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.

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.

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.

Criteria for Weighted Moving-Mean Method

The moving-mean method is one of the conventional approaches for trend-extraction from a data set. It is usually applied in an empirical way. The smoothing degree of the trend depends on the selections of window length and weighted coefficients, which are associated with the change pattern of the data. Are there any uniform criteria for determining them? The present article is a reaction to this fundamental problem. By investigating many kinds of data, the results show that: 1) Within a certain range, the more points which participate in moving-mean, the better the trend function. However, in case the window length is too long, the trend function may tend to the ordinary global mean. 2) For a given window length, what matters is the choice of weighted coefficients. As the five-point case concerned, the local-midpoint, local-mean and global-mean criteria hold. Among these three criteria, the local-mean one has the strongest adaptability, which is suggested for your usage.

动能侵彻弹装药起爆可靠性试验及敏感因素分析

为研究弹体结构设计对弹体装药起爆可靠性的影响,设计了一种低成本、便捷式引战静态匹配试验装置,开展了不同条件下引信与装药的传爆裕度试验。基于移动最小二乘法,构建了可表征起爆可靠性的多变量响应函数,定量分析了各敏感因素及其耦合作用对起爆可靠性的影响规律。结果表明:传爆间隙和缓冲层厚度对弹体装药起爆影响较大,而隔板厚度在预设3~5 mm范围内的影响较小;为保证动能侵彻弹在使用环境温度范围内可靠作用,引信相对偏离位置、隔板厚度、传爆间隙以及缓冲层厚度分别不应超过25、3.5、25以及22 mm。该试验装置、分析方法及研究成果可为动能侵彻弹结构设计及可靠性验证提供借鉴和指导。

基于改进对流粒子域插值物质点法的隧道大变形分析

物质点法(MPM)在模拟大变形问题时具有很好的效果,然而传统的MPM在粒子穿越网格边界时存在单元穿越误差,导致精度降低。为克服传统MPM的单元穿越误差,基于对流粒子域插值物质点法(CPDI)理论框架,采用自适应正交改进插值移动最小二乘法(AOIIMLS),提出了改进CPDI方法。AOIIMLS通过构造加权正交基函数,并且忽略了新对角矩阵中的零元素或极小元素的贡献,以避免求解逆矩阵,增强了鲁棒性。改进CPDI采用速度梯度计算粒子域的速度场,粒子速度和粒子域角点速度用于重构背景网格速度函数。通过一维柱在自重作用下的压缩、砂柱坍塌和隧道坍塌离心机试验验证了改进CPDI方法的准确性和适用性,结果表明改进CPDI降低了单元穿越误差,得到了更高的精度。最后,采用改进CPDI方法模拟了青岛地铁4号线静沙区间地面塌陷全过程,验证了改进CPDI方法在岩土工程大变形领域的适用性及优势。

矿区地表形变时空演化分析方法研究

用传统监测方法获取的离散点数据只能描述特定时间的空间形变状态,无法反映矿区地表形变整体时空演化。本文介绍了一种矿区地表形变时空模型的构建方法,通过对空间多项式引入时间项变为时空多项式,并基于移动最小二乘法顾及局部特征,提出时空多项式和移动最小二乘法结合完成模型拟合。实验分析表明,选取合适时空项阶次的模型具有良好的拟合精度,实现了对矿区地表形变的时空趋势拟合,能够直观地反映矿区地表形变的整体时空演化趋势和规律。

基于光谱共焦的缸套内表面微织构形貌在线测量方法研究

为实现缸套内表面微织构形貌的在线检测,设计一种非接触式测量系统。采用基于EtherCAT通信协议开发的伺服系统,通过高精度伺服电机带动光谱共焦位移传感器,一次采集多个微织构的不同截面轮廓,经特征提取与坐标变换,形成单个织构的三维点云数据。通过光强值出现局部极小值确定边缘位置,采用稳健高斯回归滤波方法滤除误差,使用移动最小二乘法拟合曲面,最终获得微织构的精准三维形貌。试验结果表明:该系统与超景深显微镜测得的直径最大差值为5.7μm,深度最大差值为0.45μm,具有较高的重复性和精度,可作为缸套内表面微织构形貌在线检测的一种手段。

汽车道路滑行阻力测量滤波算法研究

底盘测功机作为一种重要的室内测试设备,准确的道路载荷阻力系数是其精确工作的先决条件。目前经常使用VBOX测量道路载荷阻力系数。VBOX测速依赖于精确的卫星定位来实现,日常使用中卫星信号易受环境干扰,导致测量精度下降,影响试验结果的准确性。本文通过研究小波变换、最小二乘法滤波、滑动平均值滤波三种滤波算法对试验数据处理效果和稳定性的影响,得出:(1)三种滤波算法对于滑行试验数据稳定性都有着明显的提升;(2)对于单独的滑行工况,最小二乘法滤波表现最为优异;(3)对于复杂工况,小波滤波和滑动平均滤波都可进行较好的滤除噪声信号,但是小波滤波算法不易受极值影响。

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.

ANALYSIS OF 2-D THIN STRUCTURES BY THE MESHLESS REGULAR HYBRID BOUNDARY NODE METHOD

Thin structures are generally solved by the Finite Element Method(FEM), using plate or shell finite elements which have manylimitations in applications, such as numerical locking, edge effects,length scaling and the cnvergence problem. Recently, by proposing anew approach to tranting the nearly- singular integrals, Liu et al.developed a BEM to successfully solve thin structures with thethickness-to- length ratios in the micro-or nano-scales. On the otherhand, the meshless Regular Hybrid Boundary Node Method (RHBNM), whichis proposed by the current authors and based on a modified functionaland the Moving Least-Square (MLS) approximation, has very promisingapplications for engineering problems owing To its meshless natureand dimension-reduction advantage, and not involving any singular ornearly-singular Integrals. Test examples show that the RHBNM can alsobe applied readily to thin structures with high accu- Racy withoutany modification.

A 3D shell-like approach using element-free Galerkin method for analysis of thin and thick plate structures

A new efficient meshless method based on the element-free Galerkin method is proposed to analyze the static deformation of thin and thick plate structures in this paper. Using the new 3D shell-like kinematics in analogy to the solid-shell concept of the finite element method, discretization is carried out by the nodes located on the upper and lower surfaces of the structures. The approximation of all unknown field variables is carried out by using the moving least squares （MLS） approximation scheme in the in-plane directions, while the linear interpolation is applied through the thickness direction. Thus, different boundary conditions are defined only using displacements and penalty method is used to enforce the essential boundary conditions. The constrained Galerkin weak form, which incorporates only dis- placement degrees of freedom （d.o.f.s）, is derived. A modified 3D constitutive relationship is adopted in order to avoid or eliminate some self-locking effects. The numeric efficiency of the proposed meshless formulation is illustrated by the numeric examples.

AN IMPROVED HYBRID BOUNDARY NODE METHOD IN TWO-DIMENSIONAL SOLIDS

The hybrid boundary node method （HBNM） is a promising method for solving boundary value problems with the hybrid displacement variational formulation and shape functions from the moving least squares（MLS） approximation. The main idea is to reduce the dimensionality of the former and keep the meshless advantage of the latter. Following its application in solving potential problems, it is further developed and numerically implemented for 2D solids in this paper. The rigid movement method is employed to solve the hyper-singular integrations. Numerical examples for some 2D solids have been given to show the characteristics. The computation results obtained by the present method are in excellent agreement with the analytical solution. The parameters that influence the performance of this method are studied through numerical examples.

NUMERICAL ANALYSIS OF MINDLIN SHELL BY MESHLESS LOCAL PETROV-GALERKIN METHOD

The objectives of this study are to employ the meshless local Petrov-Galerkin method （MLPGM） to solve three-dimensional shell problems. The computational accuracy of MLPGM for shell problems is affected by many factors, including the dimension of compact support domain, the dimension of quadrture domain, the number of integral cells and the number of Gauss points. These factors＇ sensitivity analysis is to adopt the Taguchi experimental design technology and point out the dimension of the quadrature domain with the largest influence on the computational accuracy of the present MLPGM for shells and give out the optimum combination of these factors. A few examples are given to verify the reliability and good convergence of MLPGM for shell problems compared to the theoretical or the finite element results.

Meshless analysis of an improved element-free Galerkin method for linear and nonlinear elliptic problems

We first give a stabilized improved moving least squares （IMLS） approximation, which has better computational stability and precision than the IMLS approximation. Then, analysis of the improved element-free Galerkin method is provided theoretically for both linear and nonlinear elliptic boundary value problems. Finally, numerical examples are given to verify the theoretical analysis.

LOCAL PETROV-GALERKIN METHOD FOR A THIN PLATE

The meshless local Petrov_Galerkin (MLPG) method for solving the bending problem of the thin plate were presented and discussed. The method used the moving least_squares approximation to interpolate the solution variables, and employed a local symmetric weak form. The present method was a truly meshless one as it did not need a finite element or boundary element mesh, either for purpose of interpolation of the solution, or for the integration of the energy. All integrals could be easily evaluated over regularly shaped domains (in general, spheres in three_dimensional problems) and their boundaries. The essential boundary conditions were enforced by the penalty method. Several numerical examples were presented to illustrate the implementation and performance of the present method. The numerical examples presented show that high accuracy can be achieved for arbitrary grid geometries for clamped and simply_supported edge conditions. No post processing procedure is required to computer the strain and stress, since the original solution from the present method, using the moving least squares approximation, is already smooth enough.