渐开线蜗杆和齿轮跨线测量精确公式

本文给出了用等距曲面方法推导渐开线蜗杆和齿轮跨线测量精确公式的过程,通过与其它齿形蜗杆精确公式的比较阐明精确公式的理论意义,并利用渐开线特性简化了精确公式。     

图解法的CAD实现途径

传统图解法通常采用手工绘图解决空间几何问题,作图结果不精确。采用计算机辅助设计方法可以求解图解法中的度量、定位问题,通过建立空间几何元素的精确几何模型,利用AutoCAD软件的辅助设计功能得到空间几何问题的精确结果。     

三维激光扫描技术在犯罪现场重建中的应用

目的:研究利用三维激光扫描技术进行现场重建的技术方法。方法:首先,利用三维激光扫描仪对现场进行扫描,获取现场的点云数据;然后,依据点云数据进行现场建模和动画模拟。结果:精确地重建了犯罪现场的场景并获得具有交互性、沉浸感的动画模拟效果。结论:利用三维激光扫描技术可以精确、方便地进行现场重建。     

基于固定界面子结构模态的频响函数精确综合法

提出基于固定界面子结构模态的双协调结构频响函数精确综合方法。首先用固定界面子结构的中高阶模态与精确剩余约束模态表达子结构频域位移;再利用界面力与位移的协调关系进一步消去界面自由度,建立双协调的精确缩聚变换;然后根据里兹法,得到结构精确综合的频域运动方程与频响函数;最后通过数值结果验证该方法的综合能力与准确性。     

光谱法精密测厚的应用设计

介绍了利用激光光谱分析法测量介质厚度的一种高精度测量方法,与一般的测厚方法不同,测量越薄的介质.精度越高,并解释了其原理.通过激光垂直照射平板基体上的介质,利用光谱仪分析仪来精确测定相邻带波数差△(1/λ),利用简洁、方便的检测过程和计算,精确地得到介质的厚度.     

Hamilton-Jacobi方程的对称约化和精确解

对称群法是研究非线性偏微分方程对称约化和精确解的有效方法。本文利用广义条件对称方法研究容许二阶广义条件对称的Hamilton-Jacobi方程。对一些类型的Hamilton-Jacobi方程,我们得到了该类方程的对称约化和精确解。     

双参数弹性地基上正交各向异性矩形薄板自由振动的精确解

根据分离变量法得到了双参数弹性地基上正交各向异性矩形薄板自由振动封闭形式的精确解,其中边界条件为CCCC、SCCC和SSCC情况的精确解过去被认为是难以得到的。在分离变量方法中,利用控制微分方程本征值给出振型函数的解析形式和两个空间本征值和时间本征值的关系,再利用边界条件得到振型函数系数和本征值方程或频率方程的精确形式。数值结果与有限元结果及文献结果吻合较好,验证了本文方法和结果的正确性。     

二次锥规划的一种非精确不可行内点算法

给出了二次锥规划的一种非精确不可行内点算法。该算法允许搜索方向有相对较大的误差,且不要求迭代点的可行性。在相对不精确的假设下,利用该算法可找到二次锥规划的ε-近似解。     

三角域上Meyer-Knig-Zeller算子的二阶矩量的精确表示

利用直接法给出了三角域上Meyer-Knig-Zeller算子的二阶矩量的精确表达式.     

利用子结构模态的结构随机响应精确综合

提出基于固定界面子结构模态的结构随机响应精确综合方法。首先用固定界面子结构的中阶模态与精确剩余约束模态表达子结构频域位移;再利用界面力与位移的协调关系进一步消去界面自由度,建立双协调的精确缩聚变换;然后根据里兹法,得到结构精确综合的广义频响函数;并由此独立地计算各子结构的功率谱密度,进一步得到其均方值等响应统计;最后通过数值结果验证该方法的综合能力与准确性。     

桁架结构材料非线性弹性问题的广义逆力法

通过回顾传统位移法和传统力法的思路,比较了两种传统方法,分别指出了它们在计算机求解材料非线性问题中的优缺点。从经典力法的求解思路出发介绍了用于桁架结构材料非线性弹性问题的广义逆力法(AforcemethodbasedonGeneralizedInverseMatrix,GIM),给出了该算法的推导思路及求解过程。特别指出了传统力法用计算机求解材料非线性问题所遇到的困难,对如何解决这些困难作了探讨,从而给出了结构力学计算的一个全新视角,也使得力法在计算机计算领域重新得到发展空间。广义逆力法是一种基于力法和广义逆矩阵理论的新的迭代解法,对于材料非线性问题,由于无需像传统的基于位移法的逐步增量法那样逐步递进计算,所以也称特大增量步算法(LargeIncrementMethod,LIM)。同时也指出了该算法在结构并行计算方面不同于传统的子结构并行计算的新的特点。做为一种新的迭代算法,也给出了该算法求解的唯一性和收敛性证明。     

求解一类含阻尼的强非线性系统的改进多尺度方法

将改进LP方法参数变换思想直接应用到多尺度方法中,提出一种改进的多尺度方法,对含有阻尼的Duf-fing系统自由振动摄动解进行研究,得出了该类问题摄动解的显示表达式,这是使用MLP方法无法得到的。和数值计算比较的算例表明,所得方法计算结果与数值计算结果非常接近。     

使用单片机测频的四种方法分析——兼谈等精度测频法的实现

本文论述了使用单片机测频的四种方法,即直接计数法、周期测频法、混合测频法和等精度测频法。通过误差分析指出,直接计数法适于高频测量,周期测频法适于低频测量。在此基础上,提出具有通频带测频性质的混合测频法,并给出其测频最大相对误差和最大误差频率点的表达式。关于等精度测频法,提出利用软件查询实现同步的方法。并论证其测频精度可达10~(-6)     

提取脉冲响应函数的小波变换法及时域法分析

针对有关文献提出的利用小波变换来求取结构系统脉冲响应函数的方法,指出利用小波变换的方法与传统的基于Duharmal积分的时域法具有一致性,并且时域法具有更高的效率。文中简要地介绍了这两种方法的原理,并且在小波分解层数的意义上从多层分解到一层分解以及到时域法,详细分析了利用小波分解的实质,指出时域法是小波分解方法在层数上的延伸,因此是效率最高的。用矩阵广义逆的方法克服了时域法在对输入信号采样时存在的问题。用四自由度的弹簧-质量-阻尼系统进行了仿真,并且在悬臂梁上进行了实验,结果都表明本文得出的结论是正确的。     

Combined interior‐point method and semismooth Newton method for frictionless contact problems

In the present paper, a solution scheme is proposed for frictionless contact problems of linear elastic bodies, which are discretized using the finite element method with lower order elements. An approach combining the interior‐point method and the semismooth Newton method is proposed. In this method, an initial active set for the semismooth Newton method is obtained from the approximate optimal solution by the interior‐point method. The simplest node‐to‐node contact model is considered in the present paper, that is, pairs of matching nodes exist on the contact surfaces. However, the discussions can be easily extended to a node‐to‐segment or segment‐to‐segment contact model. In order to evaluate the proposed method, a number of illustrative examples of the frictionless contact problem are shown. The proposed combined method is compared with the interior‐point method and the semismooth Newton method. Two numerical examples that are difficult to solve using the semismooth Newton method are solved effectively using the proposed combined method. It is shown that the proposed method converges within far fewer iterations than the semismooth Newton methods or the interior‐point method. Copyright © 2009 John Wiley & Sons, Ltd.     

基于核典型相关分析的非线性相关源盲分离方法研究

针对传统的相关源盲分离方法的不足,提出了一种基于核典型相关分析的非线性相关源盲分离方法。该方法是利用了核方法来处理数据之间的非线性问题,同时还利用信号源之间的相关性来进行分离。提出的方法与传统的相关源盲分离方法进行对比分析。仿真结果表明,提出的方法明显优于传统的相关源盲分离方法,并从分离性能指标上得到了充分的反映。最后,将该方法应用到转子不对中和碰摩故障的盲分离中,实验结果进一步验证了该方法的有效性。     

Incorporation of multipoint constraints into the balancing domain decomposition method and its parallel implementation

The domain decomposition method (DDM) is a major solution algorithm that is used to parallelize the finite element method. In the case of implicit structural analysis using the DDM, the substructuring‐based iterative linear solver is a powerful tool when an effective preconditioner such as the balancing domain decomposition (BDD) method is used. In the present study, a method by which to incorporate a set of linear multipoint constraints (MPC) into the BDD method is proposed. In this method, when an MPC is enforced on the internal degrees of freedom (DOFs) in some subdomains, the DOFs are converted into interface DOFs, that is, all of the DOFs constrained by MPCs become interface DOFs. Then, the interface problem with the set of MPCs for the interface DOFs is solved by the conjugate projected gradient method. In order to combine the above procedure with the preconditioner used in the BDD method, the effect of the MPCs for the interface DOFs is also imposed on the coarse grid problem of the BDD method using the penalty method. A parallel implementation of the present method is also described. Some illustrative examples are solved and good convergence and parallel performance of the present method are demonstrated. Copyright © 2006 John Wiley & Sons, Ltd.     

显微栅线投影相关法及其在三维形貌测试中的应用

基于数字图像相关法解调被物体高度调制的投影栅线平移量的原理，提出了显微栅线投影相关法的概念。该方法是栅线投影法和数字图像相关方法相结合的产物，用于测量微结构的三维形貌和离面变形。系统阐述了该方法的测量原理和详细的标定过程，研究了该方法在微薄膜挠度测量中的应用。测量结果表明，显微栅线投影相关法简单易行，测试结果可靠，配合高速图像采集系统，可用于微结构的动态测试，从而为实现微结构动、静态测试展现了新的应用前景。     

The interpolating element-free Galerkin (IEFG) method for two-dimensional potential problems

In this paper, the moving least-squares (MLS) approximation and the interpolating moving least-squares (IMLS) method proposed by Lancaster are discussed first. A new method for deriving the MLS approximation is presented, and the IMLS method is improved. Compared with the IMLS method proposed by Lancaster, the shape function of the improved IMLS method in this paper is simpler so that the new method has higher computing efficiency. Then combining the shape function of the improved IMLS method with Galerkin weak form of the potential problem, the interpolating element-free Galerkin (IEFG) method for the two- dimensional potential problem is presented, and the corresponding formulae are obtained. Compared with the conventional element-free Galerkin (EFG) method, the boundary conditions can be applied directly in the IEFG method, which makes the computing efficiency higher. For the purposes of demonstration, some selected numerical examples are solved using the IEFG method.     

Reliability analysis of structures using neural network method

In order to predict the failure probability of a complicated structure, the structural responses usually need to be estimated by a numerical procedure, such as finite element method. To reduce the computational effort required for reliability analysis, response surface method could be used. However the conventional response surface method is still time consuming especially when the number of random variables is large. In this paper, an artificial neural network (ANN)-based response surface method is proposed. In this method, the relation between the random variables (input) and structural responses is established using ANN models. ANN model is then connected to a reliability method, such as first order and second moment (FORM), or Monte Carlo simulation method (MCS), to predict the failure probability. The proposed method is applied to four examples to validate its accuracy and efficiency. The obtained results show that the ANN-based response surface method is more efficient and accurate than the conventional response surface method.