平面电磁弹性固体的虚边界元——最小二乘配点法

从电磁弹性固体平面问题的基本方程出发,依据弹性力学虚边界元法的基本思想,利用电磁弹性固体平面问题的基本解,提出了电磁弹性固体平面问题的虚边界元——最小二乘配点法。电磁弹性固体的虚边界元法在继承传统边界元法优点的同时,有效地避免了传统边界元法的边界积分奇异性的问题。由于仅在虚实边界选取配点,此方法不需要网格剖分,并且不用进行积分计算。最后给出了一些具体算例,并和已有的解析解进行了对比,结果表明提出的虚边界元方法有很高的精度。     

基于区域分解的快速多极基本解法预测发动机表面辐射声场

针对发动机表面结构复杂,多狭长边界,用通常算法求解源点分布无法保障基本解法计算精度问题,提出改进的计算源点分布算法,利用区域分解处理影响基本解计算精度的狭长边界;结合快速多极算法,形成适于三维复杂表面辐射声场预测基于区域分解的快速多极基本解法。利用区域分解求解发动机计算模型的源点分布,在源点分布已知基础上利用快速多极基本解法预测发动机表面辐射声场。结果表明,利用区域分解求得源点与配置点最优距离为34.5mm,可提高发动机辐射声场预报精度;截断项数为15时可避免截断项数过小引起的低频不稳定,并保证计算效率;不同于快速多极边界元用网格加密提高计算精度,基于区域分解的快速多极基本解法通过区域分解进行优化源点分布可提高精度,且不增加计算负担。通过发动机表面辐射噪声实验,计算值与实验值吻合较好,说明该解法可提高发动机表面辐射声场的预测精度。     

消声器传递损失预测的边界元数值配点混合方法

将边界元法与数值配点法结合形成混合方法用于计算任意截面形状消声器的传递损失。消声器划分为若干子结构,用边界元法计算具有非规则形状的子结构阻抗矩阵,用二维有限元法提取等截面子结构特征值及特征向量,用配点法获得阻抗矩阵;将每个子结构阻抗矩阵连接用于传递损失计算。为减少计算时间提出简化方法计算消声器传递损失。结果表明,混合法在保证计算精度前提下可节省计算时间。     

初应力最小二乘配点法解弹塑性轴对称问题

本文用初应力最小二乘配点法求解并讨论了承受均布及线性分布载荷的弹塑性轴对称问题，数字算例表明，此种方法是成功的，本文的计算程序可应用于工程设计计算。     

基于最小二乘法的GPS多天线测姿及精度分析

阐述GPS测姿基本原理和采用多天线测姿方法,针对影响GPS测姿精度因素进行分析,提出应用最小二乘法进行载体姿态参数计算和动态模糊度解算的方法.比对试验和精度分析表明,使用最小二乘法进行载体姿态确定是最优的,使用最小二乘搜索法进行动态模糊度解算是非常有效的.     

复合材料序列图像的分层次配准

在复合材料图像三维重构技术中,为了避免直接运用基于特征点的整体配准陷入局部极优,采用分层次的配准方法.首先使用不变矩计算出上下层图像中最相似的颗粒轮廓,然后使用主轴的配准方法完成上下层图像的初步配准,以大幅度减少特征点配准中的优化搜索范围.在计算出轮廓曲线上特征点的基础上,应用最大熵原理和lagrange乘子将点集之间的匹配转化为一个能量函数,再使用最小二乘法计算出使该能量函数值最小的空间变换,得到配准的最优解,从而实现了序列图像的整体精确配准.实验结果表明,本文提出的分层次的配准方法极大地降低了配准过程陷入局部极优的概率,具有较强的鲁棒性和较高的配准精度.     

复合材料层合板自由振动的薄板样条无网格解

无网格全局配点法分为多项式配点法和径向基函数配点法,国内外很多文献利用径向基函数配点法对复合材料层合板进行了分析。利用一阶剪切变形理论和基于薄板样条径向基函数的无网格配点法计算了复合材料层合板自由振动的固有频率和振型。研究了薄板样条径向基函数中形状参数的选取和本工作方法的收敛性。结果表明:形状参数m=3时收敛性最好,计算精度最高。将本工作计算结果与文献中的实验结果进行了对比,验证了本文方法的精度和效率。     

正交层板弯曲问题的一种半解析法

本文提出了一个完全满足对称正交层合板弯曲基本方程的挠度级数表达式,并导出了相应的位移、变形及内力的显表达式。边界条件则用离散型最小二乘法近似满足。由于所用级数较简单且具备完备性,因而推导与计算都较简单,对于各种边界条件下的单连通板,它都能逼近其精确解。文中的例子表明,本方法往往用较少的待定系数及配点,就可获得相当好的结果。     

边界元中近奇异积分的一种解析方法

准确求解边界元方法中的近奇异积分是一个非常重要的问题。一般情况下,分析中涉及到的常规积分采用高斯方法即可获得较高的精度。但当源点位于边界附近时,采用高斯积分就会使计算结果精度大大降低,甚至得出错误的结果。对于平面问题,以源点作为原点,以所积分单元的切向和法向为坐标轴建立局部坐标系,对于线性单元可以得到所有积分的解析解。基于除角点外的所有边界点的场变量在边界上连续且有界的特点,所有在边界上引起场变量奇异的项之和必为零,故对于边界上的点可以直接在解析解中删除这些奇异项即可。算例表明,该方法可大大提高边界元的计算精度和效率。     

两种减少无单元法计算中数值误差的方法

基于无单元法的发展历史和基本理论,讨论了在无单元法计算中起重要作用的A矩阵的几种取值情况,及其对滑动最小二乘法模拟精度的影响,并修正了滑动最小二乘法计算过程中容易产生数值误差的地方。确定了影响A矩阵的几种极端的布点形式,说明了形函数的值与计算点坐标无关的而只与插值点与计算点的相对坐标相关的性质,并给出了数学理论上或数值上的证明。这对无单元法模拟函数滑动最小二乘法的模拟精度有重要的理论价值和实践意义。     

A hybrid finite difference and moving least square method for elasticity problems

In this paper, a novel hybrid finite difference and moving least square (MLS) technique is presented for the two-dimensional elasticity problems. A new approach for an indirect evaluation of second order and higher order derivatives of the MLS shape functions at field points is developed. As derivatives are obtained from a local approximation, the proposed method is computationally economical and efficient. The classical central finite difference formulas are used at domain collocation points with finite difference grids for regular boundaries and boundary conditions are represented using a moving least square approximation. For irregular shape problems, a point collocation method (PCM) is applied at points that are close to irregular boundaries. Neither the connectivity of mesh in the domain/boundary or integrations with fundamental/particular solutions is required in this approach. The application of the hybrid method to two-dimensional elastostatic and elastodynamic problems is presented and comparisons are made with the boundary element method and analytical solutions.     

Least‐squares collocation meshless method

A finite point method, least‐squares collocation meshless method, is proposed. Except for the collocation points which are used to construct the trial functions, a number of auxiliary points are also adopted. Unlike the direct collocation method, the equilibrium conditions are satisfied not only at the collocation points but also at the auxiliary points in a least‐squares sense. The moving least‐squares interpolant is used to construct the trial functions. The computational effort required for the present method is in the same order as that required for the direct collocation, while the present method improves the accuracy of solution significantly. The proposed method does not require any mesh so that it is a truly meshless method. Three numerical examples are studied in detail, which show that the proposed method possesses high accuracy with low computational effort. Copyright © 2001 John Wiley & Sons, Ltd.     

结构声辐射计算的边界无网格法

研究函数有限维逼近插值形函数的一般要求,介绍采用移动最小二乘构建无网格插值形函数的方法与步骤;通过配点法将Kirchhoff-Helmholtz边界积分方程离散为受边界条件约束的线性方程组;最后通过分块矩阵法求解约束方程组,得到离散后的声辐射传输模型数值表达式。在计算实例中,分别用边界无网格法和边界元法建立声辐射传输模型进行声场计算,计算声场值与解析值相对比的结果表明,由于边界无网格法插值形函数根据求解情况自行构建,因此更灵活,具有更高的插值和计算精度。     

The method of fundamental solutions for inverse 2D Stokes problems

A numerical scheme based on the method of fundamental solutions is proposed for the solution of two-dimensional boundary inverse Stokes problems, which involve over-specified or under-specified boundary conditions. The coefficients of the fundamental solutions for the inverse problems are determined by properly selecting the number of collocation points using all the known boundary values of the field variables. The boundary points of the inverse problems are collocated using the Stokeslet as the source points. Validation results obtained for two test cases of inverse Stokes flow in a circular cavity, without involving any iterative procedure, indicate the proposed method is able to predict results close to the analytical solutions. The effects of the number and the radius of the source points on the accuracy of numerical predictions have also been investigated. The capability of the method is demonstrated by solving different types of inverse problems obtained by assuming mixed combinations of field variables on varying number of under- and over-specified boundary segments.     

Isoparametric finite point method in computational mechanics

In this paper, a new meshless method, the isoparametric finite point method (IFPM) in computational mechanics is presented. The present IFPM is a truly meshless method and developed based on the concepts of meshless discretization and local isoparametric interpolation. In IFPM, the unknown functions, their derivatives, and the sub-domain and its boundaries of an arbitrary point are described by the same shape functions. Two kinds of shape functions that satisfy the Kronecker-Delta property are developed for the scattered points in the domain and on the boundaries, respectively. Conventional point collocation method is employed for the discretization of the governing equation and the boundary conditions. The essential (Dirichlet) and natural (Neumann) boundary conditions can be directly enforced at the boundary points. Several numerical examples are presented together with the results obtained by the exact solution and the finite element method. The numerical results show that the present IFPM is a simple and efficient method in computational mechanics.     

Virtual boundary meshless least square integral method with moving least squares approximation for 2D elastic problem

Moving least squares approximation (MLSA) has been widely used in the meshless method. The singularity should appear in some special arrangements of nodes, such as the data nodes lie along straight lines and the distances between several nodes and calculation point are almost equal. The local weighted orthogonal basis functions (LWOBF) obtained by the orthogonalization of Gramm–Schmidt are employed to take the place of the general polynomial basis functions in MLSA. In this paper, MLSA with LWOBF is introduced into the virtual boundary meshless least square integral method to construct the shape function of the virtual source functions. The calculation format of virtual boundary meshless least square integral method with MLSA is deduced. The Gauss integration is adopted both on the virtual and real boundary elements. Some numerical examples are calculated by the proposed method. The non-singularity of MLSA with LWOBF is verified. The number of nodes constructing the shape function can be less than the number of LWOBF and the accuracy of numerical result varies little.     

A dual reciprocity hybrid radial boundary node method based on radial point interpolation method

A novel truly meshless method called dual reciprocity hybrid radial boundary node method (DHRBNM) is developed in present, which combines dual reciprocity method (DRM), hybrid boundary node method (HBNM) and radial point interpolation method (RPIM). Compared to the dual reciprocity hybrid boundary node method (DHBNM), RPIM is exploited to replace the moving least square in DHRBNM, unlike HBNM, the shape function obtained by present method has the delta function property, so the boundary conditions can be applied directly and easily, and computational expense is greatly reduced. In order to get the interpolation property of different basis function in DRM, different approximate functions are applied in DRM for comparison, and the accuracy and efficiency of them are discussed. Besides, RPIM is also exploited in DRM, which can greatly improve the accuracy of present method. Moreover, the accuracy of DRM is greatly influenced by the nodes number and their location, hence, some examples are investigated to show that the internal node number is equal to boundary node number and they are arranged parallel to the high gradient direction of the problem are the best choice. Finally, DHBNM is applied for comparison and some selected numerical examples are given to illustrate that the present method is efficient and less computational expense than that of DHBNM.     

Study of radial basis collocation method for wave propagation

A numerical method based on radial basis functions and collocation method is proposed for wave propagation. Standard collocation and weighted boundary collocation approaches yield significant errors in wave problems. Therefore, a new method based on explicit time integration scheme that can correct the inaccuracy in the solutions and the errors accumulated in time integration is developed. This method can be easily applied for low and high dimensional wave problems. The stability conditions are obtained and the relationships between control parameters and stability are evaluated. Requirement of collocation points in numerical dispersion is studied and nondispersion condition is formulated. Eigenvalue analysis is investigated to evaluate the effectiveness of radial basis collocation method for solving wave problems. Eigenvalue study with and without imposing the boundary conditions are compared. The influences of shape parameters and distribution of collocation points and source points are presented. Numerical examples are simulated to examine and validate the proposed method.     

Determination of free surface and gravitational flow of liquid in triangular groove

The solution comprises of two parts. First, for a given groove's basal angle, liquid-solid contact angle, and the Bond number, the shape of free surface is determined starting from the Young-Laplace equation. The optimization technique as developed formerly is applied. Then, having determined the shape of the free surface and slope of the groove, the distribution of fluid flow is determined. The boundary value problem is solved using boundary collocation method in least square sense. Given the distribution of fluid velocity the friction factor as a function of the other parameters of the model is analyzed. Received 25 November 1998     

A robust local polynomial collocation method

In this paper, a robust local polynomial collocation method is presented. Based on collocation, this method is rather simple and straightforward. The present method is developed in a way that the governing equation is satisfied on boundaries as well as boundary conditions. This requirement makes the present method more accurate and robust than conventional collocation methods, especially in estimating the partial derivatives of the solution near the boundary. Studies about the sensitivity of the shape parameter and the local supporting range in the moving least square approach and the convergence of the nodal resolution are carried out by using some benchmark problems. This method is further verified by applying it to a steady‐state convection–diffusion problem. Finally, the present method is applied to calculate the velocity fields of two potential flow problems. More accurate numerical results are obtained.Copyright © 2012 John Wiley & Sons, Ltd.