Eight-node conforming straight-side quadrilateral element with high-order completeness (QH8-C1)

A new eight-node conforming quadrilateral element with high-order completeness, denoted as QH8-C1, is proposed in this article. First, expressions for the interpolation displacement function satisfying the requirements for high-order completeness in the global coordinate system are constructed. Second, the displacement function expression in global coordinates is transformed into isoparametric coordinates, and the relationships between the two series of coefficients for the two kinds of displacement function expressions are found. Third, the displacement function expression is modified to satisfy the requirements of nodal freedom and interelement boundary continuity. The key to the new element construction is the derivation of the linear relationship expressions among 12 coefficients of element displacement interpolation polynomials in the global and isoparametric coordinate systems. As a result, the relationship between quadratic completeness and interelement continuity is explicitly given, and a proof of the completeness and the continuity was conducted to theoretically guarantee the validity of the derivation results. Furthermore, in order to verify the correctness of the theoretical work, nine numerical examples were performed. The computation results from these examples demonstrate that QH8-C1 exhibited excellent performance, including high simulation accuracy, fast convergence, insensitivity to mesh distortion, and monotonic convergence.     

基于修正 RSSI 值的四边形加权质心定位算法

在利用接收信号强度指示(RSSI)对无线传感器网络中的未知节点进行定位时,RSSI 值易受环境的影响导致定位误差, 为此提出基于 RSSI 测距修正的四边形加权质心定位算法(QWCRC)。 先对来自同一锚节点的多个 RSSI 值进行卡尔曼滤波,得 到修正的 RSSI 值,致使测距尽可能的接近真实距离;再采用四边形加权定位对未知节点进行定位,同时利用最小二乘法进行辅 助定位,此算法对于相邻锚节点圆不相交的情况给出新的解决方案。 实验结果对比表明,改进的算法相比较于四边形加权质心 算法(QWC)和 RSSI 测距修正的三角形加权算法(TWCRC),在锚节点数目 5×5 和噪声强度为 0 dbm 时,定位精度可分别提升 87. 14%和 35. 51%。     

Strain gradient differential quadrature finite element for moderately thick micro-plates

In this study, we integrate the advantages of differential quadrature method (DQM) and finite element method (FEM) to construct a C¹-type four-node quadrilateral element with 48 degrees of freedom (DOF) for strain gradient Mindlin micro-plates. This element is free of shape functions and shear locking. The C¹-continuity requirements of deflection and rotation functions are accomplished by a fourth-order differential quadrature (DQ)-based geometric mapping scheme, which facilitates the conversion of the displacement parameters at Gauss-Lobatto quadrature (GLQ) points into those at element nodes. The appropriate application of DQ rule to non-rectangular domains is proceeded by the natural-to-Cartesian geometric mapping technique. Using GLQ and DQ rules, we discretize the total potential energy functional of a generic micro-plate element into a function of nodal displacement parameters. Then, we adopt the principle of minimum potential energy to determine element stiffness matrix, mass matrix, and load vector. The efficacy of the present element is validated through several examples associated with the static bending and free vibration problems of rectangular, annular sectorial, and elliptical micro-plates. Finally, the developed element is applied to study the behavior of freely vibrating moderately thick micro-plates with irregular shapes. It is shown that our element has better convergence and adaptability than that of Bogner-Fox-Schmit (BFS) one, and strain gradient effects can cause a significant increase in vibration frequencies and a certain change in vibration mode shapes.     

An indirect approach for automatic generation of quadrilateral meshes with arbitrary line constraints

A new approach to the automatic generation of a quadrilateral mesh with arbitrary line constraints is proposed in this paper. It is an indirect all‐quad mesh generation and presented in the following steps: (1) discretizing the constrained lines within the domain; (2) converting the above domain to a triangular mesh together with the line constraints; (3) transforming the generated triangular mesh with line constraints to an all‐quad mesh through performing an advancing front algorithm from the line constraints, which enables the construction of quadrilaterals layer by layer, and roughly keeps the feature of the initial triangular mesh; (4) optimizing the topology of the quadrilateral mesh to reduce the number of irregular nodes; (5) smoothing the generated mesh toward high‐quality all‐quad mesh generation. Finally, a few application examples are given to demonstrate the reliability and usefulness of the proposed algorithm. Copyright © 2011 John Wiley & Sons, Ltd.     

线弹性问题的locking-free双参数元

文中运用双参数法提出了一个4参数的四边形非协调有限元,讨论了该单元对纯位移边界条件下的均匀介质线弹性方程的逼近问题.证明了在材料几乎不可压时单元对弹性问题的一致最优收敛性,数值试验验证了理论分析结果.并通过构造后处理算子,得到了超收敛结果.所有的分析结果都可以推广到三维情形.     

四边形网格间接生成方法

研究了基于背景三角网格的四边形网格间接生成算法,并针对三角形合并过程中容易残留三角形的缺陷提出了确定侧边的详细算法,该算法主要是依据背景三角网格中边的位置和前沿边的情形,通过背景三角网格中已存在的边、边交换或边分割确定侧边,以避免在三角形合并过程中残留三角形单元。最后给出实例验证了算法的有效性。     

A partition of unity‐based ‘FE–Meshfree’ QUAD4 element for geometric non‐linear analysis

The recently published ‘FE–Meshfree’ QUAD4 element is extended to geometrical non‐linear analysis. The shape functions for this element are obtained by combining meshfree and finite element shape functions. The concept of partition of unity (PU) is employed for the purpose. The new shape functions inherit their higher order completeness properties from the meshfree shape functions and the mesh‐distortion tolerant compatibility properties from the finite element (FE) shape functions. Updated Lagrangian formulation is adopted for the non‐linear solution. Several numerical example problems are solved and the performance of the element is compared with that of the well‐known Q4, QM6 and Q8 elements. The results show that, for regular meshes, the performance of the element is comparable to that of QM6 and Q8 elements, and superior to that of Q4 element. For distorted meshes, the present element has better mesh‐distortion tolerance than Q4, QM6 and Q8 elements. Copyright © 2009 John Wiley & Sons, Ltd.     

四边形单端带电线路开关的导电回路电阻测试

介绍了福建水口发电集团有限公司的500 kV升压站,采用特殊四边形接线方式,共安装有4台高压开关,由于在高负荷用电环境下,无法全站停电检修,多数情况是单条线路停电,开关一端带电、致使开关不能正常进行预防性试验。而采用新型的测试计算法,检测HGIS内部开关及刀闸的接触电阻,便于和出厂数据进行对比。既确保了试验过程中设备和检修人员的人身安全,也缩短了线路停役时间,提高了社会效益。在当前新的用电环境下具有一定的推广意义。     

特殊四边形面积公式的探讨

给出四类特殊四边形面积公式，对其中部分不常见公式进行简要证明。     

四边形单元面积坐标的微分和积分公式

构造四边形单元时，应用面积坐标方法有其优点。文献［１］系统地论述了四边形单元面积坐标理论，本文是文献［１］的续篇，补充论述采用四边形单元面积坐标时的微分和积分公式。采用三角形单元面积坐标时的微分和积分公式是其特殊情况。应用面积坐标方法时，易于得出四边形单元刚度矩阵的积分显式，无需依赖于数值积分，这个优点是采用四边形等参坐标时所不具备的。