No asymptotic solution, local mesh refinement or other special treatments around a crack tip are required. Numerical examples are presented to verify the proposed technique with the analytical solutions and the results from the literature. The present results highlight the accuracy, simplicity and efficiency of the proposed technique.     

Stress analysis by combination of holographic interferometry and boundary-integral method

The paper describes a hybrid experimental and numerical method analysis of bodies. It consists of the experimental method of double-aperture speckle interferometry and the boundary-integral method. The interference patterns allowing evaluation of the displacement vector are obtained by the speckle interferometry. The boundary displacements obtained experimentally are conveniently used for the calculation of stresses in the body by the boundary-integral method. Some examples bear witness of the effectiveness and accuracy of the hybrid technique.     

压电材料平面裂纹尖端场的杂交应力有限元分析

基于复势理论和杂交变分原理建立了一种适用于力电耦合分析的杂交应力有限元模 型. 给出了建立刚度矩阵的主要公式和推导过程，单元内的位移场和应力场采用满足平 衡方程的复变函数级数解，假设的复变函数级数解事先精确满足裂纹的无应力和电位移法向 分量为零的条件，单元外边界的位移场假设按抛物线变化, 单元的刚度矩阵采用Gauss积分的方法得出. 通过对力电耦合裂尖场的数值计算验证了程序 的正确性和单元的有效性，同时也用所得结果校验了理论解.     

利用边界单元法求平面问题应力强度因子K_I的应力-位移杂交法

本文提出用裂尖附近2点或3点的应力和位移计算应力强度因子K_I的杂交方法.这种方法充分利用了边界单元法的计算结果,考虑了裂尖应力场和位移场渐近展开式的高阶项,使用远离裂尖的点算出的K_I也有较好的精度,拟合线十分平坦.用算例的结果将杂交法与一般的位移法和应力法进行了比较,同时,对常量单元和线性单元也进行了比较.     

Accuracy of Finite Element Based Shape Design Sensitivity Analysis*

ABSTRACT Accuracy of finite element based shape design sensitivity analysis, for use in shape design optimization, is analyzed and tested. A shape design sensitivity formulation that uses stress averaging to treat stress constraint func-tionals is presented. A smooth boundary parameterization is introduced to avoid the "Babuska paradox" and to improve accuracy of design sensitivity analysis. Accuracy of design sensitivity analysis with displacement and hybrid stress finite element formulations is compared. Good accuracy is obtained using higher order displacement finite elements, such as linear stress triangular and 8-noded isoparametric elements.     

A new hybrid stress element method for the analysis of elastoplastic solids

Based on a modified Hellinger/Reissner variational principle which includes the equivalent stress, equivalent plastic strain and non-conforming displacement increments as independent variables, a quadrilateral isoparametric hybrid stress element for the analysis of elastoplastic problem is proposed. By this formulation, the yield criterion and flow rule are satisfied in an average sense and greater accuracy can be obtained by using non-conforming displacement. A numerical example is presented to show that the present model has high accuracy and computational effectiveness.This project is supported by the Natural Science Foundation of the State Education Commission.     

基于辛弹性力学解析本征函数的有限元应力磨平方法

在实际工程结构的结构强度与优化等力学数值分析中,应力计算结果的精度是非常重要的。有限元法是得到最广泛应用的一类数值方法,并形成了众多通用的有限元程序系统。这些程序系统采用的几乎都是基于最小总势能的位移法,虽然其分析给出的有限元位移场具有较高的精度,但所得到的有限元应力场的精度较位移场大大降低。基于极坐标辛对偶体系所提供的平面弹性力学的解析辛本征展开解,并借用有限元程序系统所得到的节点位移,本文提出了一个应力分析的改进方法。数值结果表明,本方法给出的应力分析精度得到大幅提高,并具有良好的数值稳定性,可用于有限元程序系统的后处理,以提高应力尤其是关键区域应力的分析精度。     

Some problems in plane thermopiezoelectric materials with holes

Piezoelectric materials have recently attracted considerable attention due to their potential use in intelligent structural systems. In this paper, we treat the plane problem of thermopiezoelasticity with various holes and subject to coupled mechanical, electric and thermal loads. An analytical solution is obtained by applying the technique of conformal mapping and some identities in the Stroh formalism. The solution has a simple unified form for various holes such as ellipse, circle, triangle and square. By way of the solution, the expressions for the energy release rate and stress intensity factors of cracks are presented. Numerical results for concentration coefficients of stress and electric displacement along the hole boundary are given to assess the acceptability of the proposed method.     

周期分布多边形夹杂奇异性应力干涉问题的研究

采用一种新型的杂交元模型和一种单胞模型来解决周期分布多边形夹杂角部的奇异性应力相互干涉的问题。新型杂交元模型是基于广义Hellinger-Reissner变分原理建立的,其中奇异性应力场分量和位移场分量是采用有限元特征分析法的数值特征解得到的。使用当前的新型杂交元模型,只需要在夹杂角部邻域的周界上划分一维单元,避免了像传统有限元模型那样需要划分高密度二维单元。文中给出了代表奇异性应力场强度的夹杂角部广义应力强度因子数值解,并考虑材料属性、夹杂尺寸和夹杂位置关系的影响。算例中,考虑了夹杂和基体完全接合的情况,并给出了考核例。结果表明:当前模型能得到高精度数值解,且收敛性好;与传统有限元法和积分方程方法相比,该模型更具有通用性,为非均质材料的细观力学分析打下了基础。     

任意多孔多裂纹有限大板的应力强度因子分析

采用各向异性体平面弹性理论中的复势方法,以Faber级数为工具,应用保角映射技术和最小二乘边界配点法,导出内边界条件精确满足,外边界条件近似满足的含多椭圆孔及裂纹群有限大板在任意载荷作用下的应力场、位移场的级数解,建立了任意多椭圆孔及裂纹群有限大板应力强度因子的有效分析方法,讨论了各参数对裂尖应力强度因子及孔边应力集中的影响．数值结果表明,该方法具有计算精度高、收敛速度快、方便快捷等优点,有利于全面系统地研究各参数对结构断裂性能的影响．     

基于拟满应力设计和遗传算法的网架截面优化方法

通过在遗传算法中嵌入拟满应力算子,提出了一种以网架结构杆件截面作为离散变量的优化设计方法,即基于拟满应力设计和遗传算法的网架截面优化方法.分析结果表明,该法能够提高遗传算法的搜索效率和获得全局最优解的可靠性,对于同时有应力和位移约束的网架等空间结构截面优化问题,这种混合算法有较高的效率.     

正交各向异性弹性问题的规则化边界元法

本文致力于平面正交各向异性弹性问题的规则化边界元法研究,提出了新的规则化边界元法的理论和方法。对问题的基本解的特性进行了研究,确立基本解的积分恒等式,提出一种基本解的分解技术,在此基础上,结合转化域积分方程为边界积分方程的极限定理,建立了新颖的规则化边界积分方程。和现有方法比,本文不必将问题变换为各向同性的去处理,从而不含反演运算,也有别于Galerkin方法,无需计算重积分,因此所提方法不仅效率高,而且程序设计简单。特别是,所建方程可计算任何边界位移梯度,进而可计算任意边界应力,而不仅限于面力。数值实施时,采用二次单元和椭圆弧精确单元来描述边界几何,使用不连续插值逼近边界函数。数值算例表明,本文算法稳定、效率高,所取得的边界量数值结果与精确解相当接近。     

ANALYSIS OF 3-D NOTCHED/CRACKED STRUCTURES BY USING EXTENDED BOUNDARY ELEMENT METHOD 1)

在线弹性理论中,三维 V 形切口/裂纹结构尖端区域存在多重应力奇异性,常规数值方法不易求解. 本文提出和建立了三维扩展边界元法 (XBEM),用于分析三维线弹性 V 形切口/裂纹结构完整的位移和应力场. 先将三维线弹性 V 形切口/裂纹结构分为尖端小扇形柱和挖去小扇形柱后的外围结构. 尖端小扇形柱内的位移函数采用自尖端径向距离 $r$ 的渐近级数展开式表达,其中尖端区域的应力奇异指数、位移和应力特征角函数通过插值矩阵法获得. 而级数展开式各项的幅值系数作为基本未知量. 挖去扇形域后的外围结构采用常规边界元法分析. 两者方程联立求解可获得三维 V 形切口/裂纹结构完整的位移和应力场,包括切口/裂纹尖端区域精细的应力场. 扩展边界元法具有半解析法特征,适用于一般三维 V 形切口/裂纹结构完整位移场和应力场的分析,其解可精细描述从尖端区域到整体结构区域的完整应力场. 作者研制了三维扩展边界元法程序,文中给出了两个算例,通过计算结果分析,表明了扩展边界元法求解三维 V 形切口/裂纹结构完整应力场的准确性和有效性.     

一种新的弹塑性杂交应力元法

本文基于一个改进的弹塑性的Hellinger/Reis■ner 混合变分原理构造了一种用于解弹塑性问题的四节点等参杂交应力元.新的模型中,在单元内增加了等效应力增量、塑性等效应变增量及不协调位移变量,从而使单元内的屈服准则及流动法则平均得到满足,不协调位移改进了单元应力精度.计算表明,新的模型可以提高弹塑性杂交法的精度和计算效率.     

三维切口/裂纹结构的扩展边界元法分析

在线弹性理论中,三维 V 形切口/裂纹结构尖端区域存在多重应力奇异性,常规数值方法不易求解. 本文提出和建立了三维扩展边界元法 (XBEM),用于分析三维线弹性 V 形切口/裂纹结构完整的位移和应力场. 先将三维线弹性 V 形切口/裂纹结构分为尖端小扇形柱和挖去小扇形柱后的外围结构. 尖端小扇形柱内的位移函数采用自尖端径向距离 $r$ 的渐近级数展开式表达,其中尖端区域的应力奇异指数、位移和应力特征角函数通过插值矩阵法获得. 而级数展开式各项的幅值系数作为基本未知量. 挖去扇形域后的外围结构采用常规边界元法分析. 两者方程联立求解可获得三维 V 形切口/裂纹结构完整的位移和应力场,包括切口/裂纹尖端区域精细的应力场. 扩展边界元法具有半解析法特征,适用于一般三维 V 形切口/裂纹结构完整位移场和应力场的分析,其解可精细描述从尖端区域到整体结构区域的完整应力场. 作者研制了三维扩展边界元法程序,文中给出了两个算例,通过计算结果分析,表明了扩展边界元法求解三维 V 形切口/裂纹结构完整应力场的准确性和有效性.      

Kinked crack analysis by a hybridized boundary element/boundary collocation method

In this research a two dimensional displacement discontinuity method (which is a kind of indirect boundary element method) using higher order elements (i.e. a source element with a cubic variation of displacement discontinuities having four sub-elements) is used to obtain the displacement discontinuities along each boundary element. In this paper, three kinds of the higher order boundary elements are used: the ordinary elements, the kink elements and the special crack tip elements.The boundary collocation technique is used for the calculation of the displacement discontinuities at the center of each sub-elements. Again a special boundary collocation technique is used to treat the kinked source elements occur in the crack analysis. Considering the two source elements (each having four sub-elements) joined at a corner (kink point). The collocation points in the cubic element model which are outside of the kink point are moved to the crack kink then the displacement discontinuities on the left and right sides of the kink are calculated. The displacement discontinuities of the kink point are obtained by averaging the corresponding values of its left and right sides. The special crack tip elements are also treated by the boundary displacement collocation technique considering the singularity variation of the displacements and stresses near the crack tip. Some simple example problems are solved numerically by the proposed method. The numerical results are compared with the corresponding results obtained by the previous methods cited in the literature. This comparison shows a very good agreement between the results and verify the accuracy and validity of the proposed method.     

求解含孔边裂纹各向异性板应力强度因子的复变—广义变分方法

本文提供了一个求解含孔边裂纹正交各向异性板应力强度因子的复变一广义变分方法.首先建立满足所有弹性力学基本方程式和裂纹表面边界条件的应力与位移级数表达式.然后应用广义变分原理满足其余边界条件从而确定应力强度因子.计算表明,级数收敛迅速,结果与有限元法非常一致,而所需机时较少.     

ANALYTICAL SOLUTIONS FOR THE LAYERED GEO-MATERIALS SUBJECTED TO AN ARBITRARY POINT LOAD IN THE CARTESIAN COORDINATE

This paper presents analytical solutions for the stress and displacement field in elastic layered geo-materials induced by an arbitrary point load in the Cartesian coordinate system. The point load solutions can be obtained by referring to the integral transform and the transfer matrix technique. However, former solutions usually exist in the cylindrical coordinate system subjected to axisymmetric loading. Based on the proposed solutions in the Cartesian coordinate, it is very easy to solve asymmetric problems and consider the condition with internal loads in multi-layered geo-materials. Moreover, point load solutions can be used to construct solutions for analytical examination of elastic problems and incorporated into numerical schemes such as boundary element methods. The results discussed in this paper indicate that there is no problem in the evaluation of the point load solutions with high accuracy and efficiency, and that the material non-homogeneity has a significant effect on the elastic field due to adjacent loading.     

Calibration of Stress-triaxiality Dependent Crack Formation Criteria: A New Hybrid Experimental–Numerical Method

A new experimental technique has been developed to investigate the onset of fracture in metals at low and intermediate stress triaxialities. The gage section of a flat specimen has been designed such that cracks are most likely to initiate within the specimen center, remote from the specimen boundaries. Along with the specimen, a biaxial testing device has been built to apply a well-defined displacement field to the specimen shoulders. The stress state within the specimen is adjusted by changing the biaxial loading angle. Using this new experimental technique, the crack initiation in metals can be studied experimentally for stress triaxialities ranging from 0.0 to 0.6. The stress and strain fields within the specimen gage section are determined from finite element analysis. The reliability of the computational model of the test set-up has been verified by comparing the simulation results with laser speckle-interferometric displacement measurements during testing. Sample experiments have been performed on the Al-7Si-Mg gravity die casting alloy. A three-step hybrid experimental–numerical calibration procedure has been proposed and applied to determine a phenomenological crack formation criterion for the Al-7Si-Mg alloy.