基于线性多点逼近的载荷识别方法

利用结构响应信息进行载荷识别是结构工程重要研究内容之一.本文提出了基于时空多点线性逼近的动载荷识别方法,利用特定的载荷基函数在空问和时间上多点线性组合逼近结构的未知荷载输入,实现结构载荷的参数化表达,使得载荷识别反问题归结为一个多点权重系数求解问题.所建立的识别方法不需要对结构模型预先进行模态分析,采用一个常系数矩阵对...     

基于线性多点逼近方法的结构局部非线性损伤识别

结构损伤通常伴随一定的非线性响应特征,当非线性特征较为明显时,单纯的有限元更新方法无法克服本身所固有的非线性特征的限制,在动力特性测试中也存在许多困难.本文研究时域内损伤识别方法,将局部非线性结构损伤等效为一个的附加子结构,基于线性多点逼近方法,将一个非线性损伤识别问题转化为作用于线性模型的载荷识别问题.通过结构非线性响应识别出等效附加力的时间历程,利用附加子结构的输入输出特性识别实际结构的单元损伤特性.在所提出的识别方法理论算法基础上,对单元刚度线性损伤和非线性损伤形式进行了数值模拟,算例显示这种方法的有效性.     

多层地基的弹塑性分析

提出了多层地基的弹塑性力学分析方法,该方法建立在严格的数学、力学基础上,所推得的泛函求解式子具有可靠、明了的特点.通过有限元离散后,归结为一个求自由变量的二次规划问题,用所设计的算法进行求解,可避开传统迭代法中反复迭代的过程,具有高效、优化等特点.此方法可用于多层地基的路面设计以及对地基工作状态进行分析.     

基于插值型无单元Galerkin法的复合材料层合板自由振动分析

为了更有效地求解复合材料层合板的自由振动问题,以一阶剪切变形理论为基础,对插值型无单元Galerkin法在此类问题中的应用进行了研究,并发展了相应的计算方法.该方法采用插值型移动最小二乘法建立试函数时可以只依赖于复合材料层合板中面上的一组离散节点,在继承无单元Galerkin法前处理简单、计算精度高等优点的同时,可直接施加本质边界条件,避免了使用Lagrange乘子法和罚函数法处理本质边界条件.采用本文提出的插值型无单元Galerkin法,对不同边界条件、不同厚跨比、不同材料参数的复合材料层合板的振动频率进行了计算,通过与文献结果对比验证了本文所提方法的有效性.     

用积分变换及边界积方法求解多层地基的静力问题

本文利用积分变换及矩阵递推方法得到了任意ｎ层弹性体平面应变及轴对称问题的ｍｉｎｄｌｉｎ解。再把此解作为基本解，利用Ｓｏｍｉｇｌｉａｎａ关系式，得到计算多层弹性体内部任意点位移的简便方法，利用此法很容易编制程序，且具有较高的计算精度与速度。     

多层膜结构对硬度实验影响的数值分析

为了研究多层膜结构对纳米微硬度实验的影响,用FEPG对纳米微硬度实验中压头的压入过程进行数值模拟,分析了由TiN,Al,Ti组成的多层膜中软膜材料不同、软膜与硬膜厚度比不同以及多层膜层数不同对膜层体系产生的影响,得出梯度变化的膜层结构能够提高膜层的整体性能,为纳米微硬度实验提供了一定的参考依据．     

三维沥青路面多层体系的黏弹性力学分析

基于改进的无单元Galerkin方法(Improved Element-Free Galerkin,简称IEFG),建立了三维沥青路面多层体系的黏弹性力学模型.对交通荷载作用下沥青混凝土路面的位移及应力进行了计算,分析了不同的节点数及影响域比例参数对计算结果的影响,得到了沥青路面多层体系计算模型的合适节点数目和影响域比例参数的选择范围.同时,分析了中面层厚度对路面抗车辙性能的影响.结果 表明:改进的无单元Galerkin方法在分析沥青路面黏弹性方面是有效的;节点数在1800以上、影响域比例参数在1.8～1.9之间取值时计算结果较好;中面层厚度越小,沥青路面车辙变形越大.本文结果可为沥青路面设计提供参考.     

STUDY ON PARAMETERS FOR TOPOLOGICAL VARIABLES FIELD INTERPOLATED BY MOVING LEAST SQUARE APPROXIMATION

This paper presents a new approach to the structural topology optimization of continuum structures. Material-point independent variables are presented to illustrate the existence condition,or inexistence of the material points and their vicinity instead of elements or nodes in popular topology optimization methods. Topological variables field is constructed by moving least square approximation which is used as a shape function in the meshless method. Combined with finite element analyses,not only checkerboard patterns and mesh-dependence phenomena are overcome by this continuous and smooth topological variables field,but also the locations and numbers of topological variables can be arbitrary. Parameters including the number of quadrature points,scaling parameter,weight function and so on upon optimum topological configurations are discussed. Two classic topology optimization problems are solved successfully by the proposed method. The method is found robust and no numerical instabilities are found with proper parameters.     

多层石墨烯水分散体系的摩擦磨损性能研究

采用液相超声直接剥离法制备了不同厚度的纳米石墨烯片,用SEM、TEM对其形貌进行了表征,利用多功能往复摩擦磨损试验仪考察了石墨烯水分散体系的摩擦磨损性能.通过SEM、EDS、XPS等手段,分析了磨损表面的形貌、元素组成和典型元素的化学状态,初步探讨了石墨烯水分散体系的润滑机理.结果表明:所制备的石墨烯为厚度不一的多层石墨烯混合物,厚度范围为10~180 nm;石墨烯作为水基添加剂具有良好的减摩抗磨性能,使纯水的磨损机理发生转变,由严重的黏着磨损和腐蚀磨损转变为磨粒磨损,主要原因是在石墨烯水分散体系润滑下,磨损表面形成吸附减摩层和摩擦化学反应膜,两者协同作用,抑制Fe的氧化,减轻摩擦磨损.     

激光陀螺捷联惯导系统多位置标定方法

在建立惯性仪表简化误差模型的基础上,提出了一种多位置标定方法.该方法充分考虑标定条件、设备以及时间等因素,设计了一种多位置连续转动标定方案,充分激励惯性仪表各项误差参数,从而建立起所有误差参数与系统导航误差之间的关系,通过测量每个位置静态导航状态下的速度误差,采用最小二乘估计,全面辨识出所有21个误差参数.理论分析和实验结果表明,与传统标定方法相比,该方法对标定设备要求低,无需北向基准,实现简单方便,在较短的时间内就可以一次标定出惯性仪表所有21个误差参数,标定精度与基于精密转台的标定精度相当,具有较强的工程实用性.     

弹性力学问题的局部 Petrov-Galerkin方法

提出了弹性力学平面问题的局部Petrov-Galerkin方法,这是一种真正的无网格方法。这种方法采和移动最小二乘近似函数作为试函数,并且采用移动最小二乘近似函数的权函数作为加权残值法加权函数;同时这种方法只包含中心在所考虑点处的规则局部区域上以及局部边界上的积分,所得系统矩阵是一个带状稀疏矩阵,该方法可以容易推广到求解非线性问题以及非均匀介质的力学问题。还计算了两个弹性力学平面问题的例子,给出了位移和能量的索波列夫模及其相对误差。所得计算结果证明：该方法是一种具有收敛快、精度高、简便有效的通用方法;在工程中具有广阔的应用前景。     

A meshless method of a thin plate

A meshless approach to analysis of arbitrary Kirchhoff plates by the local boundary integral equation(LBIE) method is presented. The method combines the advantageous features of, all the three methods: the Galerkin finite element method (GFEM), the boundary element method (BEM) and the element-free Galerkin method (EFGM). It is a truly meshless method, which means that the discretization is independent of geometric subdivision into elements or cells, but is only based on a set of nodes (ordered or scattered) over a domain in question. It involves only boundary integration, however, over a local boundary centered at the node in question; It poses no difficulties in satisfying the essential boundary conditions while leading to banded and sparse system matrices using the moving least square (MLS) approximations. It is shown that high accuracy can be achieved for arbitrary geometries for clamped and simply-supported edge conditions. The method is found to be simple, efficient, and attractive. Project supported by the National Science Foundation of China (No. 19972019).     

基于神经网络学习控制的液压转台偏载干扰的抑制

飞行仿真转台是将飞行器置于一定的实际飞行环境中,研究其传感器,控制系统及执行机构等硬件设备的动态性能和定位精度时所用的种混合仿真设备。哈尔滨工业大学研制的ＨＩＴ－１型三轴飞行仿真转台中框由于存在设计上不可避免的偏载负载力矩,影响了其响应速度和动静态精度的进一步提高。本文将学习控制和神经网络方法结合起来,既避免了前者对重复性的要求,又避免了后者对快速系统实时控制的困难,将其应用于对液压转台中框偏载干扰的抑制,取得了良好的仿真结果     

用无网格局部Petrov-Galerkin法分析非线性地基梁

利用无网格局部Petroy-Galerkin法求解了非线性地基梁.在Petroy-Galerkin方法中,采用移动最小二乘(MLS)近似函数作为场变量挠度的试函数并取移动最小二乘近似函数中的权函数作为近似场函数的加权函数,采用罚因子法施加本质边界条件.文末给出了两个计算实例,算例的结果表明,Petrov-Galerkin法不仅能成功地分析线性地基梁,而且也适用于求解非线性地基梁,在分析非线性地基梁时具有收敛快,稳定性好的优点.     

A STUDY ON THE WEIGHT FUNCTION OF THE MOVING LEAST SQUARE APPROXIMATION IN THE LOCAL BOUNDARY INTEGRAL EQUATION METHOD

The meshless method is a new numerical technique presented in recent years .It uses the moving least square (MLS) approximation as a shape function . The smoothness of the MLS approximation is determined by that of the basic function and of the weight function, and is mainly determined by that of the weight function. Therefore, the weight function greatly affects the accuracy of results obtained. Different kinds of weight functions, such as the spline function, the Gauss function and so on, are proposed recently by many researchers. In the present work, the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method. The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed. Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and a in Gauss and exponential weight functions are in the range of reasonable values, respectively, and the higher the smoothness of the weight function, the better the features of the solutions.     

A MESHLESS LOCAL PETROV-GALERKIN METHOD FOR GEOMETRICALLY NONLINEAR PROBLEMS

Nonlinear formulations of the meshless local Petrov-Galerkin （MLPG） method are presented for geometrically nonlinear problems. The method requires no mesh in computation and therefore avoids mesh distortion difficulties in the large deformation analysis. The essential boundary conditions in the present formulation axe imposed by a penalty method. An incremental and iterative solution procedure is used to solve geometrically nonlinear problems. Several examples are presented to demonstrate the effectiveness of the method in geometrically nonlinear problems analysis. Numerical results show that the MLPG method is an effective one and that the values of the unknown variable are quite accurate.     

Improved non-singular local boundary integral equation method

When the source nodes are on the global boundary in the implementation of local boundary integral equation method (LBIEM),singularities in the local boundary integrals need to be treated specially. In the current paper,local integral equations are adopted for the nodes inside the domain trod moving least square approximation (MLSA) for the nodes on the global boundary,thus singularities will not occur in the new al- gorithm.At the same time,approximation errors of boundary integrals are reduced significantly.As applications and numerical tests,Laplace equation and Helmholtz equa- tion problems are considered and excellent numerical results are obtained.Furthermore, when solving the Hehnholtz problems,the modified basis functions with wave solutions are adapted to replace the usually-used monomial basis functions.Numerical results show that this treatment is simple and effective and its application is promising in solutions for the wave propagation problem with high wave number.     

改进广义移动最小二乘近似的无网格法

无网格法是求解微分方程定解问题的一种新数值方法.移动最小二乘近似只要求近似函数在各节点处的误差的平方和最小,对近似函数导数的误差没有任何约束.而广义移动最小二乘近似要求近似函数及其导数在所有节点处的误差的平方和最小.为了降低计算工作量,本文构造了要求近似函数在全部节点处和任意阶导数在部分节点处误差的平方和最小的改进广义移动最小二乘近似.数值计算显示本文提供的方法关于函数值和各阶导数值都具有很高的精度.     

运用机器学习方法设计原子链 人工边界条件

本文运用机器学习方法设计一维线性原子链的人工边界条件。该方法基于前馈神经网络,通过对一小部分数值解进行训练后得到人工边界条件。应用该法不需要较多先验知识,编程简单,实现速度快,算例表明数值反射较小。