结构力学中三铰斜拱等代梁的探索与应用

三铰斜拱的内力计算与合理拱轴线的推导与三铰平拱有所不同,在目前结构力学的教学过程中两者的整体性不强,针对这一问题,提出了一种采用等代梁计算的方法,推导了三铰斜拱的内力计算公式和三铰斜拱合理拱轴线的计算方法,并基于算例进行了验证,结果表明该方法表达式简单明确,物理概念清晰,计算结果正确,等代梁计算方法在三铰斜拱的教学过程中具有一定的实践价值.     

计算机绘制无铰拱影响线的解析法

提出了用Maple编程绘制无铰拱影响线的解析法.绘制了抛物线无铰拱在单位竖向移动载荷作用下,3个多余未知力的影响线;指定截面上的弯矩,剪力和轴力的影响线;支座水平约束力,垂直约束力及约束力矩的影响线.实例表明,利用Maple强大的符号运算功能,使用解析法绘制无铰拱影响线,速度快,方法简单,能同时给出影响线的解析表达式.     

水平弹性支撑圆拱的动力特性研究

用柔度法建立了水平弹性支撑拱结构的自由振动方程,考虑了拱脚处集中质量的附加惯性力. 计算分析了水平弹性支撑对两铰圆拱固有特性的影响,水平弹性支撑会使拱结构的自振频率减小,当拱结构的矢跨比为0.1 左右时影响最为显著,同时还会改变拱结构的振动形态,尤其在高阶振型中将完全按照梁的特点振动.分析了圆弧梁与两铰圆拱的振动内力特点,提出了柔度系数的概念,经过计算得到了水平弹性支撑拱转化为两铰圆拱和圆弧梁的临界柔度系数以及对应的临界刚度系数.     

剪力公式的论证与应用

 在结构力学中对梁和刚架绘制内力图时一般是先绘制弯矩图,再绘制剪力图. 根据 上述特点，寻求了一种应用弯矩图绘制剪力图的数值方法，即剪力公式. 该公式主要特点是： 把剪力计算的平衡问题转化为几何问题. 并且通过例题的应用，叙述了剪力公式的使用方法. 适用于静定结构和超静定结构.     

三铰拱弯矩影响线的图解法

 介绍了三铰拱弯矩影响线的一种图解方法, 并给出了完整的证明.     

一种抛物线浅拱线性单元

为研究抛物线浅拱在复杂受力状态下的线性内力及位移,考虑拱的压弯耦合作用,基于力法和浅拱假定,对抛物线拱平衡方程、几何方程和物理方程进行了分析;求得了抛物线拱内力方程通解格式,构建了抛物线浅拱位移形函数。利用最小势能原理,构造了抛物线浅拱单元。算例表明,本文构造的抛物线浅拱单元计算的抛物线拱内力与理论解计算结果符合较好,在划分一个单元时最大相对误差仅为4.03%,可用于抛物线拱分析。     

变截面弹性支承连续梁弯曲计算程序

1.程序功能 程序用BASIC语言编写,可在IBM微机系列及其兼容机上通用。 本程序可用于在各种载荷作用下,弹性支承、弹性地基和支座沉陷多种情况的变截面连续梁的弯曲计算,具有计算支座反力,计算指定截面的内力和变形,寻找最大内力和变形及其所在的截面位置,绘制全梁的内力图和变形图等多种功能。     

无结点线位移刚架在结点集中力作用下的内力分析

<正> 超静定刚架的内力计算及内力图的绘制,在结构设计中,是一项工作量很大的工作.但在某些特定的情况下,可以基本上不经计算而直接判断某些刚架的弯矩处处为零,其内力的情况如同桁架一样,只产生轴向力.这样,就大大简化了计算过程.无结点线位移刚架承受结点集中力作用时的情况就是如此.本文将用力法     

管系结构内力分析有限元软件SupPipe的研制与使用

 介绍管系结构内力分析有限元软件SupPipe的功能，计算流程 与使用说明.     

平板的内力近似计算

本文对承受均布荷载的平板的内力计算,推荐了一个近似计算方法.分别讨论了正方形板、矩形板和圆板在周边支承为铰支和固接两种情况.并提出一个力矩系数的概念.     

In-plane buckling of prismatic funicular arches with shear deformations

The in-plane buckling behavior of funicular arches is investigated numerically in this paper. A finite strain Timoshenko beam-type formulation that incorporates shear deformations is developed for generic funicular arches. The elastic constitutive relationships for the internal beam actions are based on a hyperelastic constitutive model, and the funicular arch equilibrium equations are derived. The problems of a submerged arch under hydrostatic pressure, a parabolic arch under gravity load and a catenary arch loaded by overburden are investigated. Buckling solutions are derived for the parabolic and catenary arch. Subsequent investigation addresses the effects of axial deformation prior to buckling and shear deformation during buckling. An approximate buckling solution is then obtained based on the maximum axial force in the arch. The obtained buckling solutions are compared with the numerical solutions of Dinnik (Stability of arches, 1946) [1] and the finite element package ANSYS. The effects of shear deformation are also evaluated.     

Linear and geometrically nonlinear analysis of non-uniform shallow arches under a central concentrated force

In this paper an integral equation solution to the linear and geometrically nonlinear problem of non-uniform in-plane shallow arches under a central concentrated force is presented. Arches exhibit advantageous behavior over straight beams due to their curvature which increases the overall stiffness of the structure. They can span large areas by resolving forces into mainly compressive stresses and, in turn confining tensile stresses to acceptable limits. Most arches are designed to operate linearly under service loads. However, their slenderness nature makes them susceptible to large deformations especially when the external loads increase beyond the service point. Loss of stability may occur, known also as snap-through buckling, with catastrophic consequences for the structure. Linear analysis cannot predict this type of instability and a geometrically nonlinear analysis is needed to describe efficiently the response of the arch. The aim of this work is to cope with the linear and geometrically nonlinear problem of non-uniform shallow arches under a central concentrated force. The governing equations of the problem are comprised of two nonlinear coupled partial differential equations in terms of the axial (tangential) and transverse (normal) displacements. Moreover, as the cross-sectional properties of the arch vary along its axis, the resulting coupled differential equations have variable coefficients and are solved using a robust integral equation numerical method in conjunction with the arc-length method. The latter method allows following the nonlinear equilibrium path and overcoming bifurcation and limit (turning) points, which usually appear in the nonlinear response of curved structures like shallow arches and shells. Several arches are analyzed not only to validate our proposed model, but also to investigate the nonlinear response of in-plane thin shallow arches.     

Snap-through buckling of two simple structures

The snap-through buckling of two simple structures subjected to quasistatic loading is analyzed by use of the elastica theory of prismatic bars. In the first problem, the deformation of perfect and imperfect three-hinged deep trusses is considered and the results of the previous experimental observations are explained analytically. In the second problem, the snap-through behavior of a column restrained by an elastic wire is studied and a comparison of critical loads are made with the approximate solutions obtained recently by Nachbar [1].     

Planar nonlinear dynamic analysis of cable-stayed bridge considering support stiffness

Support stiffness is one of important factors on structure dynamics. Considering the vertical support stiffness, a multi-cable-stayed shallow-arch model of the cable-stayed bridge is established. Its differential equation governing the planar motion of cables and the shallow arch and the boundary conditions are derived by Hamilton’s principle. Firstly, the in-plane free vibration of the system is explored in order to find the modal functions and the possible internal resonances of nonlinear dynamics. Then, the 1:2:2 internal resonance among the different modes of the shallow arch and two cables are investigated by the multiple time scale method and pseudo-arclength algorithm. Meanwhile, the frequency-/force–response curves are used to explore the nonlinear behaviors of the system, especially the influence of vertical support stiffness, excitation frequency and amplitude on the internal resonance of the system is considered. To a certain extent, the support stiffness can reduce the response amplitudes of members by absorbing some energy from excitation.

     

On the Collapse of Masonry Arches

In this paper a constitutive equation for masonry arches is defined and its main properties are proven; in this equation to each pair of generalized strains (, ), with the extensional strain and the curvature change of the centre line, is assigned the pair of generalized internal forces (N,M), where N is the normal force and M the bending moment. Subsequently, the collapse of masonry arches is characterized and the static and kinematic theorems proven. Finally, a method for determining the collapse load in the case of circular arches subjected to their own weight and a vertical point load applied at a point of the extrados is presented. The results obtained, of interest in some applications, are summarized in a series of graphs.     

建立基于力的变截面梁单元质量矩阵的新方法

基于位移的有限梁单元中三次Hermite插值函数不能有效地描述变截面梁单元内部位移变化,只能通过加密网格增加单元数解决,会造成计算量增大。基于力的有限梁单元由于使用的力插值函数不受截面形状变化的影响,在处理变截面梁时有很大优势,可以得到精确的位移插值函数,利用较少的单元可以达到很高的精度,解决了基于位移的有限梁单元在处理变截面梁时的不足。本文得到了考虑剪切变形的位移插值函数和考虑转动惯量的一致质量矩阵。利用算例验证了本文理论的正确性和高效性。     

考虑剪力滞后效应的钢-混凝土组合梁力法单元

本文通过在Newmark模型中引入翘曲形函数来描述楼板纵向位移的横向非均匀分布．然后采用虚余功原理建立了考虑剪力滞后效应的钢—混凝土组合梁力法单元。该力法单元严格地满足平衡条件．而仅在积分意义上满足变形协调条件，但具有与通用位移有限元法相一致的刚度矩阵形式。由于受平衡条件的限制结点外力不相互独立，而翘曲位移引起的双弯矩和双剪力使得内力关系变得非常复杂，本文给出了推导力法梁单元内力形函数的通用方法。此外．本文还考虑了梁间荷载的存在对内力形函数的影响。算例分析表明，所提出的力法单元有较高的精度，并发现：在有梁间分布荷载时．采用将梁间分布荷载等效为结点荷载的方法将显著降低应力的精度，而采用高次力法单元对于提高情度没有明显的作用。     

Determination of adhesive parameters characterizing the interaction of pneumatic tires and concrete pavement from pull-slip curves

The author has applied traction-slip curves obtained from drawbar pull tests to determine values of the adhesive parameters controlling the peripheral forces of rubber tires rolling on concrete. The method is based on an analogy with soil shear strength characterized by cohesion, the angle of internal friction, and the tangent modulus of the derived shear-deformation curve. The peripheral force generated by a tire rolling on concrete is the total force required to shear the interlocking elementary particles in the contact patch. The adhesive parameters derived using this method are average values expressing the effect of all factors which contribute to producing the peripheral force.     

标准线性固体土模型条件下桩的动力响应分析与应用

在桩侧土为标准线性固体模型条件下，建立了成层土中考虑桩端和桩侧土作用的有限长桩，桩顶受纵向激励情况下的定解问题，用拉氏变化(Laplace)求得桩顶阻抗函数和速度频率响应的函数，然后利用卷积定理和傅立叶(Fourier)逆交换求得任意激振力作用下桩顶速度响应的半解析解，并研究了模型中各个主要参数对桩顶响应及速度响应曲线的影响，并分析了缺陷桩和不同土参数对曲线的影响，得到了许多新的有意义的结论。     

A skid steering model using the Magic Formula

The paper describes a computer model for predicting the steering performance and power flows of a notional skid steered tracked vehicle. The force/slip characteristics of the rubber track pads are calculated by means of the so-called Magic Formula. Relevant parameters for the Magic Formula are derived from the limited amount of data available from traction tests with a tracked vehicle on a hard surface. The computer model considers the vehicle in steady state motion on curves of various radii and allows for lateral and longitudinal weight transfer, roll and pitch motions and the effects of track tension forces. Vehicle dimensions, Magic Formula parameters and the equations of motion are set up in a Microsoft Excel spreadsheet and solutions obtained using the Solver routine. Model outputs are described in terms of driver control input and various power flows against lateral acceleration. Maximum lateral acceleration is generally limited by the available engine power. In some conditions the outer track sprocket could be transmitting almost twice the maximum net engine power. For vehicles with a single electric motor/inverter driving each sprocket, these units would need to be able to transmit these high intermittent powers.