新型空间薄壁梁单元

基于Timoshenko梁理论和Vlasov薄壁杆件约束扭转理论,建立了具有内部结点的新型空间薄壁截面梁单元．通过对弯曲转角和翘曲角采取独立插值的方法,考虑了横向剪切变形,扭转剪切变形及其耦合作用,弯曲变形和扭转变形的耦合以及二次剪应力等因素影响,由Hellinger-Reissner广义变分原理,推得单元刚度矩阵．算例表明所建模型具有良好的精度,可用于空间薄壁杆系结构的有限元分析．     

基于抽象翘曲位移函数的箱形梁剪力滞效应分析

针对薄壁箱梁剪力滞问题,基于抽象的翘曲位移函数,通过对控制微分方程的形式进行分析研究,构造出剪力滞翘曲位移函数的基本形式;对翼板引入边界约束影响的修正系数,然后通过能量变分原理推导出了箱形梁剪力滞的控制微分方程及其解析解.根据有限元结果确定翼板边界约束影响修正系数的具体值,以带翼板的简支箱形梁分别作用集中荷载和均布荷载为数值算例,进行了计算分析.分析结果表明:采用该文方法计算的结果与有限元结果总体吻合良好,并且该文的计算结果也反映出了翼板应力小于顶板应力的分布规律,从而验证了该文分析方法的正确性.     

夹芯梁的精确解法

夹芯梁与普通梁的本质区别在于剪切引起芯层横截面严重的而又不均匀的翘曲变形,其应力分布已远非初等理论所能描述,而正在广泛应用的经典夹层理论却都建立在平面假设基础上,尤其不能正确反映弱芯的轻质夹层结构的行为,本文放弃了不合理的假设,将夹芯梁视为一般层状弹性体,严格按弹性理论导出了既满足控制方程又同时满足全部边界条件、层间的应力及位移的连续条件的封闭解.它可确切地反映夹芯梁的位移形态和应力分布,并从不同角度,包括多种实验和FEM数值解,验证了它的正确性.     

自然弯扭梁广义翘曲坐标的求解

提出了自然弯扭梁受复杂载荷作用时静力分析的一种理论方法,重点在于对控制方程的求解,其中考虑了与扭转有关的翘曲变形和横向剪切变形的影响．在特殊的情况下,可以比较容易地得到这些方程的解答,包括各种内力、应力、应变和位移的计算．算例给出了平面曲梁受水平和垂直分布载荷作用时广义翘曲坐标的求解方法．计算结果表明,求得的应力和位移的理论值和三维有限元结果非常接近．此外,该理论不限于具有双对称横截面的自然弯扭梁,同样可推广至具有一般横截面形状的情况．     

任意多连通截面扭转应力函数的有限元解法

杆件扭转问题的求解,主要有基于扭转理论翘曲函数的边界元法和有限元法、基于薄壁杆件理论的数值解法和基于扭转理论应力函数的有限元法．根据任意多连通截面直杆扭转问题的应力函数理论,讨论并改进了与微分方程及定解条件等效的泛函,在此基础上推导了求解多连通截面扭转应力函数的有限元列式,将扭转问题的翘曲位移单值条件转化为边界节点上的集中荷载．采用主从节点法满足孔洞边界上应力函数的同值条件,实现了任意多连通复杂截面扭转应力函数的有限元直接求解,通过应力函数积分获得截面的扭转常数．算例验证了方法的可行性和有效性．     

翘曲空间曲线梁自然坐标精确解

基于现有空间曲线梁理论,考虑与扭转有关的翘曲变形和横向剪切变形的影响,建立了自然标架下空间曲线梁的内力和变形的解析解答．将该解答应用于受均布扭矩和竖向分布荷载的平面曲线梁的分析,将所得结果与Heins解答进行比较,证明了理论的正确．并应用该理论分析了解析式中翘曲和横向剪切变形项的影响．     

用统一分析梁与有限节线法分析弹性薄壁截面构件

传统薄壁截面梁理论不仅与梁的长细比有关,还强烈地依赖于其横截面的形状和荷载的作用方式.为了解决任意长细比、任意形状弹性薄壁截面杆状类结构构件或结构体系受任意荷载作用的力学分析问题,提出了一种新的梁模型——统一分析梁,一种结构数值分析新方法——有限节线法.利用统一分析梁模型和有限节线法不仅可以分析任意弹性薄壁杆状类结构构件的力学行为,而且当问题的性质与传统梁理论的前提条件一致时,会得出同样精度的解答.算例计算结果证明了统一分析梁的合理性与有限节线法的正确性.     

Hamilton力学下框筒结构剪滞翘曲位移模式研究北大核心CSCD

以等效连续化方法为基础,在Hamilton力学体系下进行框筒结构剪滞翘曲位移函数精度研究.选用不同类型的函数描述翼缘板的剪滞翘曲位移,考虑等效板的剪切变形以及纵向翘曲,得到不同位移函数下结构的总势能及对应的Lagrange函数.区别于传统变分法,该文在Hamilton力学体系下进行问题研究,导出框筒结构弯曲问题的Hamilton正则方程并利用精细积分法求解,进而计算出柱轴力并进行精度分析.算例验证结果表明:使用该方法分析框筒结构的剪力滞后效应是简单可行的;不同翘曲位移函数的选择对侧移计算结果影响不大,对轴力求解结果影响较大,二次抛物线最能反映等效翼缘板的实际翘曲位移;对比不同形式荷载作用下等效翼缘板中应力分布可知,随着外荷载合力作用点位置的升高,结构顶部负剪力滞后效应逐渐减弱至消失.     

开、闭口复合型簿壁杆件的实用理论

生产实际中提出开、闭口复合型薄壁杆件的计算问题.但目前薄壁杆件的通用理论只涉及纯粹开口截面或纯粹闭口截面(今后简称开口理论和闭口理论).关于这方面[4],[5]有较全面的论述.一般认为,这两种理论除了方程相似,从基本假设到最终结果均有不相容的差别.例如在自由扭转中,开口截面的剪应力沿厚度对称地线性分布,而闭口截面——则均匀分布;开口理论假设中面剪应变为零,而闭口理论则认为中面剪应变由     

基于曲率插值的大变形梁单元

线性梁单元的形函数在单元大转动时会引起虚假应变,不适用于几何非线性分析．传统的几何非线性梁单元由于位移插值和转角插值的相干性,常常引起剪切闭锁等问题．该文 提出了一种平面大变形梁单元,通过单元域内的曲率插值以及曲率与节点位移之间的函数关系,将单元节点力和节点位移表示为节点曲率的函数．由于曲率插值本质上是对梁的应变进行插值,保证了单元任意刚体运动不会产生虚假的节点力;且将梁的截面形心位移表示为曲率的函数,避免了传统单元中的剪切闭锁问题．因而所提方法特别适用于梁的几何非线性分析．数值算例说明了所提方法的正确性和有效性.     

Experimental verification of damage detection methods based on mode shape measurements for beams and plates.

This paper presents experimental verification and comparison of damage detection methods based on changes in mode shapes such as: mode shape curvature (MSC), damage index (DI), strain energy (SE), modified Laplacian operator (MLO), generalized fractal dimension (GFD) and Wavelets Transform (WT). The object of the investigation is to determine benefits and drawbacks of the aforementioned methods and to develop data preprocessing algorithms for increasing damage assessment effectiveness by using signal processing techniques such as interpolation and extrapolation of measured points. Noise reduction algorithms are also tested. The experiments were performed on a steel cantilever beam and on an aluminium plate with riveted stiffeners. Damage was introduced in a form of open crack for beam object and damaged rivets and a saw cut in the angle bar for plate structure. Measurements were made using non-contact Scanning Laser Doppler Vibrometer (SLDV) at 125 points along beam length and 101 points in two rows, distributed on over the plate height and positioned along two reinforcing ribs. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Uncertainty and Option Value in Land Allocation Problems

In intensity-modulated radiation therapy (IMRT) not only is the shape of the beam controlled, but combinations of open and closed multileaf collimators modulate the intensity as well. In this paper, we offer a mixed integer programming approach which allows optimization over beamlet fluence weights as well as beam and couch angles. Computational strategies, including a constraint and column generator, a specialized set-based branching scheme, a geometric heuristic procedure, and the use of disjunctive cuts, are described. Our algorithmic design thus far has been motivated by clinical cases. Numerical tests on real patient cases reveal that good treatment plans are returned within 30 minutes. The MIP plans consistently provide superior tumor coverage and conformity, as well as dose homogeneity within the tumor region while maintaining a low irradiation to important critical and normal tissues.     

Vibration analysis of cracked post-buckled beams

Vibration analysis of cracked post-buckled beam is investigated in this study. Crack, assumed to be open, is modeled by a massless rotational spring. The beam is divided into two segments and the governing nonlinear equations of motion for the post-buckled state are derived. The solution consists of static and dynamic parts, both leading to nonlinear differential equations. The differential quadrature has been used to solve the problem. First, it is applied to the equilibrium equations, leading to a nonlinear algebraic system of equations that will be solved utilizing an arc length strategy. Next, the differential quadrature is applied to the linearized dynamic differential equations of motion and their corresponding boundary and continuity conditions. Upon solution of the resulting eigenvalue problem, the natural frequencies and mode shapes of the cracked beam are extracted. Several experimental as well as numerical case studies are performed to demonstrate the effectiveness of the proposed method. The investigation also includes an examination of several parameters influencing the dynamic behavior of the problem. The results show that the position and size of the crack as well as the geometric imperfection and applied load largely affect the modal shapes and natural frequencies of the beam.     

Numerisch-theoretisch und experimentelle Untersuchung einer Hochstrom-Fernfokus-Elektronenkanone vom Tetroden-Typus

Starting from a earlier investigation of a telefocus-electron gun of the triode-type (Z. angew. Phys.11, 370 (1950) which however was unable to deliver high beam currents, a telefocus-gun of the tetrode-type for high beam currents was theoretically and experimentally investigated and the main results are presented in this paper. In the first part of this work a model-system has been investigated by numerical-theoretical methods to get an idea of the electron paths inside the gun as well as to estimate the highest obtainable perveance of the gun. In these investigations an analogy-resistance-network for the plotting of potential fields and an electronic computer for the electron path calculations have been used. These calculations showed that an electron-gun of small geometrical dimensions can be built which is able to focus high beam currents at long distances from the cathode. The relevant gung parameters are a short distance from cathode to first-anode and a high negative Wehnelt-potential. In the second part of the paper the results of some experimental investigations are reported. The experiments showed that by suitable dimensioning a 50 mA, 20 kV electron beam can be focussed in a crossover of some few tenths of mm diameter at a distance of 150–250 mm from the cathode. Some examples for the gun data are given. The aberrations of the electron gun are considerable at the higher currents: At 20 kV one can easily obtain a beam current of 150 mA with a cathode of 2 mm diameter. The aberrations influence infavourably the current density distribution in the crossover. The disturbance is especially noticeable for long cathode to focus distances as was the case in some reported experiments with a cathode to focus distance of 410 mm.The described telefocus-gun has been used for electron beam welding and some practical conclusions of these experiments are discussed in the paper.

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Leicht gekürzte Fassung eines Vortrages an der Second International Conference on Electron and Ion Beam Science and Technology, New York, April 17–20, 1966.     

Euler-Bernoulli梁的非同位控制

对一端固定,一端加剪切力反馈的Euler-Bernoulli梁,运用Legendre谱方法对一个非同位控制系统进行研究,得到了最优反馈增益系数和系统衰减率.结果表明这样的非同位控制系统可以有效的增大系统衰减率,使系统具有更好的稳定性.同时指出所研究的系统是极小相位的.     

Experimental and numerical investigation of PUR foam under dynamic loading

Various factors may subject buildings to shock which continues in their structure and is perceived by the people living in them as noticeable vibrations or noise. In this context, polyurethane (PUR) foams, which have been developed to isolate vibrations, have shown to be very effective in practical use. However, whereas static properties of open-cell structures have already been determined numerically in good agreement to experimental results, cf. [1], there are hardly any investigations on the dynamical properties characterizing acoustic damping. In order to validate experimental measurements of eigenfrequencies for different PUR foam specimen we present here a strategy to reproduce the foam behavior numerically. In doing so, PUR foams are modeled using a three dimensional Voronoi-tessellation technique. The resulting Voronoi cells correspond to open pores and are scaled in such a way that the volume ratio between the pores and material matches the given PUR foam. For finite element analysis the connections between the cells are modeled as beam elements, the beam shape follows Bezièr curves. The generated model is analyzed with a finite element software and the dynamical parameters are determined. The numerical results are compared to our experimental data. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optimization of open cross sections of thin-walled beams with plate-shell-flanges

The paper is devoted to a monosymetrical cold-formed thin-walled beam with open cross section. Its flange consists of plates and circular shells. The beam is under pure bending. The cross section is characterized by dimensionless parameters. The authors are searching for an optimal cross section shape of considered beam. This optimal shape is determined by means of parametric optimization. The dimensionless objective function is so defined as to comprise both cross section area and a maximal allowable bending moment. The constraints follow from the local buckling conditions and geometric restrictions. Moreover, there are optimized cross sections of beams, for which the shear center is located either in the web or in the centroid of the cross section. Results are compared and analyzed. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

火箭、飞行器材料和薄壁压力容器的渗漏判据

本文对火箭,飞行器材料和薄壁压力容器建立了三个计算临界裂缝和临界荷载的渗漏判据,实验结果表明这种方法是成功的.     

Free vibration analysis of cracked composite beams subjected to coupled bending–torsion loads based on a first order shear deformation theory

In this paper, free vibration analysis of cracked composite beam subjected to coupled bending–torsion loading is presented. The composite beam is assumed to have an open edge crack of length a. A first order shear deformation theory is applied to count for the effect of shear deformations on natural frequencies as well as the effect of coupling in torsion and bending modes of vibration. Governing equations and boundary conditions are derived using Hamilton principle. Local flexibility matrix is used to obtain the additional boundary conditions of the beam in cracked area. After obtaining the governing equations and boundary conditions, generalized differential quadrature (GDQ) method is applied to solve the obtained eigenvalue problem. Finally, some numerical results of beams with various boundary conditions and different fiber orientations are given to show the efficiency of the method. In addition, to study the effect of shear deformations, numerical results of the current model are compared with previously given results in which shear deformations were neglected.