热机载荷下多边形夹杂角端部应力场的杂交元分析

开发了一种多边形夹杂角端部超级单元模型,并将其与传统四节点单元组装,用于分析热-机载荷下结构中多边形夹杂角端部的应力场.与机械载荷作用下超级单元模型的区别在于,该模型将夹杂角部邻域应力场分为奇异项和非奇异项,而奇异性项又可分解为热致部分和力致部分.在数值计算中,首先分析了单正方形夹杂问题,验证了模型的有效性,考察了材料匹配的影响;然后分析了双正方形夹杂的干涉问题,考察了夹杂间距的影响.结果表明,当前模型可避免局部网格的高度加密,从而提高有限元计算的效率.     

夹杂角端部奇异热应力场分析

本文提出了一种分析热载荷作用下夹杂角端部奇异应力场的简便方法。该方法是通过三个物理过程来完成的,研究结果发现夹杂角端部奇异热应力场问题可以等效地表示成一个双向等拉伸载荷作用下的奇异应力场弹性问题。换句话说,我们可以直接利用双向拉伸载荷作用下夹杂角端部奇异应力场现有数值结果计算奇异热应力场数值解。与有限元热弹性分析结果表明,本文提出的等效方法是正确的、有效的     

复合材料中矩形夹杂角端部力学行为分析

提出了一种分析矩形夹杂角端部奇异应力场的新型杂交有限元方法,该方法在分析矩形夹杂角端部奇异应力场时,需要在夹杂端部构造一个超级单元。超级单元的刚度矩阵可以通过夹杂端部特征问题数值解建立。我们用这种方法计算了单向载荷作用下无限大均质板中单个矩形夹杂角端部奇异应力场,并与现有的数值解进行了比较。比较结果表明:本文提出的方法是可行的、有效的,而且数值结果精度高。为说明本文方法适用范围更广,文章最后讨论了各向异性弹性材料和横观各向同性压电材料中矩形夹杂角端部电弹性场行为。     

尖锐夹杂角端部局部应力场杂交有限元分析

本文首先利用作者曾提出的一维有限元特征分析方法计算所得到的尖锐夹杂角端部应力奇异指数和奇异应力场、位移场角分布函数,并依据Hellinger-Reissner原理,开发出了一个特殊的、能够反映夹杂角端部局部弹性现象的n结点多边形超级角端部单元,然后将该超级单元与标准的4结点杂交应力单元耦合在一起构建了一种分析异形夹杂角端部奇异弹性场的新型特殊杂交应力有限元方法.文中给出了两个应用算例,算例结果表明:本文方法不仅使用单元少、计算结果精度高,而且适用范围广,可拓展应用于分析复合材料微结构组织与力学行为关系.     

夹杂角端部奇异应力场分析

提出一种分析夹杂角端部奇异应力场的新型杂交有限元方法.构造了一个角端部奇异单元,该单元刚度建立不依赖数学解析解.用这种方法计算了单向载荷作用下无限大板含单个方形夹杂和菱形夹杂角端部奇异应力场,并与现有的数值解进行了比较,结果表明:目前的数值方法是可行的、有效的、数值结果精度高,适用范围广.作为应用讨论了双方形夹杂刚度和位置对夹杂角端部奇异应力场的影响.     

受热载荷两相材料界面端应力场的新型有限元分析

基于一种特殊有限元特征分析方法获得两相材料界面端奇异性应力和位移场数值特征解, 据此开发了一种新型超级单元模型, 用于分析热载荷作用下两相材料界面端的应力场. 与机械载荷作用下超级单元模型的区别在于, 该模型在能量泛函中考虑了热-机耦合的影响, 将应力场分为奇异项和非奇异项, 而奇异性项又可分解为热致部分和力致部分. 模型的有效性通过了经验解和传统有限元方法的验证;模型可以避免在界面端邻域网格高度加密, 提高了计算速度, 对于分析多奇异性点应力干涉问题有重要意义.     

QFP结构中引脚焊缝界面端的奇异性热应力问题研究

由于引脚、印制电路板和焊接剂的热-机材料属性不同,在受到热载荷或机械载荷时,引脚焊接界面端会产生奇异性应力,有可能产生界面开裂.为了基于界面端奇异场来评价QFP结构引脚界面端力学行为,本文拟采用数值方法求解引脚焊缝任意角度尖劈界面端的应力强度系数.具体步骤为:首先,基于高次内插有限元特征分析法确定两相任意角度尖劈界面端的奇异性指数和应力角分布函数,并引入常数热应力项,获得热-机耦合奇异性应力场表达式;采用有限元分析技术和最小二乘拟合法来获得应力强度系数的数值解.文中考察了热-机材料属性对热载荷下焊接剂/印制电路板界面端应力强度系数的影响,并给出改善界面端热应力状态的建议.     

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。     

复合材料补片加固钢板的粘接应力与失效模拟

在ANSYS有限元软件中建立三维有限元模型,对复合材料补片单面加固钢板进行数值模拟,使用内聚力单元模拟胶层脱粘和扩展过程,有限元模型计算结果与试验结果吻合较好,弹性极限载荷和失效载荷的相对误差分别为9.6%和4.2%。计算得到了模型在拉伸载荷作用下的载荷-位移曲线、胶层剪应力和剥离应力分布情况以及补片x轴向应力分布情况。结果表明,胶层端部最先达到极限强度后出现开裂,脱粘从补片两端开始逐渐向中心扩展,且扩展过程是非对称的;当补片发生部分脱粘后,补片应力集中在未脱粘处,承载长度逐渐减小、承载能力逐渐降低。     

球形闭孔泡沫金属材料力学行为研究

利用面心立方单元胞模型计算了球形闭孔泡沫金属材料的宏观弹塑性特性,建立了弹性参数和屈服强度与相对密度的关系,所得结果与球形(类球形)闭孔泡沫铝合金试验结果进行了比较,二者吻合较好.此外,利用所建立的单元胞模型计算了等比例多轴载荷下的应力-应变曲线,针对现有的泡沫金属材料弹塑性宏观唯象本构框架,得到了球形孔闭孔泡沫金属材料在不同特征应变下应力势函数曲面及其演化规律,确定了其宏观本构理论模型的材料参数.结果表明,该理论模型能较好模拟有限元数值计算结果.     

An effective boundary element method for analysis of crack problems in a plane elastic plate

A simple and effective boundary element method for stress intensity factor calculation for crack problems in a plane elastic plate is presented. The boundary element method consists of the constant displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements proposed by YAN Xiangqiao. In the boundary element implementation the left or the right crack-tip displacement discontinuity element was placed locally at the corresponding left or right each crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. Test examples (i. e. , a center crack in an infinite plate under tension, a circular hole and a crack in an infinite plate under tension) are included to illustrate that the numerical approach is very simple and accurate for stress intensity factor calculation of plane elasticity crack problems. In addition, specifically, the stress intensity factors of branching cracks emanating from a square hole in a rectangular plate under biaxial loads were analysed. These numerical results indicate the present numerical approach is very effective for calculating stress intensity factors of complex cracks in a 2-D finite body, and are used to reveal the effect of the biaxial loads and the cracked body geometry on stress intensity factors.     

A novel hybrid finite element analysis of inplane singular elastic field around inclusion corners in elastic media

This paper deals with the inplane singular elastic field problems of inclusion corners in elastic media by an ad hoc hybrid-stress finite element method. A one-dimensional finite element method-based eigenanalysis is first applied to determine the order of singularity and the angular dependence of the stress and displacement field, which reflects elastic behavior around an inclusion corner. These numerical eigensolutions are subsequently used to develop a super element that simulates the elastic behavior around the inclusion corner. The super element is finally incorporated with standard four-node hybrid-stress elements to constitute an ad hoc hybrid-stress finite element method for the analysis of local singular stress fields arising from inclusion corners. The singular stress field is expressed by generalized stress intensity factors defined at the inclusion corner. The ad hoc finite element method is used to investigate the problem of a single rectangular or diamond inclusion in isotropic materials under longitudinal tension. Comparison with available numerical results shows the present method is an efficient mesh reducer and yields accurate stress distribution in the near-field region. As applications, the present ad hoc finite element method is extended to discuss the inplane singular elastic field problems of a single rectangular or diamond inclusion in anisotropic materials and of two interacting rectangular inclusions in isotropic materials. In the numerical analysis, the generalized stress intensity factors at the inclusion corner are systematically calculated for various material type, stiffness ratio, shape and spacing position of one or two inclusions in a plate subjected to tension and shear loadings.     

A NEW SPATIAL THIN-WALLED BEAM ELEMENT INCLUDING TRANSVERSE AND TORSIONAL SHEAR DEFORMATION

基于Timoshenko梁及Benscoter薄壁杆件理论,建立了考虑剪切变形、弯扭耦合以及翘曲剪应力影响的空间任意开闭口薄壁截面梁单元. 通过引入单元内部结点,对弯曲转角和翘曲角采用三节点Lagrange独立插值的方法,考虑了剪切变形和翘曲剪应力的影响并避免了横向剪切锁死问题;借助载荷作用下薄壁梁的截面运动分析,在位移和应变方程中考虑了弯扭耦合的影响. 通过数值算例将该单元的计算结果与理论解以及商用有限元软件和其他文献中的数值解进行对比和验证,结果对比表明该薄壁梁单元具有良好的精度和收敛性.     

COUPLED THERMO-MECHANICAL ANALYSIS OF FUNCTIONALLY GRADIENT WEAK/MICRO-DISCONTINUOUS INTERFACE WITH GRADED FINITE ELEMENT METHOD

Coupled thermo-mechanical analysis of two bonded functionally graded materials subjected to thermal loads is conducted in this study with the graded finite element method. The thermal-mechanical properties of the bi-material interfaces are classified based on discontinuity degrees of their material properties and their derivatives at the interfaces. Numerical results indicate that discontinuity exerts remarkable effect on the temperature profile and stress value at the interface of two bonded functionally-graded materials. Under the thermal flux loading conditions, the stronger the interface discontinuity is, the smaller the heat flux is.     

Numerical analysis of convection-diffusion with chemical reaction by combined finite and boundary element methods

A numerical method is presented to analyse a steady convection-diffusion problem with a first-order chemical reaction defined on an infinite region. The present method is based on the combined finite element and boundary element methods. For one- and two-dimensional examples in an infinite region the numerical results by the present method are in excellent agreement with the exact solutions. As a practical application, the simulation of the concentration distribution of the chemical oxygen demand at Kojima Bay is carried out.     

A numerical analysis of cracks emanating from an elliptical hole in a 2-D elasticity plate

This paper is concerned with the stress intensity factors (SIFs) of cracks emanating from an elliptical hole in an infinite or a finite plate under biaxial loads by using a boundary element method, which consists of the non-singular displacement discontinuity element presented by Crouch and Starfield and the crack-tip displacement discontinuity elements due to the author. In the boundary element implementation the left or the right crack-tip element is placed locally at the corresponding left or right crack tip on top of the constant displacement discontinuity elements that cover the entire crack surface and the other boundaries. A few numerical examples are included to show that the present approach is very efficient and accurate for the calculating the SIFs of crack problems in an infinite or a finite plate. The present numerical results of cracks emanating from an elliptical hole under biaxial loads can reveal the effect of the elliptical aspect ratio and the transverse load on the SIFs.