p-Version hierarchical two dimensional curved beam element for elastostatics

This paper presents a completely hierarchical two dimensional curved beam element formulation where the element displacement field can be of arbitrary polynomial orders p_ξ and p_η in the axial and the transverse directions of the element. The approximation functions and the corresponding nodal variables for the beam element are derived by first constructing the hierarchical one dimensional approximation functions of orders p_ξ and p_η, and the corresponding hierarchical nodal variable operators for each of the two directions ξ and η and then taking their product. This procedure yields approximation functions and nodal variables for the curved beam element that correspond to polynomial orders p_ξ and p_η in ξ and η directions. The element approximation is hierarchical, i.e. the approximation functions and the nodal variables are both hierarchical. Thus, the element matrix and the load vectors corresponding to the polynomial orders p_ξ and p_η are a subset of those corresponding to the polynomial orders (p_ξ + 1) and (p_η + 1). The element formulation ensures C⁰ continuity.

The element properties are derived using the principle of virtual work and the hierarchical element displacement approximation. The element geometry is constructed using the coordinates of the nodes located on the elastic axis of the element and the node point vectors indicating nodal depths and the element width at the nodes. The orders of approximation along the length of the element as well as in the transverse direction can be chosen independently to obtain optimum (maximum) rate of convergence.

Numerical examples are presented to demonstrate the accuracy, simplicity of modeling, effectiveness, faster rate of convergence and overall superiority of the present formulation. Results obtained from the present formulation are also compared with h-approximation models and available analytical solutions.     

Circularly polarized beam‐steering antenna array for ultra‐high frequency radio frequency identification applications

A circularly polarized beam‐steering antenna array with Butler matrix is designed in this letter for ultra‐high frequency radio frequency identification applications. To achieve the identification of the fast‐moving tag groups, a 3 × 4 Butler matrix is utilized to switch the radiation directions at ?25°, 0°, and +25°, respectively. Besides, series‐fed patch antenna element is designed and the 1 × 4 antenna array is built with element rotation for a good polarization performance. Finally, the proposed antenna system is fabricated and the identification area and radiation performance are tested.     

Calculating surface Laplacians as a boundary element method postprocess

Postprocessing boundary element method solutions to Laplace's equation in arbitrarily shaped domains is routinely used to find surface fluxes (first-order partial derivatives) in normal and tangential directions. This paper describes a method to calculate second-order partial derivatives by postprocessing the same solutions. These derivatives allow the calculation of the surface Laplacian at the centre nodes of each element on the surface of the volume conductor. In the examples considered, the relative error between analytically determined surface Laplacians and those calculated via the methods presented is 1.0% or less, with correlation coefficients very close to 1.0.     

On the use of a modified Newton method for nonlinear finite element analysis

In this paper, the usefulness of modified Newton methods for solving certain minimization problems arising in nonlinear finite element analysis is investigated. The application considered is nonlinear elasticity, in particular geometrically nonlinear shells. On a test problem, it is demonstrated that a particular implementation of a modified Newton method using both descent directions and directions of negative curvature is able to identify a minimizer, whereas an unmodified Newton method and modified Newton methods using only descent directions fail to converge to the minimizer. The use of modified Newton methods is suggested as a useful complement to the present continuation methods used for nonlinear finite element analysis.     

Circularly polarized high efficiency wideband reflectarray using rectangle‐shaped patch element

A single‐layer circularly polarized reflectarray using rectangle‐shaped elements in X‐band is presented in this article. The designed element is analyzed and optimized with parametrical studies to obtain good performance at the operating frequency. The phase shifts can be controlled by varying the dimensions in two orthogonal directions of the element for circular polarization. A reflectarray antenna with 27 × 27 elements has been designed, manufactured and measured. The measured results show that the proposed reflectarray antenna provides a 1‐dB gain bandwidth of 18% and a 3‐dB axial ratio of 13%. The measured peak gain at 10 GHz is 26.1 dBi, which corresponds to the high aperture efficiency of 40.3%.     

Finite element analysis of composites using chebyshev polynomials

A finite quasi-prismatic (FQP) element is modified to analyze anisotropic materials. The finite quasi-prismatic element is a three-dimensional finite element which uses conventional interpolating functions in two directions and functions based on Chebyshev polynomials in the third direction. This element is used to solve different anisotropic problems and the results are compared with that of conventional finite elements and analytical solutions.     

基于Cosserat理论的平面等参元

为解释材料在微尺度下的尺度效应,基于Cosserat理论,从势能泛函驻值条件出发提出构造8节点Serendipity平面等参元,并建立平面有限元法．每个节点拥有3个独立节点自由度,分别为2个方向的线位移和1个逆时针方向的角位移．用该方法分析含中心小孔的无限平板在单轴拉伸情况下的应力集中问题．数值计算结果与Cosserat理论的解析解非常符合,表明应力集中因数k受泊松比μ,常数c及a／l值的影响很大;由于偶应力的存在,小孔周围的应力分布明显小于经典弹性力学理论的预测．通过对材料常数c的调节可以将该方法推广应用于基于Mindlin偶应力理论的数值分析中．     

A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems

We analyze the discontinuous finite element errors associated with p-degree solutions for two-dimensional first-order hyperbolic problems. We show that the error on each element can be split into a dominant and less dominant component and that the leading part is O(h^p+1) and is spanned by two (p+1)-degree Radau polynomials in the x and y directions, respectively. We show that the p-degree discontinuous finite element solution is superconvergent at Radau points obtained as a tensor product of the roots of (p+1)-degree Radau polynomial. For a linear model problem, the p-degree discontinuous Galerkin solution flux exhibits a strong O(h^2p+2) local superconvergence on average at the element outflow boundary. We further establish an O(h^2p+1) global superconvergence for the solution flux at the outflow boundary of the domain. These results are used to construct simple, efficient and asymptotically correct a posteriori finite element error estimates for multi-dimensional first-order hyperbolic problems in regions where solutions are smooth.     

Piecewise hierarchical p-version axisymmetric solid element for laminated composites

This paper presents a piecewise hierarchical p-version finite element formulation for laminated composites axisymmetric solids for linear static analysis. The element formulation incorporates higher order deformation theories and is in total agreement with the physics of deformation in laminated composites. The element geometry is defined by eight nodes located on the boundaries of the element. The lamina thicknesses are used to create a nine-node p-version configuration for each lamina of the element. The displacement approximation for the element is piecewise hierarchical and is developed by first establishing a hierarchical displacement approximation for the nine-node configuration of each lamina of the laminate and then imposing interlamina continuity condition of displacements at the interfaces between laminas. The hierarchical approximation functions and the corresponding nodal variables for each lamina are derived from the Lagrange family of interpolation functions and can be of arbitrary polynomial order p_c and ^kp_η in the ε and ^kη directions for a typical lamina k. The formulation ensures C⁰ continuity, i.e., continuity of displacement across interelement as well as interlamina boundaries.

The element properties are constructed by assembling individual lamina properties which are derived using the principle of virtual work and the hierarchical displacement approximation for the laminas. Transformation matrices, formed based on interlamina continuity conditions, are used to transform each lamina's degrees of freedom into the degrees of freedom for the laminate. Thus, each individual lamina stiffness matrix and equivalent load vector are transformed and then summed to establish the laminate stiffness matrix and equivalent load vector. There is no restriction on either the number of laminas or their lay-up pattern. Each lamina can be generally orthotropic and the material directions and the layer thickness may vary from point to point within each lamina.

Numerical examples are presented to demonstrate the effectiveness, modeling convenience, accuracy, and overall superiority of the present formulation for laminated composite axisymmetric solids and shells.     

一种新的强抗噪边缘检测方法

针对传统形态学边缘检测方法存在去除噪声与边缘细节保留矛盾的问题,提出了一种能有效去除噪声且准确检测图像边缘的方法.该方法首先利用多结构元素对图像进行滤波,然后用全方位多角度线结构元素结合一种改进的形态学算子检测图像边缘,最后将所得结果进行自适应权重求和,得到噪声存在下较理想的图像边缘.实验表明,该方法对噪声具有较强的抑制能力,在准确检测图像边缘、保留更多细节边缘的同时,能够有效地去除图像中的多种噪声,具有较高的信噪比.     

p-Version axisymmetric shell element for geometrically nonlinear analysis

This paper presents a p-version geometrically nonlinear (GNL) formulation based on total Lagrangian approach for a three-node axisymmetric curved shell element. The approximation functions and the nodal variables for the element are derived directly from the Lagrange family of interpolation functions of order p_ξ and p_η. This is accomplished by first establishing one-dimensional hierarchical approximation functions and the corresponding nodal variable operators in the ξ and η directions for the three- and one-node equivalent configurations that correspond to p_ξ + 1 and p_η+ 1 equally spaced nodes in the ξ and η directions and then taking their products. The resulting element approximation functions and the nodal variables are hierarchical and the element approximation ensures C⁰ continuity. The element geometry is described by the coordinates of the nodes located on the middle surface of the element and the nodal vectors describing top and bottom surfaces of the element.

The element properties are established using the principle of virtual work and the hierarchical element approximation. In formulating the properties of the element complete axisymmetric state of stresses and strains are considered, hence the element is equally effective for very thin as well as extremely thick shells. The formulation presented here removes virtually all of the drawbacks present in the existing GNL axisymmetric shell finite element formulations and has many additional benefits. First, the currently available GNL axisymmetric shell finite element formulations are based on fixed interpolation order and thus are not hierarchical and have no mechanism for p-level change. Secondly, the element displacement approximations in the existing formulations are either based on linearized (with respect to nodal rotation) displacement fields in which case a true Lagrangian formulation is not possible and the load step size is severely limited or are based on nonlinear nodal rotation functions approach in which case though the kinematics of deformation is exact but additional complications arise due to the noncummutative nature of nonlinear nodal rotation functions. Such limitations and difficulties do not exist in the present formulation. The hierarchical displacement approximation used here does not involve traditional nodal rotations that have been used in the existing shell element formulations, thus the difficulties associated with their use are not present in this formulation.

Incremental equations of equilibrium are derived and solved using the standard Newton method. The total load is divided into increments, and for each increment of load, equilibrium iterations are performed until each component of the residuals is within a preset tolerance. Numerical examples are presented to show the accuracy, efficiency and advantages of the preset formulation. The results obtained from the present formulation are compared with those available in the literature.     

Recent advances in the DtN FE Method

Summary The Dirichlet-to-Neumann (DtN) Finite Element Method is a general technique for the solution of problems in unbounded domains, which arise in many fields of application. Its name comes from the fact that it involves the nonlocal Dirichlet-to-Neumann (DtN) map on an artificial boundary which encloses the computational domain. Originally the method has been developed for the solution of linear elliptic problems, such as wave scattering problems governed by the Helmholtz equation or by the equations of time-harmonic elasticity. Recently, the method has been extended in a number of directions, and further analyzed and improved, by the author's group and by others. This article is a state-of-the-art review of the method. In particular, it concentrates on two major recent advances: (a) the extension of the DtN finite element method tononlinear elliptic and hyperbolic problems; (b) procedures forlocalizing the nonlocal DtN map, which lead to a family of finite element schemes with local artificial boundary conditions. Possible future research directions and additional extensions are also discussed.     

鞭天线线性阵列方向图的数值计算

采用矩量法计算了2元和6元鞭天线线性相控阵的方向图,分析了天线单元之问的耦合对方向图的影响,计算结果表明,鞭天线单元问的耦合对相控阵方向图的主瓣影响不大,对旁瓣产生一定影响,且对偏离主瓣越远的旁瓣影响越严重;方向图中增益低的方向受耦合的影响较严重。     

SHB8PS––a new adaptative,assumed-strain continuum mechanics shell element for impact analysis

This paper presents the formulation of a new adaptative shell element. This is an eight-node brick element in which one chooses a special direction denoted “thickness”. The element is an assumed-strain element based on the formulation first proposed by Belytchko and Bindeman. It is integrated with a set of Gauss points through the thickness and with only one point in the other directions. A new assumed-strain formulation for the element is proposed and its development is carried out in elastoplasticity. The element adjusts to the physical situation automatically in the sense that the stabilizing forces are chosen to be proportional to the mean tangent modulus of the material across the thickness. This is a most important assumption because if the stabilizing forces were calculated without regard to the physical state of the element they would turn out to be too large. The element is then tested on simple academic cases and applied in a more complex situation.     

Automatic generation of mapping functions for infinite elements using REDUCE

C₀ continuous basis functions for use in the finite element method when the elements extend to infinity in one or more directions can be derived simply following the method of Zienkiewicz. The numerical code for these functions can be generated automatically using computer algebra languages such as REDUCE. This paper describes the method and explains how REDUCE is used to easily produce numerical code.     

Millimeter‐wave antenna with wide‐scan angle radiation characteristics for MIMO applications

A three‐element quasi Yagi‐Uda antenna array with printed metamaterial surface generated from the array of uniplanar capacitively loaded loop (CLL) unit‐cells printed on the substrate operating in the band 25‐30 GHz is proposed. The metamaterial surface is configured to provide a high‐refractive index to tilt the electromagnetic (EM) beam from the two dipole antennas placed opposite to each other. The metamaterial region focuses the rays from the dipole antenna and hence increases the gain of the individual antennas by about 5 dBi. The antenna elements are printed on a 10 mil substrate with a center to center separation of about 0.5 λ ₀ at 28 GHz. The three‐element antenna covers 25‐30 GHz band with measured return loss of 10 dB and isolation greater than 15 dB between all the three ports. The measured gain of about 11 dBi is achieved for all the antenna elements. The three antenna elements radiate in three different directions and cover a radiation scan angle of 64°.     

混凝土三维钢筋埋置组合式有限单元模型及其网格自动生成

为克服三维钢筋混凝土有限单元模型中网格划分存在的缺陷，提出了埋置组合式有限单元模型。该模型在形成混凝土三维单元时可不考虑钢筋的方位，只要给出钢筋起点与终点的坐标，即可自动形成钢筋在组合单元中的信息，实际应用表明，该模型方便可行，单元划分效率较高。     

均匀圆阵阵元缺损对阵列方向图影响的分析

阵列中阵元接收信号按照一定加权方式合成,使波束方向图指向期望信号同时抑制其他方向的干扰信号。但是当阵列中有阵元缺损时,会对阵列方向图产生一定影响。本文分析并仿真了均匀加权情况下,均匀圆阵无缺损的波束方向图,同时对比了具有相同波束指向的均匀圆阵和均匀线阵在缺损阵元位于不同位置的波束方向图。仿真表明缺损一个阵元后,均匀加权的均匀圆阵性能下降较多。而当缺损阵元位于不同阵列不同位置时,对均匀线阵影响有较大不同,但是对均匀圆阵的影响则相差不多。     

The show must go on:1 Problems of tagging performance texts

A dramatic work may be seen either as an event or as a text; the TEI guidelines make it possible to encode a dramatic work in either way, but do not attempt to solve the difficult problem of doing both at once. The basic element of a dramatic work, when seen as a text, is the speech; the guidelines also provide elements for encoding other familiar parts of dramatic texts (such as stage directions and cast lists), as well as for encoding analytic information on various aspects of texts and performances that is not normally included in printed dramatic texts. There are often other formal structures in dramatic works that intersect with the structure of speeches — metrical structures, for example; we discuss approaches for encoding these structures.