Suppressing the mechanical quadrature error of a quartz double-H gyroscope through laser trimming

In this paper,we introduce a z-axis quartz gyroscope using a double-H tuning fork,which has a high sensitivity.However,it also causes a large mechanical quadrature error.The laser trimming method is used to suppress this error at quartz level.The trimming law is obtained through the finite element method(FEM).A femtosecond laser processing system is used to trim the gold balancing masses on the beams,and experimental results are basically consistent with the simulated ones.The mechanical quadrature error is suppressed by 96%,from 26.3°s-1 to 1.1°s-1.Nonlinearity changes from 1.48%to 0.30%,angular random walk(ARW)is reduced from 2.19°h-1/2 to 1.42°h-1/2,and bias instability is improved by a factor of 7.7,from 197.6°h-1 to 25.4°h-1.     

Orientation effect on the Boussinesq indentation of a transversely isotropic piezoelectric material

Three-dimensional finite element analysis was used to study the effect of the angle between the loading direction and the axisymmetric direction on the indentation behavior of a transversely isotropic piezoelectric half-space by a cylindrical indenter of flat end. Two cases were considered in the analysis, which included (a) the indentation by an insulating indenter, and (b) the indentation by a conducting indenter. Both the indentation load and the indentation-induced potential were found to be proportional to the indentation depth. Using the simulation results and the analytical relationship for the indentation by a rigid, insulating indenter, semi-analytical relationships were developed between the indentation load and the indentation depth and between the indentation-induced potential on the indenter and the indentation depth for the conducting indenter, respectively. The proportionality between the indentation-induced potential and the indentation depth is only a function of the angle between the loading direction and the poling direction, independent of the type of indenters, which may be used to measure the relative direction of the loading axis to the axisymmetric axis of transversely piezoelectric materials from the indentation test.     

动态冲击下铝板中不同深度空洞演化的有限元分析

通过建立样品厚度为飞片厚度2倍的铝板撞击有限元模型,采用Johnson-Cook本构方程研究了纯铝材料中不同深度空洞的演化过程.研究结果表明:微空洞从杂质周围形核并呈近球形长大;由于靶板不同深度拉伸应力的峰值以及加载持续时间不同,空洞的长大速率与其在靶板的位置有关;由于冲击过程中没有形成三向拉应力,材料表面的空洞长大速度为零;靶板中间层位置首先出现拉伸应力,最先开始长大,靶板中间层位置的三向拉应力最大且作用时间较长,空洞长大速度最快;从靶板中间往两表面的方向,空洞依次开始长大,长大速度逐渐减小;模拟结果与实验观察结果相符,为研究动态冲击下空洞的演化提供参考.     

Mixed finite element and differential quadrature method for free and forced vibration and buckling analysis of rectangular plates

This paper presents a combined application of the finite element method (FEM) and the differential quadrature method (DQM) to vibration and buckling problems of rectangular plates. The proposed scheme combines the geometry flexibility of the FEM and the high accuracy and efficiency of the DQM. The accuracy of the present method is demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate results can be obtained by using a small number of finite elements and DQM sample points. The proposed method is suitable for the problems considered due to its simplicity and potential for further development.     

Hybrid graded element model for transient heat conduction in functionally graded materials

This paper presents a hybrid graded element model for the transient heat conduction problem in functionally graded materials (FGMs). First, a Laplace transform approach is used to handle the time variable. Then, a fundamental solution in Laplace space for FGMs is constructed. Next, a hybrid graded element is formulated based on the obtained fundamental solution and a frame field. As a result, the graded properties of FGMs are naturally reflected by using the fundamental solution to interpolate the intra-element field. Further, Stefest’s algorithm is employed to convert the results in Laplace space back into the time-space domain. Finally, the performance of the proposed method is assessed by several benchmark examples. The results demonstrate well the efficiency and accuracy of the proposed method.     

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。     

数值流形方法中线性相关性问题的研究

数值流形方法的形函数由覆盖函数和局部近似函数组成,形函数之间往往存在线性相关性。在现有研究成果的基础上对形函数线性相关性进行了分析,指出线性相关性的根源在于覆盖函数具有单位分解特性,并与单元形状有关。研究了线性相关性与整体刚度矩阵奇异性以及求解收敛性之间的关系,指出形函数线性相关不一定导致整体刚度矩阵奇异。对8结点六面体高阶流形单元的局部近似函数及单元形状与线性相关性之间的关系进行了分析,构造出一种完全线性独立的流形单元。通过算例分析了8结点六面体流形单元局部近似函数中一次完全多项式对求解精度和收敛性的影响,发现采用一次完全多项式局部近似函数的形函数虽然线性相关,但求解仍然收敛,且精度高于线性无关的单元。     

Effective thermal conductivity of foam concretes: Homogenization schemes vs experimental data and FEM simulations

This paper focuses on the prediction of thermal conductivity of foam concretes. Various analytical forms for their effective thermal conductivity according to their porosity p (air voids volume) have been first derived based on five well-known Mean-Field Homogenization (MFH) schemes. These predictions were found to be very close for low porosities but move away gradually with increasing porosity. Thus, in order to determine the best homogenization scheme predicting the effective thermal conductivity of foam concretes, MFH predictions were confronted with experimental data obtained on nineteen foam concretes and also with numerical results obtained from 3d Finite Element Method (FEM) simulations conducted on an idealized foam concrete. These comparisons have shown that the normalized effective thermal conductivity of foam concrete is closely framed by the power law (1- p)^3/2 given by the Differential scheme and by the hyperbolic law (1- p)/(1+ p/2) given by the Mori-Tanaka scheme.     

汽车法兰盘热锻模具磨损失效的实验分析和数值研究

采用扫描白光干涉仪和扫描电镜对汽车法兰盘热锻模具的表面磨损形貌进行观察,分析其磨损失效机理.同时,基于Archard磨损模型,建立热模锻过程的热-力耦合有限元模型,研究模具预热温度、锻造速率和模具热处理工艺等因素对模具磨损的影响.结果表明,锻后模具表面出现黏着磨损、氧化磨损和磨粒磨损现象,其中磨粒磨损造成的模具损伤程度最高,最大磨损深度约为100μm;数值分析表明,当模具预热温度为250℃,锻造速率为300 mm/s时,锻后模具最高温度低于模具材料AISI H13钢的许用温度(620℃),且模具磨损深度达到最低水平;相比于淬回火热处理工艺,采用离子渗氮处理可使锻后模具最大磨损深度由7.2×10–5 mm下降至1.3×10–5 mm,磨损幅度降低82%,模具服役寿命提高约5.5倍,模拟结果与实际生产情况吻合.     

一维Ritz有限元EEP超收敛位移计算简约格式的直接推导与证明

一维Ritz有限元后处理超收敛计算的EEP(单元能量投影)法简约格式中,若问题和解答足够光滑,其m(1)次单元的超收敛位移解在单元内任一点均可以达到至少hm+2的超收敛阶。对此,本文提出一套全新的推证方法,通过对单元能量投影的等效变形,直接推导出EEP简约格式位移解的计算公式及其误差项,进而采用更为简单通用的数学证明方法,证明了这一超收敛性。