弹性结点结构的内力计算

本文视某些结构的全部或部分结点为弹性结点，对此类弹性结点结构的内力计算进行了探讨，给出了杆端为不同弹性约束时的等直杆转角位移方程，举例说明了用位移法求解此类结构内力的方法步骤。     

矩阵位移法分析桁架结构

矩阵位移法分析桁架结构,具有易于实现计算自动化的优点,得到广泛应用.它的主要解题思路是:首先将结构离散成为有限个独立的单元,进行单元分析,建立单元杆端力与单元杆端位移之间的关系式---单元刚度方程;然后利用结构的变形连续条件和平衡条件将各单元组成整体,建立结点力与结点位移之间的关系式---结构刚度方程,这一过程为整体分析;最后求得结构的位移和内力.矩阵位移法就是在一分一合,先拆后搭的过程中,把复杂结构计算问题转化为简单的单元分析和集合问题.     

关于内力,杆端位移关系和弯矩分析的研究

用广义图乘法基本公式，得到了常见杆的内力，荷载和杆端位移的基本关系，当取值参数是０，１时，某些基本关系是超静定杆的转角位移方程，在１／３，１／２，２／３点上，弯矩与杆端位移有特定关系，得到杆端位移与荷载的关系（一般杆件除外）利用基本关系分析结构，形成了分析结构的弯矩分析法，对于某些常见刚架用弯矩分析求解，其未知量较少。     

简化位移法正则方程的一种方法

本文将超静定结构中的结点转角和位移进行了重新组合,建立了新的位移弯矩系统,使得位移法正则方程为之简化,这个问题有一定的实际意义。     

求解杆系结构自由振动问题的力法

杆系结构的静力分析有两类方法——力法和位移法,而自由振动分析却仅有位移法。针对这一缺失,提出杆系结构自由振动的力法分析方法。通过放松某个位移约束并施加相应的动内力来建立力法的基本体系。当动内力的频率等于结构自振频率时被放松的约束位移重新得到满足,此时基本体系与原结构等价,由此建立力法的控制方程。该控制方程为频率的非线性方程,对该方程的求解建立了Newton法的迭代格式。数值算例表明该法是一个精确、高效、实用的方法。     

用转移矩阵法计算连续梁

本文提出用转移矩阵法计算连续梁的内力和位移。将连续梁两端结点的位移和杆端力，用转移矩阵来表达，然后由边界条件求解，再求出各单元的位移和杆端力。对有ｎ个结点的连续梁，每个结点的未知量为Ｚ，采用一般矩阵位移法计算，未知量数目为ｎＺ个，而按本文方法计算，未知量数目仅为２Ｚ个。未知量数目与结点总数无关。这将大大减少存贮量和计算工作量，结点数目越多，优点越明显。     

结构地震响应分析的波动方法

在结构中构造被研究块体,针对其质心建立动力平衡方程;由考虑弯剪变形的杆端力与杆端位移之间关系式推导出段间内力计算公式;在时间域上交替运用动力平衡方程和段间内力计算公式进行递推计算,给出高耸结构、三维框架结构地震响应分析的波动方法。对于高耸结构,考虑了被研究块体质心与空间离散结点之间的偏心问题,给出了修正的动力学方程。利用框架结构地震响应分析的波动方法研究了短跨结构的行波效应问题。结果表明:采用传统方法计算给出的电视塔地震响应结果会偏小。考虑行波效应时,二维和三维框架结构柱子的剪力和梁端弯矩存在显著增大现象。     

一维C~1有限元后处理超收敛计算的新型算法

该文针对一维C~1有限元提出一种新型后处理超收敛算法,由该法可求得全域超收敛的位移和内力。该法在单个单元上逐单元实施,通过将单元端部结点位移有限元解设为本质边界条件,在单元域上建立单元位移恢复的局部边值问题。对该局部边值问题,以单元内任一点为结点将单元划分为两个子单元进行有限元求解,子单元次数与原单元相同,由此获得该点位移的超收敛解。对单元内所有点均作这样的超收敛求解,可获得整个单元上位移的超收敛解。该位移超收敛解光滑、连续,通过对该位移超收敛解求导可获得转角和内力的超收敛解。数值结果表明,对于m次元,该法得到的挠度和转角具备与结点位移相同的h~(2m-2)阶的最佳收敛阶;弯矩和剪力则分别具备h~(2m-3)、h~(2m-4)阶的收敛阶,均比相应有限元解高出m-2阶。该法可靠、高效、易于实施,是一种颇具潜力的后处理超收敛算法。     

运动方程自适应步长求解的高性能Galerkin时程单元初探

该文以一阶运动方程为例,利用其非自伴随性质,构建了新型的凝聚检验函数,进而提出了一套高性能Galerkin有限单元——凝聚单元.该单元为无条件稳定的单步法单元,对于(m)次多项式单元,其端结点位移和速度均可达到O(h2(m)+2)阶的超高收敛性,比常规Galerkin单元的结点精度高2阶.采用此单元,该文进而实现了无需...     

一种计算功能梯度材料杆与轴弹性模量的方法

介绍一种功能梯度材料杆和轴的弹性模量E和剪切模量G的测定方法,考虑弹性模量E和剪切模量G为杆和轴长度方向的函数,将杆和轴离散化。在保证离散化后的单元满足平衡方程的条件下,分别建立单元节点处的弹性摸量E和位移、剪切模量G和转角的关系。此关系表明,当单元节点处的位移和转角被分别测定后,可得到离散分布的弹性摸量E和剪切模量G。数字仿真时假设弹性模量E和剪切模量G为沿长度方向的指数函数,用有限元软件计算了单元节点处的位移和转角。用这些位移和转角反过来计算得出的离散弹性摸量和剪切模量和假设的指数函数值的误差是可以控制在一定范围的。     

厚薄通用板元在厚筏基础中的应用

Timoshenko厚梁理论提供了随梁厚变化的剪应变函数,将其应用于厚板中,得到板剪应变场,此外,假设整个板元的挠度场为不完全四次式,引入广义协调理论,建立了两个变量场的协调方程,从而构建了一个无剪切闭锁的厚薄通用板元。在此基础上,利用最小位能原理,得出考虑转角支撑作用的厚筏基础和Winkler弹性地基的共同作用方程。最后,将其首次应用于实际工程的分析中。     

Frequency equation and mode shape formulae for composite Timoshenko beams

Exact expressions for the frequency equation and mode shapes of composite Timoshenko beams with cantilever end conditions are derived in explicit analytical form by using symbolic computation. The effect of material coupling between the bending and torsional modes of deformation together with the effects of shear deformation and rotatory inertia is taken into account when formulating the theory (and thus it applies to a composite Timoshenko beam). The governing differential equations for the composite Timoshenko beam in free vibration are solved analytically for bending displacements, bending rotation and torsional rotations. The application of boundary conditions for displacement and forces for cantilever end condition of the beam yields the frequency equation in determinantal form. The determinant is expanded algebraically, and simplified in an explicit form by extensive use of symbolic computation. The expressions for the mode shapes are also derived in explicit form using symbolic computation. The method is demonstrated by an illustrative example of a composite Timoshenko beam for which some published results are available.     

管道内旋转细长梁的固液耦合方法研究

管道内旋转细长梁是石油钻采工程中的特有结构,旋转细长梁不仅与管道内壁产生随机多向碰撞,还与细长梁内外管道和环空流体耦合,是一个复杂的非线性固液耦合系统,迄今还未见该方面的研究文献.该文考虑管道内旋转细长梁的结构和工作状态,将结构动力学方程、流体连续方程和动量方程耦合,推导了界面力和界面位移的计算公式、迭代格式及收敛准则...     

Impulsive motion of ideally constrained mechanical systems via analytical dynamics

This paper formulates the general variational equation, or principle, for the impulsive motion of mechanical systems subjected to ideal impulsive constraints, in both holonomic and nonholonomic coordinates, then applies it to problems with persistent impulsive constraints and, with the help of Lagrange's method of undetermined multipliers, produces all possible impulsive equations of motion, with or without the associated reactions, in holonomic or nonholonomic coordinates. These equations are the impulsive counterparts of the well-known finite motion equations of Routh/Voss, Maggi, Hadamard, Boltzmann/Hamel, Chaplygin/Voronets, and Appell. Finally, a simple example is presented and solved with several of the above methods.     

Numerical method of inertance tube pulse tube refrigerator

A nodal analysis method for simulating inertance tube pulse tube refrigerators is introduced. The energy equation, continuity equation, momentum equation of gas, energy equation of solid are included in this model. Boundary condition can be easily changed to enable the numerical program calculate thermal acoustic engines, inertance tube pulse tube refrigerators, double inlet pulse tube refrigerators, and others. Implicit control volume method is used to solve these equations. In order to increase the calculation speed, the continuity equation is changed to pressure equation with ideal gas assumption, and merged with momentum equation. Then the algebraic equation group from continuity and momentum equation becomes one group. With this numerical method, an example calculation of a large scale inertance tube pulse tube refrigerator is shown.     

Brachistochronic motion of a nonholonomic rheonomic mechanical system

The brachistochrone problem of the rheonomic mechanical system whose motion is subject to nonholonomic constraints is solved with nonlinear differential equations of motion. Apart from control forces, the system is influenced by the action of other known potential and nonpotential forces as well. The problem of optimal control is solved by applying Pontryagin’s Maximum Principle and the singular optimal control theory. This procedure results in the two-point boundary value problem for the system of ordinary nonlinear differential equations of the first order, with a corresponding number of initial and end conditions. This paper determines the control forces that are realized by imposing on the system a corresponding number of independent ideal holonomic constraints, without the action of active control forces. These constraints must be in accordance with the previously determined brachistochronic motion. The method is illustrated with a single complex example that represents the first known concrete demonstration of brachistochronic motion of the nonholonomic rheonomic mechanical system.     

热-力-粘弹耦合多孔FGVM梁的动力学特性

研究了初始轴向机械力作用下三参数Winkler-Pasternak粘弹性地基上多孔功能梯度粘弹性材料(FGVM)梁在热环境中的自由振动特性.考虑满足热传导方程的稳态温度分布以及材料性质的温度相关性,采用Kelvin-Voigt模型并由含孔隙率修正的混合幂率梯度分布来表征内含均匀孔隙FGVM梁的材料属性.基于n阶广义梁理...     

均布荷载作用下一次超静定梁的弹塑性分析

通过虚功原理和单位荷载法分析了均布荷载作用下一次超静定梁的弹塑性加载及变形过程。受力变形可分为四个阶段:弹性阶段、固支端附近产生塑性变形阶段、固支端为塑性铰而固支端附近塑性区卸载阶段、固支端保持为塑性铰而梁中部部分区域产生塑性变形直至形成塑性流动阶段。给出了加载各阶段的弯矩、位移公式及外荷载与支反力的关系式,可供工程结构设计和力学教学参考。     

Postbuckling characteristics of nanobeams based on the surface elasticity theory

In the present paper, an attempt is made to numerically investigate the postbuckling response of nanobeams with the consideration of the surface stress effect. To accomplish this, the Gurtin–Murdoch elasticity theory is exploited to incorporate surface stress effect into the classical Euler–Bernoulli beam theory. The size-dependent governing differential equations are derived and discretized along with various end supports by employing the principle of virtual work and the generalized differential quadrature (GDQ) method. Newton’s method is applied to solve the discretized nonlinear equations with the aid of an auxiliary normalizing equation. After solving the governing equations linearly, to obtain each eigenpair in the nonlinear model, the linear response is used as the initial value in Newton’s method. Selected numerical results are given to show the surface stress effect on the postbuckling characteristics of nanobeams. It is found that by increasing the thickness of nanobeams, the postbuckling equilibrium path obtained by the developed non-classical beam model tends to the one predicted by the classical beam theory and this anticipation is the same for all selected boundary conditions.     

考虑粘结层滑移效应的组合梁弯曲

针对粘结型组合梁,在粘结层仅沿轴向剪切变形的假定下,给出了组合梁大挠度弯曲的一般非线性控制方程,指出仅在一阶近似下,组合梁子梁的轴线挠度相等.其次,在Euler-Bernoulli 梁变形的条件下,通过线性化方法,由上述非线性控制方程得到以挠度和轴向位移为基本未知量的组合梁线性弯曲耦合控制方程,该耦合方程组可分别退化为经典组合梁和叠梁的控制方程.最后,分析了悬臂组合梁在端部集中力作用下的线性弯曲,得到了问题的解析解,给出了不同梁长下组合梁自由端挠度、粘结层滑移位移和剪切应力等随粘结层剪切模量和厚度的变化曲线,进行了参数分析,结果表明:粘结层厚度和剪切模量对组合梁挠度和粘结层滑移有较为显著的影响,而对粘结层剪力影响很小.