基于双面双参数理论的全长黏结性锚索内力分析

基于岩质边坡全长黏结性锚索的受力特性,采用双参数地基梁模型建立了锚索受力方程,推导得到了考虑轴向应变和地基切向抗力作用的岩质边坡全长黏结性锚索的径向位移和内力、挠度公式,进一步运用推导的公式对实际工程中的全长黏结性锚索结构内力进行了计算。结果表明:①全长黏结性锚索的剪力和弯矩均出现两段式的变化,均呈现先增后减的趋势,但弯矩值很小,可忽略不计,其轴力曲线整体呈现抛物线式减小,且最大轴力出现在全长黏结性锚索的锚头位置;②运用双参数地基梁模型对全长黏结性锚索进行计算时,仅需确定地基基床系数等参数即可,这为缺少黏聚力和内摩擦角时计算全长黏结性锚索内力提供了一种新方法。     

含孔软铁磁材料Mindlin板中弹性波散射问题

基于考虑磁弹相互作用的Mindlin板弯曲波动方程，采用波函数展开法，分析研究 了含孔软铁磁材料Mindlin板中弹性波散射与动应力集中问题，给出了问题的分析 解和数值算例. 通过分析发现：磁感应强度对动弯矩集中系数和动剪力集中系数有 增加的作用，特别是在低频的情况下.     

基于平板振动精确化方程求解动应力集中问题

基于文献[8]给出的平板弯曲振动精确化方程,对含圆孔平板中弹性波散射与动应力集中问题进行了研究.文中给出了分别基于Mindlin板与精确化板方程在不同参数下圆孔动弯矩集中系数的数值结果,并对结果进行了对比分析和讨论.结果表明:在较低频率和薄板情况下,基于文献[8]的方程与基于Mindlin板理论得到的动弯矩结果是基本一致的;在较高频率和厚板情况下,基于文献[8]的方程与基于Mindlin板理论的动弯矩结果相差较大,最大值超出可达16%.由于文献[8]给出的平板振动精确化方程是在没有任何工程假设条件下得到的,因此其分析计算结果更精确一些.      

单索面斜拉桥活载作用下主梁负剪力滞效应研究

以沈阳某单索面斜拉桥为研究背景,采用有限元理论,通过建立空间有限元模型研究了单索面斜拉桥主梁成桥阶段均布车载及偏载对控制截面最大负弯矩加载情况下截面的受力特性和负剪力滞效应.结果表明:在车辆荷载作用下,主梁各板产生了横向弯曲正应力及剪应力,使截面应力发生了变化;对控制截面最大负弯矩加载时,各控制截面剪力滞系数为0.64~0.983,主梁截面出现负剪力滞效应.偏载作用使得箱梁截面应力分布很不均匀,但其应力量值小于均匀车载作用下的应力水平,偏载工况并不控制箱梁截面设计.     

考虑切向摩擦力时弹性地基梁的振动

假定切向摩擦力与梁底面的纵向位移成正比,通过引入广义剪力,得到了梁的位移型平衡方程。将位移及荷载展开为带附加项的Fourier级数,利用平衡方程和边界条件研究了弹性地基梁的自由振动和简谐振动。通过算例结果分析表明:纵向摩擦力对梁的固有频率、位移和内力均有影响。梁的最大挠度、转角、弯矩及剪力随着地基纵向反力系数的增大而减小;梁的固有频率、轴向位移和轴力则随着地基纵向反力系数的增大而增大;同时轴力引起的轴向位移和转角引起的梁底面纵向位移具有同一数量级。     

锚索抗滑桩工程的优化设计研究

锚索抗滑桩与普通抗滑桩相比,其受力状态更加合理。本文通过建立合理的计算模型和计算简图,推导出锚索在桩身任意位置的计算公式,并编制程序实现弯矩和应力的计算,确定出最优的锚固角和最优的锚索位置,可以有效减小抗滑桩的弯矩,更加充分的发挥锚索的作用。文中最后结合延安宝塔山滑坡治理,给出了实际应用结果。     

采用精确化理论求解厚板任意形开孔动应力集中

摘要：本文基于复变函数与保角映射法,采用平板弯曲振动精确化方程[9],对含任意形开孔平板中弹性波散射与动应力集中问题进行了研究。利用正交函数展开的方法将待解的问题归结为对一组无穷代数方程组的求解。作为算例,计算了自由边界条件下圆孔和椭圆孔的动弯矩集中系数的数值结果,并对板厚与孔径比对动弯矩分布的影响做了分析研究。结果表明：入射波数、平板厚度和椭圆偏心率等参数对动弯矩的分布都有很大的影响。在较低频率和平板较薄的情况下,基于文献[9]的方程与基于Mindlin板的动弯矩结果在数值分布上是基本一致的;在较高频率和平板较厚的情况下,基于文献[9]的方程与基于Mindlin板的动弯矩结果在数值分布计算结果相差较大。由于文献[9]给出的平板振动精确化方程是在没有任何工程假设条件下得到的,因此本文的分析计算结果更精确一些。     

对压弯构件附加弯矩的研究

 分析轴向力对压弯构件弯曲变形的影响，导出了轴向力对压弯构件引起的附加弯矩的一 般表达式. 通过实例计算，定量分析了附加弯矩对压弯构件的最大弯矩的影响，得出了在实 际问题中可否忽略附加弯矩的判别条件.     

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提出该结构体系在水平载荷作用下,可视为夹层复合构件,并提出了计算模型. 根据 变形协调原理对其进行受力分析,建立了多层多跨密肋复合墙体结构横向位移及各组成构件承 受剪力和弯矩表达式. 通过计算分析指出,各组件剪力分配只与各组件刚度及宽度比有关, 内墙板上部分配剪力大于下部,边框反之;各组件局部弯矩系数随$\lambda $的增加而减小,其整体工作性能增强,当$\lambda $增加到一定数值时,其工作性能与悬壁构件类似.     

考虑桩头约束的纵横向受荷微倾单桩响应分析

考虑桩身初始微倾斜,假定地基水平抗力系数沿深度线性增加,推导出纵横向荷载下桩周土屈服时桩身挠曲线微分方程,继而求得桩身响应的幂级数解。采用桩头约束度表征桩头转动约束,结合已有的自由段和弹性段桩身响应的幂级数解及桩底的边界条件,并基于各分界点处桩身响应的连续性,提出了桩身变形和内力的计算方法。与模型实验结果及已有解计算结果的对比验证了该法的可靠性。计算结果表明:随着桩头约束度的增加,桩顶位移和地表以下桩身最大弯矩近似线性减小;桩头约束度存在一临界值,在该值处桩身最大弯矩达到最小值;随着桩身初始倾角的增加,桩顶位移和桩身最大弯矩近似线性增大,其变化速率随纵向荷载的增加而增大。     

Orbital oscillations of an elastic vertically-tethered satellite

The motion of a satellite in a circular orbit with respect to its center of mass is considered. The satellite bears an elastic tether system unrolled along the local vertical. The load at the end of the tether oscillates harmonically. The satellite motion under the action of the gravitational moment and the moment due to the tether tension force is studied. The bifurcation diagram is constructed and the hetero- and homoclinic separatrix trajectories are determined. Mel'nikov's method is used to study the satellite chaotic behavior near separatrices under the action of the periodic tether tension force. The results of the present paper can be used to analyze tether systems of gravitational stabilization and to study the orbital behavior of a satellite with an unrolled tether system with respect to the satellite center of mass.     

含剪力销(锥)螺栓法兰连接结构非线性特性

连接结构广泛应用于航空航天、化工装备和核电站等大型工业装备中。对于轴弯剪组合作用下的连接结构,需要螺栓、法兰和剪力销的联合工作以抵抗外力。本文针对含剪力销(锥)的螺栓法兰连接结构的动力学问题开展研究,将该类结构抽象为三自由度的质量-双线性弹簧系统,建立非线性动力学模型的数学列式,并进行数值求解。重点研究该系统在横向冲击(剪力)下的动力学特性。通过理论分析与数值计算,指出该非线性系统存在3个方向自由度全耦合的振动现象,并阐述该系统自由度的解耦条件;对纵向振动与横向错动的耦合振动频率关系进行讨论并分析其相互联系;研究剪力销倾角对螺栓最大轴向拉力的影响规律并给出关系曲线,指出其最佳设计角度区间。     

固定结构下的两向力及弯矩传感器设计

为了刀板切削过程中的受力满足最合理的设计准则,专用传感器设计须基于固定总体结构,对局部结构优化,以达到设计合理的目的。刀板切削时受到土体的阻力可分解为水平力和垂直力,多维力传感器测量了两个力的大小和对传感器产生的弯矩。刀板工作中,弯矩引起的正应力比垂直力引起的拉应力及水平力引起的切应力要大得多,因此特别设计了弹性体的局部结构使得三个应力值接近于同一量级。传感器的标定结果显示,输入输出有良好的线性关系,并且很好地消除了耦合效果。最终,将该传感器应用于土体切削测试并验证了其可靠性。     

Large deflections of cantilever beams of non-linear elastic material under a combined loading

Large deflection of cantilever beams made of Ludwick type material subjected to a combined loading consisting of a uniformly distributed load and one vertical concentrated load at the free end was investigated. Governing equation was derived by using the shearing force formulation instead of the bending moment formulation because in the case of large deflected member, the shearing force formulation possesses some computational advantages over the bending moment formulation. Since the problem involves both geometrical and material non-linearities, the governing equation is complicated non-linear differential equation, which would in general require numerical solutions to determine the large deflection for a given loading. Numerical solution was obtained by using Butcher's fifth order Runge-Kutta method and are presented in a tabulated form.     

Deformation analysis of infinite-strip bearings of laminated elastic material interleaving with tension-only reinforcements

Bonding with fiber reinforcements can increase the stiffness of elastic layers only when the elastic layer is compressed. Fiber loses its rigidity when it is not stretched. The procedure to include this ‘tension-only’ nonlinearity in the deformation analysis of the fiber-reinforced bearing is developed. In the elastic layers bonded with tension-only reinforcements, the responses to the compression force and the bending moment are coupled unless the reinforcements are entirely in tension. The coupled relation, which is not linear, depends on the length of the tension zone in the reinforcement. Increasing the compression force on the bearings will extend the tension zone in the reinforcements and enhance the stiffness of the bearing, but the compression force may add more bending moment to the bearings and increase the lateral deformation. The vertical buckling load of the bearings with tension-only reinforcements varies with the lateral force and is smaller than the buckling load of the bearings with linear reinforcements.     

DYNAMIC ANALYSIS OF A LOADED SHOULDER-POLE DURING WALKING

建立了扁担挑物的动力学模型和动力学方程,并进行了数值求解。扁担挑物时存在三种频率,即重物类似于单摆的振动频率、挑运者的步行频率和扁担-重物系统铅垂方向的振动频率。计算结果表明,为了获得较好的挑担体验,三种频率应该相互协调。当人挑担行走的频率为扁担-重物系统铅垂方向振动频率的70%,$\sim$,80%时,肩部铅垂附加动反力为重物重力的30%左右且与肩部铅垂运动同相,当重物类似于单摆的振动频率为人步行频率的25%,$\sim$,30%时,重物的摆角和肩部受到的水平附加动反力均较小,从而有利于人挑担行走。     

Eigenanalysis and continuum modelling of pre-twisted repetitive beam-like structures

A repetitive pin-jointed, pre-twisted structure is analysed using a state variable transfer matrix technique. Within a global coordinate system the transfer matrix is periodic, but introduction of a local coordinate system rotating with nodal cross-sections results in an autonomous transfer matrix for this Floquet system. Eigenanalysis reveals four real unity eigenvalues, indicating tension–torsion coupling, and equivalent continuum properties such as Poisson’s ratio, cross-sectional area, torsion constant and the tension–torsion coupling coefficient are determined. A variety of real and complex near diagonal Jordan decompositions are possible for the multiple (eight) complex unity eigenvalues and these are discussed in some detail. Analysis of the associated principal vectors shows that a bending moment produces curvature in the plane of the moment, together with shear deformation in the perpendicular plane, but no bending–bending coupling; the choice of a structure having an equilateral triangular cross-section is thought responsible for this unexpected behaviour, as the equivalent continuum second moments of area are equal about all cross-sectional axes. In addition, an asymmetric stiffness matrix is obtained for bending moment and shearing force coupling, and possible causes are discussed.     

非贯穿直裂纹管局部柔度系数的理论研究

局部柔度是裂纹结构力学响应分析和损伤识别的重要参数之一,然而目前尚缺乏裂纹管局部柔度系数的求解方法.本文根据线性断裂力学理论,获得了轴力、剪力和弯矩等荷载作用下非贯穿直裂纹管单元的附加局部柔度方程,利用自适应的Simpson数值积分方法计算得到裂纹引起的附加局部柔度系数.通过与Naniwadekar等裂纹管模型试验进行...     

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。     

A general analytic solution for plane strain bending under tension for strain-hardening material at large strains

A new analytic solution for plane strain bending under tension of a sheet is proposed for elastic-plastic, isotropic, incompressible, strain-hardening material at large strains. Numerical treatment is only necessary to calculate ordinary integrals and solve transcendental equations. No restriction is imposed on the hardening law. All governing equations and boundary conditions are exactly satisfied. The only exception is that the actual stress distribution over the ends of the sheet is replaced with a concentrated force and a concentrated bending moment. The through-thickness distribution of residual stresses and a measure of springback are also found. The range of validity of the solution is determined. An illustrative example is provided for Swift’s hardening law.