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 α 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.

Assessing dynamic response of multispan viscoelastic thin beams under a moving mass via generalized moving least square method

Dynamic response of multispan viscoelastic thin beams subjected to a moving mass is studied by an efficient numerical method in some detail. To this end, the unknown parameters of the problem are discretized in spatial domain using generalized moving least square method （GMLSM） and then, discrete equations of motion based on Lagrange＇s equation are obtained. Maximum deflection and bending moments are considered as the important design parameters. The design parameter spectra in terms of mass weight and velocity of the moving mass are presented for multispan viscoelastic beams as well as various values of relaxation rate and beam span number. A reasonable good agreement is achieved between the results of the proposed solution and those obtained by other researchers. The results indicate that, although the load inertia effects in beams with higher span number would be intensified for higher levels of moving mass velocity, the maximum values of design parameters would increase either. Moreover, the possibility of mass separation is shown to be more critical as the span number of the beam increases. This fact also violates the linear relation between the mass weight of the moving load and the associated design parameters, especially for high moving mass velocities. However, as the relaxation rate of the beam material increases, the load inertia effects as well as the possibility of moving mass separation reduces.

ELASTO-PLASTICITY ANALYSIS BASED ON COLLOCATION WITH THE MOVING LEAST SQUARE METHOD

A meshless approach based on the moving least square method is developed for elasto-plasticity analysis,in which the incremental formulation is used.In this approach,the dis- placement shape functions are constructed by using the moving least square approximation,and the discrete governing equations for elasto-plastic material are constructed with the direct collo- cation method.The boundary conditions are also imposed by collocation.The method established is a truly meshless one,as it does not need any mesh,either for the purpose of interpolation of the solution variables,or for the purpose of construction of the discrete equations.It is simply formu- lated and very efficient,and no post-processing procedure is required to compute the derivatives of the unknown variables,since the solution from this method based on the moving least square approximation is already smooth enough.Numerical examples are given to verify the accuracy of the meshless method proposed for elasto-plasticity analysis.

Calculation of stratum surface principal curvature based on a moving least square method

With the east section of the Changji sag Zhunger Basin as a case study, both a principal curvature method and a moving least square method are elaborated. The moving least square method is introduced, for the first time, to fit a stratum surface. The results show that, using the same-degree base function, compared with a traditional least square method, the moving least square method can produce lower fitting errors, the fitting surface can describe the morphological characteristics of stratum surfaces more accurately and the principal curvature values vary within a wide range and may be more suitable for the prediction of the distribution of structural fractures. The moving least square method could be useful in curved surface fitting and stratum curvature analysis.

二维MLSPH无网格方法

给出MLSPH无网格方法的控制方程、移动最小二乘近似、MLSPH守恒格式等,重点研究MLSPH守恒格式中MLS面积向量的数值求解方法,以提高求解的精度.对激波管问题和平面Noh问题进行模拟,得到较好的结果,确定用三次样条积分公式计算面积向量.

基于MLS拟合带容差的测量数据加工刀位面生成算法

传统的刀位面生成算法无法直接生成存在缺陷的离散数据的刀位面,因此,针对球头铣刀提出了一种基于MLS拟合带容差的离散数据加工刀位面生成算法。该方法首先依据球头铣刀构造离散数据的点膨胀球模型,然后根据凸包原理获取该模型的最外层包络面,最终通过MLS投影拟合方法剔除奇异点、修补裂缝,生成刀位面网格模型。实例表明,该算法具有较高的稳定性,能够有效解决存在缺陷的离散数据刀位面生成问题,适用于实际工程应用加工。

新型无网格法(IMLS方形域法)的研究及其应用

根据最新无网格法的前沿研究,提出了一种新型无网格法-IMLS方形域法。该法在场函数近似、权函数选取以及方形域数值积分等方面给出了全新的格式。方法中未知变量的近似采用IMLS技术,局部影响域形状采用方形几何形态。这些技术的具体实施展现了节点布置和数值积分的无网格特点,并自然满足Dirichlet边界条件。该方法可以容易求解偏微分方程初值或边值问题上实现,此外,计算了一维固结问题、二维弹性力学平面问题的算例,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。

基于MLS改进算法的曲线拟合技术研究

针对散乱点拟合曲线的算法问题,分析了移动最小二乘逼近法(MLS)的特点,提出了用MLS改进算法对散乱点进行曲线拟合,并结合实例进行了验证.结果表明,MLS改进算法在拟合曲线时,选取不同阶的基函数和不同的权函数,在保证精度和光滑度的基础上,解决了传统曲线拟合方法在拟合曲线时出现的运算不稳定现象,显示了MLS改进算法在曲线拟合中的优越性.

基于MLS的FLAC3D复杂三维地质建模

针对岩土力学分析软件FLAC3D建模效率较低的不足之处,在分析FLAC3D建模命令以及网格模型*.FLAC3D文件格式特点的基础上,介绍了空间坐标变换、MLS插值的方法与意义,并提出了新的建模方法,开发了相应的计算机辅助建模程序。该程序直接读取原始数据点,无需借助第三方软件,通过坐标变换、MLS插值,可快速生成具有复杂边界的地质模型,且便于材料参数和应力边界条件参数的赋值,可有效地提高工作效率。

IMLS方形影响域法

展示了一些最新无网格法的研究进展,给出了一种新型无网格法-IMLS方形域无网格法。该法中未知变量的近似采用IMLS技术,局部影响域形状采用方形几何形态。这些技术的具体实施展现了节点布置和数值积分的无网格特点,并自然满足Dirichlet边界条件。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。此外,还计算了两个弹性力学平面问题的例子,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。

求解重调和方程的混合MLS方法

以重调和方程的混合变分形式为基础,采用移动最小二乘方法建立插值形函数空间,给出了重调和方程的混合MLS数值解法。这种方法降低了对解空间的光滑度要求,同时高精度地获得了解的高阶导数值,并且避免了求解过程中划分网格所带来的计算复杂性等问题。最后给出了这一方法的误差估计。

基于MLS的航空叶片中弧线提取方法

航空发动机叶片是高性能航空发动机的核心部件,其几何形状和加工精度对航空发动机的使用性能有很大影响。因其特殊的工作环境和功能要求,一般将其设计加工为变截面、强扭曲、薄壁曲面,其中弧线是表征其几何形状的重要参数之一,如何快速高效地提取叶片截面中弧线参数已成为航空叶片检测中亟待解决的关键问题。为此结合移动最小二乘法(MLS)提取中弧线,该方法首先将叶片二维截面点云进行分段处理,并通过带影响域的移动最小二乘对叶盆、叶背稀疏点进行加密,进而利用等距曲线原理提取航空叶片中弧线参数。同时就中弧线提取算法精度评价和噪声影响进行分析。

泥石流平均流速的MLS模型预测

泥石流的流速预测是泥石流灾害防治的核心问题之一。由于泥石流流速的影响因素众多,需要寻求能够综合反映泥石流流速影响因素的预测模型。移动最小二乘法(MLS)预测模型具有自学习和自组织及捕捉到影响因素数值微小变化的能力,可以解决泥石流流速预测存在的一些问题。采用云南蒋家沟泥石流流速实测数据作为训练样本和预测样本,以泥深、比降、密度、颗粒的平均粒径作为输入因子。讨论了用MLS方法进行泥石流平均流速预测的可行性与有效性,并将预测结果与经验公式、BP神经网络以及支持向量机进行了对比。结果表明,MLS方法的最大预测误差为4.6%,平均误差为2.7%,预测精度优于经验公式、BP神经网络及支持向量机方法。MLS方法可以为泥石流防治提供更准确的科学依据。

无网格法中SPH法和MLS法的对比

无网格法是近期发展起来的一种数值计算方法,其的形函数构造有多种方法。为此,着重介绍了较常用的两种方法:移动最小二乘法(MLS)和光滑粒子法(SPH),并对这两种不同的方法进行了阐述,对比了这两种插值函数的异同,最后又用数值算例对其计算精度进行了比较。

基于MLS的三维扩展目标PMBM跟踪算法

针对传统三维扩展目标跟踪算法形状估计精度低的问题,提出了一种基于移动最小二乘的泊松多伯努利混合(Poisson multi-Bernoulli mixture based on the moving least square,MLS-PMBM)滤波跟踪算法。该算法基于MLS模型构建三维扩展目标的形状矩阵,通过PMBM滤波器预测和更新目标的运动状态,利用移动最小二乘算法更新形状矩阵,结合目标质心状态与形状估计完成对三维扩展目标的跟踪。仿真实验与实际点云数据的验证表明,与现有算法相比,本文所提算法在多扩展目标的形状估计方面具有更优的性能,具有较高的泛用性。

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.

A meshless algorithm with moving least square approximations for elliptic Signorini problems

Based on the moving least square （MLS） approximations and the boundary integral equations （BIEs）, a meshless algorithm is presented in this paper for elliptic Signorini problems. In the algorithm, a projection operator is used to tackle the nonlinear boundary inequality conditions. The Signorini problem is then reformulated as BIEs and the unknown boundary variables are approximated by the MLS approximations. Accordingly, only a nodal data structure on the boundary of a domain is required. The convergence of the algorithm is proven. Numerical examples are given to show the high convergence rate and high computational efficiency of the presented algorithm.

非连续变形分析的MLS后处理方法

非连续变形分析(discontinuous deformatrion analysis,DDA)通过引入虚拟节理网格将块体离散成子块体系统进行断裂扩展数值模拟.针对这种方法难以获得精确块体应力分布的问题,提出一种基于无网格法移动最小二乘(moving least squares,MLS)插值的应力恢复算法.利用DDA计算得到的节点位移,通过恰当构造MLS形函数及其导数,推导了块体任意点应力的计算公式.数值算例将基于MLS后处理的结果与解析解及平均值法后处理结果进行比较,验证了所提出方法的精确性和有效性.

Global interpolating meshless shape function based on generalized moving least-square for structural dynamic analysis

A global interpolating meshless shape function based on the generalized moving least-square （GMLS） is formulated by the transformation technique. Both the shape function and its derivatives meet the Kronecker delta function property. With the interpolating GMLS （IGMLS） shape function, an improved element-free Galerkin （EFG） method is proposed for the structural dynamic analysis. Compared with the conven- tional EFG method, the obvious advantage of the proposed method is that the essential boundary conditions including both displacements and derivatives can be imposed by the straightforward way. Meanwhile, it can greatly improve the ill-condition feature of the standard GMLS approximation, and provide good accuracy at low cost. The dynamic analyses of the Euler beam and Kirchhoff plate are performed to demonstrate the feasi- bility and effectiveness of the improved method. The comparison between the numerical results of the conventional method and the improved method shows that the proposed method has better stability, higher accuracy, and less time consumption.

基于MLS无网格思想的数值流形方法

介绍了一种基于无网格思想的数值流形方法。用移动最小二乘法(MLS)构造插值函数,罚函数法处理位移边界条件,根据变分原理导出整体离散方程,最后用算例验证本文方法是可行的。