剪力墙的面外刚度对建筑结构计算结果的影响

剪力在钢筋混凝土建筑结构中有着广泛的应用,在计算时一般都忽略剪力面外刚度的贡献。本文利用一种同时具有面内刚度和面外刚度的剪力墙模型,研究了剪力墙的面外刚度对整体结构的控制位移和固有频率的影响。结果表明,剪力面外刚度的贡献与剪力墙之间的耦合程度以及是要用刚性楼板假定有关,在大型复杂的纵横剪力墙结构中,剪力墙面外刚度的贡献不可忽略。     

一维周期性梁结构等效性能计算方法讨论

具有轴向周期微结构的复合梁结构,通常在宏观上简化为一维欧拉-伯努利梁。由于缺乏基于严格数学理论、同时考虑降维及均匀化的等效性能计算方法,已有研究或采用基于平截面假定的弯曲能量近似方法,或采用基于三维周期性介质等效性质的方法。本文首先介绍了基于一维周期性梁的渐近均匀化理论求解新方法,并在此基础上与上述两种方法进行比较。结果表明,基于平截面假定的近似方法忽视了这类梁结构内的三维应力状态,过高地估计了梁的等效性质。     

Mechanics of adhesive joints

Summary Taking into consideration both the pulling and bending actions of the external force, the differential equations for bending of a partly attached tape in a peeling test have been derived. The equations relating the peeling load to the adhesive force were derived under the assumption that the peeling may proceed step by step from the attached end when the adhesive force is overcome by either the tensile stress along the interface (shearing peeling) or that which is perpendicular to the interface (tensile peeling). To verify the validity of the obtained equations, the dependence of the peeling load P on the angle between the direction of the action of the load and the adhering surface has been investigated using plasticized polymer films. In view of the elementary mechanics, the results were satisfactory, while a modification was attempted by introducing the stress concentration factor.     

任意光滑梯度变化的功能梯度材料纯弯曲梁的弹塑性分析

假设功能梯度材料为理想弹塑性材料,其屈服强度和弹性模量均沿梁的高度方向按任意光滑函数连续变化,在小变形及平截面假定下,导出了功能梯度材料纯弯曲梁弹性极限弯矩及塑性极限弯矩的解析表达式,建立了弹塑性应力状态下截面弯矩和截面的弹、塑性应力分布之间的解析关系．研究表明,功能梯度材料梁存在多种可能的屈服模式,其最先屈服的点不一定位于截面应力最大处,而可能位于截面的其他任意位置;屈服强度及弹性模量的梯度变化对梁的弹塑性力学性能有很大影响．研究结果可为功能梯度材料纯弯曲梁的弹塑性问题研究提供一定的参考．     

Photoelasticity with additional physical fields and optically active models

The aim of the paper is to enlarge the class of three-dimensional stress distributions which can be investigated in a transmission polariscope. The experimental data are shown to contain more information about the stress distribution on the wave normal if the rotation of the principal axes or that of the plane of polarization is induced. This can be obtained by additional physical fields or by using optically active models. Three examples are described. First, an exact theory for investigating bending stresses in plates by the aid of prefrozen models has been developed and applied to evaluate the experimental data. Second, the application of the magnetophotoelastic method to determine stress-concentration factors by cylindrical bending of plates is considered. Third, a nonlinear stress distribution along the wave normal has been determined experimentally in an optically active model.     

考虑边界层影响时溢流坝动水压强分布规律的研究

根据溢流坝反弧段水流运动的基本方程,考虑水流边界层的影响,在流线曲率同心圆假设条件下,得到了溢流坝反弧段水流压强计算的表达式。通过引入近壁薄流层要领和缓和过渡流线假设,在水工模型试验的基础上,得到了溢流坝反弧段水流流线曲率半径的计算公式,使反弧段离心力影响范围内的水流流线曲率光滑连续,从而得到反弧段水流压强分布规律的统一表达式,该表达式能够反映水流压强沿反弧法线方向及切线方向的变化规律。     

Finite deformations of fibre-reinforced elastic solids with fibre bending stiffness

In the conventional theory of finite deformations of fibre-reinforced elastic solids it is assumed that the strain-energy is an isotropic invariant function of the deformation and a unit vector A that defines the fibre direction and is convected with the material. This leads to a constitutive equation that involves no natural length. To incorporate fibre bending stiffness into a continuum theory, we make the more general assumption that the strain-energy depends on deformation, fibre direction, and the gradients of the fibre direction in the deformed configuration. The resulting extended theory requires, in general, a non-symmetric stress and the couple-stress. The constitutive equations for stress and couple-stress are formulated in a general way, and specialized to the case in which dependence on the fibre direction gradients is restricted to dependence on their directional derivatives in the fibre direction. This is further specialized to the case of plane strain, and finite pure bending of a thick plate is solved as an example. We also formulate and develop the linearized theory in which the stress and couple-stress are linear functions of the first and second spacial derivatives of the displacement. In this case for the symmetric part of the stress we recover the standard equations of transversely isotropic linear elasticity, with five elastic moduli, and find that, in the most general case, a further seven moduli are required to characterize the couple-stress.     

集中载荷作用下具有光滑中心波纹膜片的非线性分析

波纹膜片是一种薄壳弹性体，由于它的参数很多，又相互制约，所以使得它的设计很复杂。在大多数位移式仪器仪表中，要求波纹膜片产生至少和膜片厚度是同样数量级的弹性位移。这就要求使用薄壳的几何非线性理论进行分析。大多数学者研究波纹膜片的弯曲问题，是采用扁壳理论讨论具有浅波纹的膜片。而工程实际中，经常遇到深波纹膜片，这就要求从一般壳体大挠度方程进行求解。本文采用轴对称旋转壳体的简化Re-issner方程。研究了在中心集中载荷作用下具有光滑中心波纹膜片的非线性弯曲问题。应用积分方程方法，可以获得膜片的特征关系（载荷-中心挠度关系）和应力分布。文末给出实例计算的数值结果。     

Shear instability direction at a crack-tip in a thermoviscoplastic body

Deformation fields near a crack tip are analyzed for a thermoviscoplastic body deformed either in an antiplane shear or in plane strain. The effects of inertia forces and heat conduction are considered, but those of material elasticity are neglected. By assuming that a shear band initiating from the crack-tip propagates in the direction of the maximum effective stress. It is found that a shear band propagates along the crack ligament in the body deformed in an antiplane shear. For a body undergoing plane strain deformations, the direction of the propagation of the shear band depends upon the mode-mixity parameter and agrees with that observed by Kalthoff.     

The solution of dynamic Point-Ring-Couple in an elastic space and its properties

The solution of dynamic Point-Ring-Couple at the origin,on z=0 plane,in an elastic space is presented and its properties are discussed.Let shocking loads be uniformly distributed,along the direction of circumference,at a circle,on z=0 plane,with radius a and centered at the origin.Then,the solution of our problem is obtained via integral calculation for a→0.When the intensity of this dynamic Point-Ring-Couple is varied with sinωt,the cones in the elastic space with apex at the origin and the z-axis be its symmetric axis,become zero stressed surfaces at any time instance.The solution of dynamic torsion problem of revolution solids with these cones as boundary under the application of torque varied with sinωt is found.     

Propagation of thin plastic zones in the vicinity of a normally separating crack

A problem of the development of a plastic zone in the vicinity of a physical cut in the plain strain and stress states is posed and solved on the basis of a discrete deformation model under the assumption of an ideal elastoplastic medium. The Tresca yield condition and the ultimate plasticity condition are used in studying the plane stress state. The dependence of the plastic zone length on the external load is compared with a similar dependence obtained on the basis of the Leonov-Panasyuk-Dugdale model. In contrast to the Leonov-Panasyuk-Dugdale model, the distributions of stresses and lengths of plastic zones in the plane strain and stress states are found to be substantially different if elastic compressibility and compressive-tensile stresses along the cut direction are taken into account.     

纯滚动圆轮静摩擦力方向的确定

给出了匀质圆轮受力偶或水平力作用在水平地面上作纯滚动时, 其静摩擦力方向的确定方 法. 只受力偶作用作纯滚动的圆轮, 其摩擦力的方向仅取决于外力偶矩的转向, 判断依据为 摩擦力在该圆轮的平面运动中起阻碍圆轮的转动和为圆轮的平移提供主动力两相对的作用. 当圆轮只受水平力作用作纯滚动时, 用刚体平面运动微分方程和动能定理两种方法对摩擦力 方向进行了推导判定, 摩擦力的方向不仅与水平力的作用位置相关, 还与圆轮的大小和相对 质心的惯性半径等因素相关.     

Elasticity solutions for functionally graded plates in cylindrical bending

The plate theory of functionally graded materials suggested by Mian and Spencer is extended to analyze the cylindrical bending problem of a functionally graded rectangular plate subject to uniform load. The expansion formula for displacements is adopted. While keeping the assumption that the material parameters can vary along the thickness direction in an arbitrary fashion, this paper considers orthotropic materials rather than isotropic materials. In addition, the traction-free condition on the top surface is replaced with the condition of uniform load applied on the top surface. The plate theory for the particular case Of cylindrical bending is presented by considering an infinite extent in the y-direction. Effects of boundary conditions and material inhomogeneity on the static response of functionally graded plates are investigated through a numerical example.     

三向应力Mohr圆的真实构成及剪应力作用方向的确定

三向应力Mohr圆的构成在传统上是借助公式推证而得，并以平面图形来表示，缺乏三维的真实感和直观性。在应力应变分析中，对于平面应力问题，可以通过平面应力摩尔圆确定过一点不同斜面上的应力分量及其作用方向。对于三维问题，利用摩尔圆图解法可以确定某一斜面上的正应力和剪应力的数值，但不能表示剪应力的作用方向。剪应力的作用方向需要通过另外的图解方法来确定。本文分别从坐标系旋转和数值计算的角度解释了三向应力Mohr圆的构成过程，形象地说明了Mohr圆的物理本质。针对三向应力Mohr圆不能表示剪应力作用方向的问题，通过矢量运算，给出了剪应力作用方向的确定公式。     

Effects of material properties on the total stored energy of a hybrid flywheel rotor

Summary A numerical method based on the assumption of a generalized plane strain (GPS) state is presented for calculating the stress and strength ratio distributions of the rotating composite flywheel rotor of varying material properties in the radial direction. The rotor is divided into many rings and each ring has constant material properties. All the rings are assumed to expand and have the same axial strain. A three-dimensional finite element method is then used to verify the accuracy of the present method. This method gives a better solution for most of the rotors than other methods of a plane stress or plane strain state. After verification, the effects of material properties on the total stored energy (TSE) of the composite flywheel rotor are investigated. For this purpose, the material properties of the rotor, i.e. circumferential and radial Young's moduli, ply angles and mass densities are expressed by power functions of the radius, and the rotor is analyzed. The analysis shows that TSE can be most effectively increased by changing the circumferential Young's moduli along the radius, which amounts to over 300% of TSE of the constant material properties. The variation of ply angles along the radius can increase TSE by about 30% at most. The method of changing the mass densities along the radius could be also effective but its effects are not so noticeable in the rotor where the circumferential stiffness is properly arranged. Received 7 June 1999; accepted for publication 15 January 2000     

On a Pseudo-Differential Equation¶for Stokes Waves

It is shown that the existence of a smooth solution to a nonlinear pseudo-differential equation on the unit circle is equivalent to the existence of a globally injective conformal mapping in the complex plane which gives a smooth solution to the nonlinear elliptic free-boundary problem for Stokes waves in hydrodynamics. A dual formulation is used to show that the equation has no non-trivial smooth solutions, stable or otherwise, that would correspond to a Stokes wave with gravity acting in a direction opposite to that which is physically realistic.     

An Extension of the Complex Variable Method in Plane Elasticity to Domains with Corners: A Notch Problem

A severe limitation on the complex variable method in plane elasticity is the requirement that the region in which the stresses and strains are sought admits a rational conformal mapping into the half-plane or the unit circle. Of course, this limitation has not prevented the solution of many fundamental and interesting problems. However, the extension of this method to more general regions remains a source of debate. We here present an attempt in this direction. If the conformal mapping of the region is an algebraic function, it is still possible to find mathematical conditions defining the complex-valued stress function, but its explicit representation now requires the solution of a singular, linear, complex-valued, integro-differential equation.     

Experimental studies on the dynamic stability of liquid in a spherical tank covered with diaphragm under vertical excitation

Experimental studies are conducted on the liquid sloshing characteristics in a spherical tank covered with a flexible diaphragm. A spherical acrylic tank with 145.2 mm radius is used as a test tank, and is filled with water. Silicon diaphragms, plane or hemispherical type, with 0.2 mm thickness are used as test diaphragms. The test tank is harmonically excited in the vertical direction by an electro-dynamic exciter. During the test, vibrations due to parametric instability occur when the excitation frequency is twice the natural frequency. Parametric instability regions for some natural modes are measured and are presented in the excitation frequency–excitation acceleration diagram for three cases: liquid surface is uncovered (i.e., free surface), covered with a plane diaphragm, and covered with a hemispherical diaphragm, with the volume of filling water being changed appropriately.     

Photoelastic investigation of a shrink-fit problem

Stress analysis of the components of a shrinkfit assembly has been carried out by the three-dimensional photoelastic technique. Experimental results obtained from the analysis of a typical shrink-fit assembly, wherein a cylindrical wheel is shrink fitted onto a hollow cylindrical hub in an asymmetrical position. Photoelastic models made from hot-setting Araldite B were loaded at the critical temperature in a stress-freezing oven and the meridional and the hoop slices were observed in a transmission polariscope. It is concluded from this investigation that the bending induced in the components due to the asymmetrical placement of the wheel and the contact shear at the interface influences the stress distribution quite considerably. Also, the dimensions of the components in the axial direction have an influence on the mode and contribute to the magnitude of the variation of stress components.     

Analytical solutions for bending and flexure of helically reinforced cylinders

There has been a great deal of interest in the problems of modelling cables and ropes. A recent review by Cardou and Jolicoeur [Appl. Mech. Rev. 50 (1997) 1] considers the modelling of a cable which consists of a central core surrounded by one or several helically wound wire layers. One approach has been to consider the deformations of an individual helical wire and to synthesise the model of a cable by using contact conditions between the various wires. Other authors have adopted a continuum approach regarding each layer as a transversely isotropic material whose principal direction is along a helix surrounding the central axis of the cable. In each layer the helix angle is constant so that, when referred to cylindrical polar co-ordinates, the cylinder has a constant stiffness matrix in each layer. The intention in this paper is to use the continuum approach and describe the analytical solutions that govern the simple bending, flexure, or bending under a uniform load, of an anisotropic elastic cylinder consisting of a single material of this type. The extension of this work to a composite cylinder consisting of several concentric layers, surrounding a central core, which are either bonded together or make a frictionless contact, is briefly described.