V形切口应力强度因子的一种边界元分析方法

将V形切口结构分成围绕切口尖端的小扇形和剩余结构两部分. 尖端处扇形域应力场表示成关于尖端距离$\rho$的渐近级数展开式,从线弹性理论方程推导出了一组分析平面V形切口奇异性的常微分方程特征值问题,通过求解特征方程,得到前若干个奇性指数和相应的特征向量. 再将切口尖端的位移和应力表示为有限个奇性阶和特征向量的组合. 然后用边界元法分析挖去小扇形后的剩余结构. 将位移和应力的线性组合与边界积分方程联立,求解获得切口根部区域的应力场、应力幅值系数和整体结构的位移和应力. 从而准确计算出平面V形切口的奇异应力场和应力强度因子.      

共面闭合断续节理岩体直剪强度特性研究

介绍了节理面和岩桥各自的抗剪强度机制,引入法向变形协调条件,基于Mohr-Coulomb理论,推导了共面闭合断续节理岩体的直剪强度公式。模型试验发现,剪切破坏面以拉剪复合破坏为主,同时岩块中伴随大量的拉张微裂隙。试样的强度和变形具有明显的阶段性,全应力应变曲线主要经历了线弹性增长、节理面错动、次生裂纹起裂稳态扩展、节理面贯通破坏和残余强度5个阶段。对比发现,理论计算结果与试验值吻合较好。     

PARALLEL FINITE ELEMENT ANALYSIS OF HIGH FREQUENCY VIBRATIONS OF QUARTZ CRYSTAL RESONATORS ON LINUX CLUSTER

Quartz crystal resonators are typical piezoelectric acoustic wave devices for frequency control applications with mechanical vibration frequency at the radio-frequency （RF） range. Precise analyses of the vibration and deformation are generally required in the resonator design and improvement process. The considerations include the presence of electrodes, mountings, bias fields such as temperature, initial stresses, and acceleration. Naturally, the finite element method is the only effective tool for such a coupled problem with multi-physics nature. The main challenge is the extremely large size of resulted linear equations. For this reason, we have been employing the Mindlin plate equations to reduce the computational difficulty. In addition, we have to utilize the parallel computing techniques on Linux clusters, which are widely available for academic and industrial applications nowadays, to improve the computing efficiency. The general principle of our research is to use open source software components and public domain technology to reduce cost for developers and users on a Linux cluster. We start with a mesh generator specifically for quartz crystal resonators of rectangular and circular types, and the Mindlin plate equations are implemented for the finite element analysis. Computing techniques like parallel processing, sparse matrix handling, and the latest eigenvalue extraction package are integrated into the program. It is clear from our computation that the combination of these algorithms and methods on a cluster can meet the memory requirement and reduce computing time significantly.     

磁电热弹耦合材料三维多裂纹超奇异积分法

用超奇异积分方程法将多场耦合载荷作用下磁电热弹耦合材料内含任意形状和位置三维多裂纹问题转化为求解一以广义位移间断为未知函数的超奇异积分方程组问题,退化得到内含任意形状平行三维多裂纹问题的超奇异积分方程组;推导出平行三维多裂纹问题的裂纹前沿广义奇异应力场解析表达式、定义了广义(应力、应变能)强度因子和广义能量释放率;应用有限部积分概念及体积力法,为超奇异积分方程组建立了数值求解方法,编制了FORTRAN程序,以平行双裂纹为例,通过典型算例,研究了广义(应力、应变能)强度因子随裂纹位置、裂纹形状及材料参数变化规律,得到裂纹断裂评定准则. 最后,分析了裂纹间干扰、屏蔽作用及其在工程实际中的应用.      

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根据抗拉刚度等效及抗弯刚度等效将换热器管束简化为当量圆筒以考察其对 斜锥壳应力状况的影响,同时根据轴向载荷等效及泊松效应等效,对作用在管板布管限定圆 内的压力载荷及作用在管束外表面的压力载荷进行了当量转换,建立了考虑管板及管束影响 的斜锥壳应力分析简化模型. 有限元计算结果表明,大端转角过渡区存在较大的弯曲应力. 对一系列结构尺寸的斜锥壳进行了计算,整理了斜锥壳大端转角过渡区基于分析设计的应力 强度水平系数.     

压缩载荷作用下岩石类材料的断裂模式研究

为了解岩石类材料在压缩条件下的裂纹扩展规律,本文对含有内部倾斜裂纹的石膏板试件进行了双轴压缩实验. 研究表明:在通常情况下岩石裂纹按I 型张拉模式扩展,但随着裂纹表面摩擦系数μ和围压与纵向荷载比值λ的提高,翼裂纹扩展的偏转角随之减少.当裂纹表面摩擦系数和围压与纵向荷载比值足够大时,例如,μ=0.83和λ=0.315,岩石裂纹按Ⅱ型剪切模式扩展.然而,当裂纹表面摩擦系数和围压与纵向荷载比值进一步增加时,石膏板试件将发生强度破坏.本文提出了一个理论模型用以解释和描述这一实验现象.     

调制误差对谐振式集成光学陀螺性能的影响

采用LiNbO3相位调制器代替移频器可以明显提高调制的稳定性,但同时会引入相位调制波形失真产生的误差.分析了在采用正弦波开环相位调制技术对光路进行调制和解调时,相位调制器波形失真与陀螺输出特性的关系.通过数值仿真计算可知,调制波形的频率失真与由此引起的标度因数误差大致成线性关系;调制波形峰峰值波动引起的标度因数误差随着失真幅度的增大而急剧增大;并且当陀螺零偏为1 (°)/s时,要求调制波形频率失真小于0.07%,峰峰值失真小于1.5%,波形频率失真的影响为峰峰值失真的20倍.因此在陀螺系统设计中应保证调制频率的稳定性.     

割口单向叠层板的拉伸应力集中与强度

基于剪滞理论,建立一种分层剪滞模型,分析了含割口的单向叠层板在拉伸载荷作用下的应力重新分布问题,获得了割口前缘完整纤维的应力集中因子.在此基础上,采用细观统计破坏理论,研究了割口单向叠层板的拉伸破坏强度,得到了与现有实验较吻合的结果.     

孔洞裂纹问题的一种数值方法

研究孔洞与裂纹的相互作用问题,通过把适于单一裂纹的Bueckner原理扩充到含有多孔洞多裂纹的一般体系,将原问题分解为承受远处载荷不含裂纹不含孔洞的均匀问题,和在远处不承受载荷但在裂纹面上和孔洞表面上承受面力的多孔洞多裂纹问题.于是,以应力强度因子作为参量的问题可以通过考虑后者来解决,而利用笔者提出的杂交位移不连续法,这种多孔洞多裂纹问题是容易数值求解的.算例说明该数值方法对分析平面弹性介质中孔洞与裂纹的相互作用既简单又有效.     

Application of scaled boundary finite element method in static and dynamic fracture problems

The scaled boundary finite element method (SBFEM) is a recently developed numerical method combining advantages of both finite element methods (FEM) and boundary element methods (BEM) and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors (SIFs) directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion. For dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.The project supported by the National Natural Science Foundation of China (50579081) and the Australian Research Council (DP0452681)The English text was polished by Keren Wang.