Spatial stability of shear deformable curved beams with non-symmetric thin-walled sections. I: Stability formulation and closed-form solutions

For spatial stability analysis of shear deformable thin-walled curved beams with non-symmetric cross-sections, an improved analytical formulation is proposed. Firstly the displacement field is introduced considering the second order terms of semi-tangential rotations. Next an elastic strain energy is derived by using transformation equations of displacement parameters and stress resultants and considering shear deformation effects due to shear forces and restrained warping torsion. And then the potential energy due to initial stress resultants is consistently derived with accurate calculation of Wagner effect. In addition, closed-form solutions for in-plane and lateral-torsional buckling loads of curved beams subjected to uniform compression and pure bending are newly derived. In the companion paper, FE procedures are developed by using curved and straight beam elements with arbitrary thin-walled sections. In numerical examples, to illustrate accuracy and validity of this study, closed-form solutions for in-plane and out-of-plane buckling loads are presented and compared with those obtained from analytical solutions by other researchers.     

空间曲梁非线性动力学方程

基于有限变形原理,采用微分几何的方法推导了不考虑剪切、转动惯量和翘曲影响的曲梁的二维变形的应力-应变关系．然后利用Hamilton变分原理推导了三维空间曲梁在考虑三个位移自由度和三个转动自由度下的非线性动力学方程．把得到的非线性动力学方程退化为面内圆弧拱的线性动力学方程,并与已有结果进行了对比．非线性动力学方程的建立为曲梁的非线性动力学分析做好了必要的准备．     

A consistent discrete elements technique for curved members

A general solution method of a system of coupled differential equations governing the elastic behavior of curved members is presented. The finite element displacement method is formulated based on a variational principle. The stiffness, stability and mass matrices of the discrete finite element are consistent and are obtained within the bounds of linearized displacement theories. Examination of a convergence test indicated an extremely fast converging upper bound solutions, as expected, due to the utilization of the variational procedure. Critical loads and natural frequencies were obtained using computer programs developed. A measure of warping contribution to torsional behavior is assessed and the effects of antisymmetry of the cross sections are examined. An excellent correlation has been observed in comparative studies.     

基于球体图像的变换方程

视点变换就是在虚拟现实技术中求视点移动后原始图像变换生成的新视图。以前给出的用于全景图像的变换公式都是基于平面或柱面全景图像。论文给出了球体针孔摄像机模型在warping方程中生成新视图的公式,以及具体推导过程。     

CSA--一种加速的图像逆映射算法

采用方程求解代替逐像素搜索,提出一种加速的图像逆映射CSA算法．首先根据深度信息标记出参考域中的边界像素,并在映射时保存在像素链表中;然后将链表中的像素逐个映射到其他参考域建立线段方程,并与对应的极线方程联立求解,若有解则求出匹配的参考像素,否则标记为空洞;最后利用插值或其他参考信息填补空洞．由于仅处理边界像素,降低了计算复杂度,经实验证实,该算法有较好的加速作用．     

A simple method to determine the critical buckling loads for axially inhomogeneous beams with elastic restraint

In this paper, a new and simple approach is presented to exactly calculate the critical buckling loads of beams with arbitrarily axial inhomogeneity. For various end boundary conditions, we transform the governing equation with varying coefficients to linear algebraic equations; then a characteristic equation in critical buckling loads will be obtained. Several examples of estimating buckling loads under typical end supports are discussed. By comparing our numerical results with the exact and existing results for homogeneous and nonhomogeneous beams, it can be found that our method has fast convergence and the obtained numerical results have high accuracy. Moreover, the buckling behavior of a functionally graded beam composed of aluminum and zirconia as two constituent phases is investigated for axially varying material properties. The effects of gradient parameters on the critical buckling loads are elucidated. Finally, we give an example to illustrate the enhancement of the load-carrying capacity of tapered beams for admissible shape profiles with constant volume or weight. The proposed method is of benefit to optimum design of beams against buckling in engineering applications.     

Vibration response of geometrically nonlinear elastic beams subjected to pulse and impact loading

The governing equations for the geometrically non-linear deformation of elastic beams subjected to dynamic bending loads are developed and solved for various initial conditions. Of primary interest is the response to pulse loading and simulated impact. Both transient and several cycle solutions are generated for the free vibration response to pulse loading. The results obtained are compared to a first mode analysis approximation.A new model is developed to simulate impact loading by the distribution of additional mass to the elastic system and subjecting it to a velocity pulse. The governing equations are solved using second order finite differences in space and time. The solutions obtained are in reasonable agreement with experimental results previously obtained [1].     

Composition of novel views through an efficient image warping

This paper presents an efficient inverse warping algorithm for generating novel views from multiple reference images taken from different viewpoints. The method proceeds in three steps: preprocess for edge-pixel extraction, inverse warping from the primary image, and hole filling from remaining reference images. In using advantages of epipolar-line features and the depth discontinuity in the reference images, the inverse warping can be efficiently applied in segments, accelerating the rendering process substantially. Two acceleration techniques are proposed at the last stage for hole filling. By using the algorithm proposed, we may navigate a virtual environment at an interactive rate.     

Numerical solution of slender channel laminar flows

The slender channel approximate equations are used to describe flows in curved channels of varying height. The governing equations are transformed in order that similar solutions can be obtained and used as initial profiles. A second-order accurate Crank-Nicolson finite difference scheme is developed with the pressure treated directly as one of the dependent variables. The rechnique is applied to several channel geometries, and solutions are obtained at various Reynolds numbers.     

Stability of beamlike lattice trusses

A simple procedure is presented for predicting the buckling loads associated with general instability of large repetitive beamlike trusses. The procedure is based on replacing the original lattice structure by an equivalent continuum beam model and obtaining analytic solutions for the beam model. The continuum beam model accounts for warping and shear deformation in the plane of the cross section and is characterized by its strain energy and potential energy due to initial stresses from which the governing differential equations are derived. The high accuracy of the buckling predictions of the proposed continuum beam is demonstrated by means of numerical examples.     

基于几何与图像混合绘制中的快速WARP变换算法研究

基于几何与图像的混合绘制中，3D Warp算法以严格的数学变换为基础，从而能够保证准确的投影关系，但该算法在实时绘制阶段需进行大量的数学运算，故其时间复杂度较高，该文提出了一种新的快速Warp变换算法，算法以3D Warp算法为基础，采用了崭新的投影过程，从而使时间复杂度较3D Warp算法有较大幅度的下降（降低约7．51倍）。同时，该算法是一种流水结构，能够有效利用现有的加速硬件，而无需改变图形硬件的体系结构。     

一种光学镜头摄像机图象几何畸变的修正方法

由于光学镜头会产生几何畸变,并且摄像机成象平面与景物平面间存在着倾角和转角,因而光学镜头摄像机获取的图象存在着非线性的几何畸变,在对图象进行检测和定量分析之前,应消除这些畸变。为此,应用多项式变形技术和双线性插值方法,研究了一种摄像机拍摄图象几何畸变的修正方法,并讨论了控制点的选取方法。实验结果表明,应用三次多项式变形技术,选取少量控制点即可得到理想的校正结果。该方法简便实用,可用于固定条件下摄像     

Galerkin method as a tool to investigate the planar and non-planar behavior of curved beams

The equations of equilibrium which describe the three-dimensional behavior of curved beams are derived. These equations include first order geometric nonlinear influences. The equations are solved by the Galerkin method. The method is very general and allows general variation of the geometric and structural properties along the beam. Any combination of boundary conditions is possible and the most general distribution of loads along the beam can be treated. Numerical results for a few examples are presented and compared to other theoretical and experimental results. The agreement between the results is generally good. It is shown that Galerkin method is an efficient method which enables one to solve the problem using small number of unknowns compared to other methods which are in use.     

基于分段线性频谱弯折函数的说话人归一化方法

在传统的声道长度归一化方法中 ,基于声道无损级联短管模型假设 ,用一个简单的声道因子来确定频谱弯折函数 ,无法描述出不同说话人的频谱差异的细节 .针对这一缺陷 ,提出用细致的分段线性频谱弯折函数来描述说话人差异 ,在适当的频谱分段下 ,较好地完成了频谱对齐的任务 .此外 ,由于利用了与模型无关的频谱弯折函数 ,该方法被证明是一种快速的、尤其适用于无监督模式的说话人鲁棒性方法     

Online signature verification using a new extreme points warping technique

There are two common methodologies to verify signatures: the functional approach and the parametric approach. In this paper, we propose a new warping technique for the functional approach in signature verification. The commonly used warping technique is dynamic time warping (DTW). It was originally used in speech recognition and has been applied in the field of signature verification with some success since two decades ago. The new warping technique we propose is named as extreme points warping (EPW). It proves to be more adaptive in the field of signature verification than DTW, given the presence of the forgeries. Instead of warping the whole signal as DTW does, EPW warps a set of selected important points. With the use of EPW, the equal error rate is improved by a factor of 1.3 and the computation time is reduced by a factor of 11.     

Spatial stability of shear deformable curved beams with non-symmetric thin-walled sections. II: F. E. solutions and parametric study

In the companion paper, an improved formulation for spatial stability analysis of shear deformable thin-walled curved beams with non-symmetric cross-sections is presented based on the displacement field considering both constant curvature effects and the second-order terms of semi-tangential rotations. Thus the elastic strain energy and the potential energy due to initial stress resultants are consistently derived. Also closed-form solutions for in-plane and lateral-torsional buckling of curved beams subjected to uniform compression and pure bending are newly derived for mono-symmetric thin-walled curved beams under simply supported and clamped end conditions. In this paper, F. E. procedures are developed by using curved and straight beam elements with non-symmetric cross-sections. Analytical and numerical solutions for spatial buckling of shear deformable thin-walled circular beams are presented and compared in order to illustrate the accuracy and the practical usefulness of this study. In addition, the extensive parametric studies are performed on spatial stability behavior of curved beams. Particularly transition and crossover phenomena of buckling mode shapes with change in curvature and length of beam on buckling for curved beams are investigated for the first time.     

Stability of composite thin-walled beams with shear deformability

In this paper, a theoretical model is developed for the stability analysis of composite thin-walled beams with open or closed cross-sections. The present model incorporates, in a full form, the shear flexibility (bending and non-uniform warping), featured in a consistent way by means of a linearized formulation based on the Reissner’s Variational Principle. The model is developed using a non-linear displacement field, whose rotations are based on the rule of semi-tangential transformation. This model allows to study the buckling and lateral stability of composite thin-walled beam with general cross-section. A finite element with two-nodes and fourteen-degrees-of-freedom is developed to solve the governing equations. Numerical examples are given to show the importance of the shear flexibility on the stability behavior of this type of structures.     

桌面环境下拼贴显示的自动对准

通过拼贴一组投影仪来构建高分辨率显示系统已成为现在一个较实际的办法.但是,这样的高分辨率显示系统用途有限,因为它们需要在定制的并行机或个人计算机集群上运行一些专门开发的并行形象化程序才能实现.针对个人计算机桌面环境下的任意拼贴显示给出了一种自动对准机制,使得桌面用户可以在其上运行普通的桌面应用软件.该系统包括3个步骤:检测投影仪对齐失准,计算出纠正所需之变换,对桌面环境进行实时的变形.这样就允许用户在运行任何2D,3D或视频程序时无须作任何修改,也无须使用专门的硬件支持.实验结果表明,系统能够获得亚像素级的精度,并且能在系统性能衰减最小的情况下达到实时变形.     

一种人脸图像局部变形技术

图像局部变形是指仅在图像的一小部分区域内做变形,改变某些局部范围的特征,同时保持其它区域不发生变化。目前常用的图像变形方法基本上考虑的是图像的整体变形,在直接运用于局部变形时效果不佳。文章提出了一种人脸图像局部变形方法,它首先在局部变形区域内确定特征点和影响半径,然后计算出区域像素点几何位置的变化,最后使用双线性插值原理进行灰度赋值。该方法可以获得很好的人脸局部变形效果,具有连续性好、算法简洁、实时互动等优点,在人脸识别领域有可观的应用前景。     

Vibration and stability of a non-uniform double-beam subjected to follower forces

An analysis is presented for the vibration and stability of a non-uniform double-beam subjected to tangential follower forces distributed over the center line by use of the transfer matrix approach. For this purpose, the governing equations of the beam are written as a coupled set of first-order differential equations by using the transfer matrix of the beam. Once the matrix has been determined by numerical integration of the equations, the eigenvalues of vibration and the critical flutter loads are obtained. The method is applied to beams with linearly varying depths and breadths, subjected to a concentrated follower force, and the natural frequencies and flutter loads are calculated numerically, to provide information about the effects on them of varying cross-section span and stiffness of intermediate supports, and the slenderness ratio.