RPIM-FEM耦合法在电机运动问题的应用

有限单元法在计算电机定、转子运动问题的时候,遇到了困难.运动时,定、转子的相对角度不断的改变,对不同转角的转子要进行多步的电磁场计算.而运动会造成气隙单元发生畸变,造成了有限元法求解运动问题时前处理复杂;由于不需要构成单元,无单元法可从根本上消除由转子位置变化引起的网格扭转变形.可将无单元法同有限元法耦合来求解运动问题,在气隙使用无单元法,在其他区域使用有限元网格.采用径向基点插值型无单元法(RPIM)和有限元(FEM)直接耦合方法来解决定、转子之间相对运动问题.计算结果证明,该耦合方法的计算精度满足要求.将其应用在电机电磁场数值计算中,可解决由于有限元法气隙单元畸变产生的误差.     

预报振动噪声的径向基点插值无网格与无限元耦合方法

为克服传统的有限元耦合无限元方法中的单元匹配问题,研究了径向基点插值法和无限元法的耦合规律,提出了一种预报无限域结构振动噪声的径向基点插值无网格与可变阶无限声波包络单元耦合方法,推导了预报声压的计算公式。为提高声场预报精度和满足声波在无限域的自由衰减,结构外部无限声场分为使用无网格表示的近场和可变阶声波包络单元离散的远场。在该耦合方法中,通过在近场与远场之间的交界面上配置虚拟网格来构造具有连续性的声压形函数,确保了声压的连续与一致性。采用数值仿真和试验对该耦合方法进行了验证,结果表明该耦合方法拥有无网格法的高精度和可变阶声波包络单元法满足声波自由衰减的特点,具有良好的精度和收敛性,可用于实际噪声预报。     

Mesh‐free radial point interpolation method for the buckling analysis of Mindlin plates subjected to in‐plane point loads

In this paper, a mesh‐free approach is employed for buckling analysis of Mindlin plates that are subjected to in‐plane point loads. The radial point interpolation method (RPIM) is used to approximate displacements based on nodes. Variational forms of the system equations are established. Two‐step solution procedures are implemented. The non‐uniform pre‐stress distribution of plate is first obtained using the RPIM based on a two‐dimensional (2D) elastic plane stress problem. This predetermined non‐uniform pre‐stress distribution is then used to compute buckling loads of plate using the RPIM based on Mindlin's plate assumption. The RPIM can easily handle any number and location of nodes in the plate domain for a desired computational accuracy without major difficulties in solving the initial stresses and buckling loads. Numerical examples considered here include circular and rectangular Mindlin plates that are subjected to in‐plane uniform and point loads with different aspect ratios and boundary conditions. The present results are validated against the available analytical and numerical solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

基于RPIM 法的圆极化天线特性参数快速测试

为提高圆极化天线特性参数的测试精度,线极化分量法往往需要对线分量场进行多次测量。文中在天线测试系统中引入插值算法,减少采样点,提高圆极化天线测试效率。将径向基函数的点插值无网格(RPIM)法引入圆极化天线参数合成算法中,首先使用RPIM 拟合出测试场的幅值和相位,然后再使用解析的方式合成圆极化天线的轴比和方向图,算法性能与基于分段线性插值技术的模型参数估计法(MBPE)和基于三次样条插值的移动最小二乘法(MLS)进行比较,数值实验显示,当采样点数仅为测试点数的4%时,MLS 失效,MBPE 和RPIM 误差均为10-3量级;而当采样点数减少为测试点数的2%时,MBPE 和MLS 均失效,RPIM 的误差虽然增大到10-1 量级,但仍能保持稳定。数值实验证明,在采样点数较少情况下,RPIM 性能优于其它两种算法。     

基于无网格界面模拟方法的面板坝防渗体跨尺度分析

混凝土面板作为面板坝关键的防渗结构,其安全性态至关重要。由于防渗面板与堆石体尺寸相差悬殊,如何在保证面板高精度模拟的前提下提高计算效率是一个亟待解决的难题。通过引入背景网格线及径向插值函数(RPIM),开发了基于无网格的界面模拟方法,实现了界面两侧节点自由分布,克服了Goodman单元点对点的限制。该方法可灵活地连接两侧不同尺寸的面板及堆石体网格,进而建立面板与垫层跨尺度分析模型。同时采用"面向对象"及"超单元"技术将该方法集成到自主开发的GEODYNA计算平台中,实现了与传统有限元法的无缝耦合,并可应用界面弹塑性本构模型模拟堆石和面板复杂的接触关系。在此基础上,通过引入虚节点进一步提高了径向插值函数(RPIM)在边界附近的模拟精度。研究表明,基于无网格的非点对点界面模拟方法可高效、灵活地实现面板坝跨尺度分析,在保证高精度的前提下大幅度降低自由度和提高计算效率。本文研究方法可以很容易地扩充到三维问题,并为面板坝面板精细化损伤演化分析提供有力的技术手段。     

An enriched radial point interpolation method (e-RPIM) for analysis of crack tip fields

In this paper, an enriched radial point interpolation method (e-RPIM) is developed for the determination of crack tip fields. In e-RPIM, the conventional RBF interpolation is novelly augmented by the suitable trigonometric basis functions to reflect the properties of stresses for the crack tip fields. The performance of the enriched RBF meshfree shape functions is firstly investigated to fit different surfaces. The surface fitting results have proven that, comparing with the conventional RBF shape function, the enriched RBF shape function has: (1) a similar accuracy to fit a polynomial surface; (2) a much better accuracy to fit a trigonometric surface; and (3) a similar interpolation stability without increase of the condition number of the RBF interpolation matrix. Therefore, it has proven that the enriched RBF shape function will not only possess all advantages of the conventional RBF shape function, but also can accurately reflect the properties of stresses for the crack tip fields. The system of equations for the crack analysis is then derived based on the enriched RBF meshfree shape function and the meshfree weak-form. Several problems of linear fracture mechanics are simulated using this newly developed e-RPIM method. It has demonstrated that the present e-RPIM is very accurate and stable, and it has a good potential to develop a practical simulation tool for fracture mechanics problems.     

A thin plate formulation without rotation DOFs based on the radial point interpolation method and triangular cells

A formulation for thin plates with only the deflection as nodal variables has been proposed using the generalized gradient smoothing technique and the radial point interpolation method (RPIM). The deflection fields are approximated using the RPIM shape functions which possess the Kronecker Delta property for easy impositions of essential boundary conditions. Three types of smoothing domains, which are also serving as the numerical integrations domains, are constructed based on the background three‐node triangular cells and the generalized gradient smoothing operation is performed over each of them to obtain the smoothed curvatures. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. The essential boundary conditions of rotations are imposed in the process of constructing the curvature field, and the translation boundary conditions are imposed as in the standard FEM. A number of numerical examples, including both static and free vibration analysis, are studied using the present methods and the numerical results are compared with the analytical ones and those in the open literatures. The results show that the present formulation can obtain very stable and accurate solutions, even for the extremely irregular background cells. Copyright © 2010 John Wiley & Sons, Ltd.     

Hamilton体系下含弱粘接复合材料层合板的无网格求解方法

该文结合径向基点插值函数、弹簧层模型和弹性材料修正后的H-R（Hellinger-Reissner）变分原理,推导了含弱粘接复合材料层合板控制方程的无网格列式。利用典型径向基函数Multiquadric（MQ）,计算了含弱粘接复合材料层合板的应力与位移。通过与精确法的对比,证明了控制方程无网格列式的正确性,并研究了弱粘...     

Nonuniform transmission lines analysis by meshless point interpolation methods

Three meshless time domain methods are investigated for the solution of the telegrapher's equation applied to the nonuniform transmission line. The approach is based on a combination of the point interpolation methods and the leapfrog algorithm. The accuracy of the proposed methods is confronted with both the Finite‐Difference Time‐Domain (FDTD) and the wavelet expansion methods. The strong stability, the flexibility, and the fast convergence of the computing scheme are set in evidence from the computational results for two examples: the linear tapered transmission line and the transmission line balun. Copyright © 2015 John Wiley & Sons, Ltd.     

A radial point interpolation meshless method extended with an elastic rate-independent continuum damage model for concrete materials

An advanced discretization meshless technique, the radial point interpolation method (RPIM), is applied to analyze concrete structures using an elastic continuum damage constitutive model. Here, the theoretical basis of the material model and the computational procedure are fully presented. The plane stress meshless formulation is extended to a rate-independent damage criterion, where both compressive and tensile damage evolutions are established based on a Helmholtz free energy function. Within the return-mapping damage algorithm, the required variable fields, such as the damage variables and the displacement field, are obtained. This study uses the Newton–Raphson nonlinear solution algorithm to achieve the nonlinear damage solution. The verification, where the performance is assessed, of the proposed model is demonstrated by relevant numerical examples available in the literature.