Response of a “Plastic hinge” to low-cycle alternating deflections

The paper describes an experimental technique for obtaining the response of a “plastic hinge” to low-cycle alternating loads in which a deflection (strain) range is prescribed. The cycle of loading is confined to equal amplitudes of positive and negative curvature. This response is expressed in terms of a nonlinear moment-curvature relationship which may subsequently be employed in “pseudo-static” structural analysis to derive the load-deflection characteristics of elastic-plastic beams at various stages of cyclic history. A brief account is presented of a fatigue machine designed and constructed for testing mild steel at low endurance levels. A fixture for pure bending is designed to adapt the machine for testing beams and also to provide a measuring system for the applied alternating moments. A meter to measure the curvature in this environment is also described in detail. Similar fixtures are also described for testing cantilever-beam specimens. Moment-curvature models are generated for beams under terminal alternating moments in which ambient strain conditions are controlled. Paper was presented at 1967 SESA Annual Meeting held in Chicago on October 31–November 3.     

Identification of pulse shapes during transverse impact on composite beams and plates

A test facility for transverse shock loading of beams and plates at small impact velocities (up to 40 km/sec) is described. The impact contact force and unsteady strains are determined for a transverse impact on fiber-layered beams and plates from fiberglass and carbon fiber-reinforced plastic. Pulse shapes are determined for various impact velocities in the range of 5–40 m/sec. The shock loading and unsteady strain of composite beams and plates are calculated by the finite element method. The finite elements take into account transverse shears according to the Timoshenko theory and the viscoelastic material behavior according to the Voigt model.     

Bending theories for beams and plates with single generalized displacement

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Prevention of thermal bending of multilayered beams and plates

A method is described to prevent bending in multilayered beams and plates of different isotropic materials with uniform and nonuniform temperature distribution through the thickness. The method involved the addition of an extra layer to the multilayered beams or plates. With the proper selection of the thermoelastic properties, the added layer would eliminate the curvature produced prior to this addition. A complete analysis for the determination of the various thermoelastic parameters of the extra layer was made. In addition, to ensure that the multilayered beams and plates actually remained straight, a thermoelastic analysis was performed for the solution of thermal stresses and strains in the laminate. The results gave assurance to the straightness of the laminate since the calculated strains have the same value throughout the thickness. The solutions are valid for any given uniform temperature change and for any given nonlinear temperature distribution through the thickness of the multilayered beams and plates. Several numerical examples are presented that illustrate the application of the method for various temperature distributions. A simple experiment was conducted that showed the validity of the analytical method. A brass strip was added to a bimetalic strip made of aluminum and steel at room temperature. The thickness of the brass strip was calculated from the theory to prevent bending. The trimetal strip was placed in a furnace and, as expected, it remained straight for varying temperatures.     

ESPI技术对外贴纤维混凝土加固承载的实验研究

采用电子散斑干涉技术,对外贴碳纤维加固混凝土梁的外贴材料位移的分布特征,进行了全场实时测量,通过实验获得的散斑干涉条纹图可以得到外贴材料与混凝土梁的粘结传力长度随粘结长度及初始载荷之间的关系;了解用于加固的碳纤维材料的应变分布特点和产生梁侧剥离破坏时的碳纤维表面位移(应变)的演化过程。实验还说明了电子散斑干涉技术不仅可用于位移的测量,而且也可用于结构安全监测和破坏预报。文中给出了对C20D、C25A和C60C侧贴碳纤维板加固在不同载荷作用直到构件破坏前的位移测试及对试件C60C轴线上的剪应力分析结果。     

基于梁挠度函数的板解法

基于相应边界支撑和载荷下的梁挠度形函数, 构建板的挠度形函数,求解板的变形, 并用典型算例进行了验证; 对于狭长矩形板,依据其变形特点进行了修正; 结果与三维有限元结果基本一致,说明了该方法的适用性和准确性. 由于板结构内部的相互作用没有得到充分反映,为了更贴近板变形的物理实际, 引入弹性基础梁的挠度函数代替普通梁的挠度函数,进一步完善本文方法. 本文研究成果为工程板件变形的理论分析提供了准确且简便易行的计算方法.     

一种适用于下承式钢桁结合桥计算的板梁组合单元

下承式钢桁结合桥具有建筑高度较低、行车时燥声、震动较小、刚度较大等优点,是高速铁路桥梁中比较理想的结构形式之一。为了能较合理和方便地分析下承式钢桁结合桥的力学行为,本文提出了一种考虑板梁共同作用和相对滑移的板梁组合单元。该单元以矩形板的4个结点的结点位移和板梁结合面3个点的相对滑移作为单元的基本自由度,板的位移模式通过对常规4结点矩形平板壳单元的形函数修正得到,梁的位移模式则根据板和梁之间的变形协调条件来确定。文末的算例表明,本文的解与试验结果和通用工程软件解较为吻合,说明了本文理论和方法的正确性。     

On shear lag effects in orthotropic composite beams

Based upon the linearised theories of the bending and stretching of thin plates, an analysis is presented for the interaction between non-prismatic beams and an orthotropic concrete plate. It is shown that an exponential representation for the steel beam profiles provides a suitable basis for studying interaction in continuous non-prismatic beams, and for deducing suitable effective widths of slab for design purposes. The influence of “elastic” shear connection modulus is studied, as well as the effect of the varying flexural rigidity of the steel beams. The dependence of interaction on shear connection modulus in continuous beams is demonstrated through deflexion and slip characteristics, and so also is the dependence of interaction on the severity of the variation of flexural rigidity. The solution can be specialised to the limiting case of prismatic steel beams and a concrete slab and also to the solutions of rectangular plates with certain edge conditions.     

Shear deformable bending solutions for nonuniform beams and plates with elastic end restraints from classical solutions

Summary The relationships of bending solutions between Timoshenko beams and Euler-Bernoulli beams are derived for uniform and non-uniform beams with elastic rotationally restrained ends. Extensions of these relationships for the cylindrical bending of Mindlin and Kirchhoff plates and for the bending of symmetrically laminated beams are also discussed. The new set of general relationships is useful because the more complex Timoshenko beam and Mindlin plate solutions may be readily obtained from their simpler Euler-Bernoulli beam and Kirchhoff plate solutions respectively, without much tedious mathematics. Received 16 March 1997; accepted for publication 26 November 1997     

Energy theorems for solving equations of deflections

In this paper the unit-dummy-load method is generalized on the basis of Castigliano’s Theorem. On these grounds the general eguations of deflection surfaces of the structures, such as a kind of beams,plates and shells, are directly derived by the force method.We derived the eguations of the deflection surfaces of the rectangular thin plates and thick plates considering the effect of transverse shearing deformations with the inhomogeneous displacement boundary conditions. At the same time we give the equations of deflection axes of the corresponding straight beams.The applications of the reciprocal theorem are also generalized.Three simple calculated examples are given.     

MODAL RESPONSE OF A BEAM WITH IMPERFECT BOUNDARY CONDITIONS

The introduction of non-contacting dynamic measurement techniques such as holographic interferometry and laser vibrometry has led to increased usage of model testing. Without having to add mass, stiffness, or damping due to sensor attachment, small scale models can be employed, thus permitting the use of less expensive specimens, fixtures, and excitation sources. An additional driver towards model testing is the dynamic characterization of exotic materials for which only small samples are available. One of the disadvantages of small scale testing is the necessity to provide accurate placement of the specimen in a clamping fixture (the most often used boundary condition for beams and plates). This work is an effort to characterize the effect of imperfect boundary conditions on the resulting data.     

Test method for measuring strength of a curved sandwich beam

A fixture for testing curved sandwich beams in flexure was designed and evaluated. The test specimen is a continuous sandwich beam consisting of a central circular 90° region connected by two straight legs. The fixture was designed according to the four-point flexure principle to produce a pure bending moment in the curved region. The validity of the test fixture in producing the desired loading was examined by fitting a curved aluminum bar of similar bending stiffness as the sandwich beams considered. Strain gage readings were successfully compared to predictions from curved homogeneous beam theory. In addition, the deflection of the beam at the loading points was analyzed using straight and curved beam theory for the various sections of the beam, and predictions were compared to measured load-displacement response. Good agreement was achieved between experimental and analytical results lending confidence to the test principle. Curved sandwich beams consisting of glass/polyester face sheets over a PVC foam core were tested to failure and the loading response of the beams and their failure behavior are discussed. It was found that the beams failed at the upper face/core interface due to radial tension stress.     

基于mbS模式的有限单元法

mbS模式及其有限元法是在固体和结构分析模型中引入薄膜、弯曲和剪切理论,且采用纯拉压、纯弯和纯剪单元进行分析的数值方法。在时空系中剖分物质单元和时间单元上构造以指数函数和贝塞尔函数为插入函数且按Lagrange插值条件的薄膜、弯曲和剪切等基本位移函数,由此得到更加完备和耦合的固体和结构实体单元的变形模式,根据能量泛函变分原理得到静动力有限元基本方程的一致格式。研究表明,mbS模式及其有限元法可用于梁柱和板壳等结构的静动力分析及屈曲分析。     

Stress-optic law in a single crystal and its application to photo-anisotropic elasticity

A general stress-optic law in a plate made of a single crystal with birefringence is developed, the plate has an arbitrary crystallographic direction. From the general stressoptic law, a condition for obtaining stress distributions in the plate under a plane stress state is derived. Some optical and mechanical properties when the plate is used as a photoanisotropic model are also explained. Experiments on silicon beams in pure bending are performed by using an infrared photoelastic method. Experimental results show that the stress-optic law is valid. The optical and mechanical properties of silicon beams are shown in tables.     

Experimental techniques for testing unstiffened plates in compression and bending

We present details of a dual-actuator rig developed for testing rectangular plates supported on three sides, with the remaining (longitudinal) edge free, under combined uniaxial compression and in-plane bending. Particular attention is given to ensuring a constant strain gradient at the loaded ends, as opposed to a constant load eccentricity, in order to determine the post-buckling behavior and ultimate load and moment capacities of unstiffened thin-walled elements. Strain gradients varying from pure compression to pure bending are facilitated. Attention is also given to ensuring simply supported boundary conditions, and the methods used for anchoring the tensile stresses that develop at the loaded edges as a result of large plate deflections. Details of the methods for controlling the applied displacements are given, for which a system of four laser displacement devices was employed in order to achieve the required strain gradient. The operation of the rig is verified against established theoretical solutions.     

Elastic springback in plates and beams formed by bending

A plane-strain solution is presented to predict the springback of plates formed by bending. The solution assumes that the strains are small, that the material is an isotropichardening von Mises material, and either that the stress-strain diagrams for tension and compression are identical or that an average diagram can be employed. The plastic portion of each stress-strain diagram is approximated by a finite number of straight lines. Both analytical solutions and experimental evidence indicate that the much simpler plane-stress solution can be used to predict springback for both beams and plates. Experimental data confirm that the type of die has a pronounced effect on the springback for beams and plates if the material exhibits a yield point.     

Application of holography to anisotropic composite plates

The application of holography to stress analysis of opaque, anisotropic composite plates subjected to static or dynamic transverse and in-plane loads is presented. The equations of motion show that, for flexed, anisotropic, laminated composite plates, the complete state of stress at a generic point in any lamina, plus the moments and shear forces, are related to the temporal and spatial partial derivatives of the transverse displacement of the middle surface. Interferometric holography is shown to be well suited for obtaining the transverse displacement. Methods of determining the required spatial and temporal partial derivatives are discussed, an example being demonstrated. The holographic determination of anisotropic-material properties, stress and strain concentrations and the nondestructive evaluation of critical buckling loads for composite structures, plus the use of holographically obtained isopachics to supplement photoelastic analyses of composites, are also discussed. Experimental results for statically and dynamically loaded composite plates and beams with and without geometric discontinuities are presented to illustrate the concepts and techniques.     

Lueders' lines detection by means of brittle coatings

The objective of this paper is to compare some of the techniques used to detect Lueders' lines and present the results of a more extensive study using the brittle-coating method. A hot-rolled steel tensile specimen was yielded plastically under successively higher amounts of load and the resulting Lueders' lines were recored using oblique-incident light, etching, photoelastic coatings and brittle coatings. When the results from the various methods were compared, the authors found some advantages in the use of brittle coatings. This method was then used to record the Lueder's lines in beams under pure bending and simple bending, and in plates with notches and holes.     

含ER流体板结构的振动特性研究

本文制作了含电流变体夹层梁和模拟飞机蒙皮结构的含电流变体加筋层合板,采用响应幅频法,测试了在不同电场强度梁和层合加筋板结构各阶固有频率和振幅的变化;并着重测试了加筋层合板结构在改变板材料、电流变体作用面积等条件时各阶频响特性的变化。实验结果表明,随着电场强度的增加,夹层梁的频响特性有很大变化;而层合板的固有频率变化不大,但振幅却有显著变化,其中铝－层合加筋板的频响幅值的变化率达到５０．１％。