箱形梁剪力滞效应的分离求解方法及参数影响分析

选取剪力滞效应引起的附加挠度为广义位移,将箱梁的剪力滞变形状态从初等梁挠曲变形状态中分离出来,作为一种独立的变形状态进行分析,运用能量变分法建立了以附加挠度为未知量的截面控制微分方程及边界条件;结合简支边界条件分别导出了集中荷载和均布荷载作用下箱梁的附加挠度和纵向应力计算公式.纵向应力分析表明:该文方法计算的应力结果和样条函数法计算的应力结果吻合良好,从而验证了其方法的正确性.挠度研究表明:剪力滞附加挠度由跨中向两侧支点递减;针对于该文算例而言,均布荷载和集中荷载作用下跨中截面的剪力滞附加挠度分别占初等梁挠度的2. 57%和3. 03%;随着高跨比和宽跨比的增大,相应箱梁跨中截面的附加挠度逐渐减小,且宽跨比对附加挠度的影响远大于高跨比的影响.     

移动荷载作用下黏弹性地基-Timoshenko梁振动响应对比分析

基于Fourier变换方法,对移动荷载作用下三维、二维和一维轨道-地基模型的振动响应特征进行了研究,将轨道视为Timoshenko梁,比较了不同速度和地基厚度下各计算模型之间的响应差异.研究结果表明:三维模型存在一个地基等效刚度,为波数和频率的函数.二维和三维模型的临界速度较为接近,但比一维地基梁模型要小得多.荷载速度小于地基临界速度时,三维模型的梁挠度幅值最小,二维模型次之,一维模型梁挠度最大.当荷载速度达到或超过临界速度时,二维模型的梁挠度幅值变得最大,此时三者的挠度时程曲线存在明显差别.二维和三维模型的地层水平位移幅值先随地基深度增加而增大,在某一深度达到最大值后随深度增加逐渐减小,竖向位移幅值则随深度的增加逐渐减小.     

双层0.618法在某力学问题中的应用

建立了一组平行移动荷载作用下,简支桥梁挠度的数学模型;利用双层0.618法搜索梁的绝对最大挠度对应的最危险截面位置以及移动荷载最不利位置,计算该位置相应的挠度得到梁的绝对最大挠度.本文算法以计算机为工具,适用于任意有限多个平行移动荷载,对于桥梁的设计计算与安全评估,有一定的实用价值.     

有限位移理论的功的互等定理及其应用

提出了有限位移理论三维线弹性力学的功的互等定理.基于这一定理,导出了大挠度弯曲矩形板的功的互等定理.同时,应用简化矩形板的定理,直接得到了大挠度板条的功的互等定理.作为应用,计算了在均载作用下两端固定大挠度板条的弯曲和在均载作用下4边固定大挠度矩形板的弯曲.计算表明,根据弯曲薄板大挠度功的互等定理,大挠度弯曲矩形板可应用小挠度的相应基本解得以简单解决.     

双向弹簧夹层假定的弹性地基上双层板的解

建立了轴对称条件下,层间有双向弹簧夹层的弹性地基上双层板力学模型,应用Hankel(汉克尔)变换法推演得到了任意轴对称荷载作用下的Winkler(文克勒)地基、双参数地基和弹性半空间体地基上无限大双层板的一般解析解,给出了双层板的挠度、弯矩、剪力,以及层间反力和位移的计算公式.进而,利用该力学模型的解,分析了层间条件对双层板挠度、弯矩的影响规律,计算了上、下层板的中性轴位置,讨论了层间双向弹簧系数的取值方法.结果表明:1)随着层间竖向弹簧参数增大,上层板挠度和弯曲应力减小,下层板挠度和弯曲应力增大;随着层间水平摩阻参数增大,上、下层板的挠度和弯矩均减小;2)当双层板的剪切和压缩效应系数分别取2/3,3/5时,双层板的剪切和压缩效应可较好地被考虑;3)上、下层板的中性轴位置是变化的,它随着距荷载圆中心点的距离增大而向上、下层板各自中面趋近.     

圆板在局部Gauss温度场作用下的响应分析

基于薄板热弯曲理论,推导了圆板在Gauss(高斯)温度场作用下的挠度和热应力解析表达式,分析了边界条件和局部温度参数对圆板挠度和热应力的影响,为局部温度变化薄板结构的热力学分析提供理论依据.研究结果表明:圆板中心处的挠度和压应力有最大值;在热影响区内,圆板内一点的挠度随着该点到板中心距离的增大呈Gauss型减小趋势;在热影响区外,圆板挠度的变化趋势与圆板边界约束形式和辐照因子有关,辐照因子越大,边界简支圆板挠度越先呈线性减小趋势;圆板挠度的解析解与有限元解一致.在热影响区内,圆板内一点的热应力随着该点到板中心距离的增大呈Gauss型减小趋势,两种边界约束圆板的热应力变化趋势相似;在热影响区外,圆板热应力的变化趋势与圆板边界约束形式和辐照因子有关.     

有曲率突变的轴对称壳(波纹壳)的有限元解

本文指出了在一般用直线单元的轴对称壳的有限元法中,由于忽视了曲率对斜度变形的影响,并不能用以处理曲率突变的轴对称壳问题.本文提出了考虑曲率影响的、以壳的斜度变形为连续参数的直线单元有限元法,并用以处理C型波纹壳的计算.和Turner-Ford的实验结果比较,以及和钱伟长教授的解析解比较,都证明这个理论是正确的.     

浅谈梯子滑动问题——勾股定理的小应用

人民教育出版社八年级下册中有一道关于梯子滑动的例题:一个长3m的梯子AB,斜靠在一竖直的墙AE上,此时AE高为2.5m,如果梯子的顶端A沿墙下滑0.5m,那么梯子底端B也外移0.5m吗?按人们主观想象,底端也会外移0.5m,但是当我们通过仔细观察和严格的数学计算后,发现梯子外移约0.58m,这个问题引发了师生们浓厚的兴趣和深入的思考.梯子上、下端滑动的距离为什么会不一样呢?它们之间的大小关系和哪些因素有关呢?下面我们就通过做数学实验和利用刚刚学习的勾股定理来解释这个小问题.实验一:长5m的梯子AB斜靠在一竖直的墙上,AE的距离为4m,则EB的距离…     

球壳轴对称弯曲问题精确的挠度微分方程及其奇异摄动解

本文提出了球壳轴对称弯曲问题精确的挠度(ω)微分方程和精确的转角(dω/da)微分方程.本文重点研究了挠度微分方程的精度,基本思路是:首先假设边缘效应时经线中面位移u=0,从而建立挠度微分方程,然后再精确地证明挠度微分方程与原来微分方程内力解答完全相同.再精确地证明边缘效应时经线中面位移u=0是精确解.本文给出了挠度微分方程的奇异摄动解,最后验算了平衡条件,证明摄动解求出的内力和外荷载是完全平衡的.这一方面表明摄动解的计算是正确的;另一方面也再二次表明挠度微分方程是精确的微分方程.新微分方程的优点是:1.新微分方程和原来微分方程精度完全相同;2.新微分方程满足的边界条件非常简单;3.新微分方程便于使用摄动解;4.新微分方程可以得到挠度(ω)和转角(dω/da)的表达式.新微分方程使球壳的计算得到很大的简化.本文采用的符号与徐芝纶《弹性力学》第二版下册相同[1].     

计算主梁绝对最大挠度的数学模型与0.618法

纵横梁桥面系统中主梁的跨度较长,纵梁上直接承受的车队荷载数量多且数值大,主梁设计中绝对最大挠度的确定是关键内容.研究了一组平行车队荷载直接沿着纵梁移动时,主梁承受结点活载下绝对最大挠度数学模型的建立;并给出了相应的计算方法,以计算机为工具,适用于任意有限多个平行移动荷载作用工况,对于主梁的设计计算与安全评估,有一定的实用价值.     

Influence of homogenization models on size-dependent nonlinear bending and postbuckling of bi-directional functionally graded micro/nano-beams

In this work, different homogenization schemes are employed to analyze both size-dependent postbuckling and nonlinear bending behavior of micro/nano-beams, made of a bi-directional functionally graded material (BDFGM), under external axial compression and distributed load. To such different homogenization models, including Reuss, Voigt, Mori-Tanaka, and Hashin–Shtrikman bounds schemes, together with nonlocal strain gradient elasticity theory are adopted within the framework of refined exponential shear deformation beam theory, to develop a comprehensive size-dependent BDFGM beam model. Deviation of associated physical neutral plane, from mid-plane counterpart, is also considered. Nonlocal strain gradient load-deflection responses of BDFGM micro/nano-beam are obtained by numerical solution methodology for both nonlinear bending and postbuckling behaviors corresponding to different values of the lateral and longitudinal material property indices and various small scale parameters. We observed that by decreasing the values of material property gradient indices, associated with BDFGM, difference between the estimations of various homogenization schemes is raised. We also indicated that increasing maximum deflection, decreasing the significance of nonlocal size effect on the bending strength of BDFGM micro/nano-beams, whereas strain gradient size effect becomes more important. In addition, we found that at lower material property gradient indices, bending strength reduction in BDFGM micro/nano-beams, causes by the axial gradient property is higher than lateral gradient property. At higher values of these indices, however, the trend is opposite.     

考虑二次梯度项影响的非线性不稳定渗流问题的精确解

考虑了二次梯度项影响的非线性径向流动问题的无限大地层和有界地层渗流模型．在井底定流量和定压生产时,对无限大地层及有界地层(包括封闭和定压地层)六种情况,利用广义Weber变换和广义Hankel变换求得了实空间的解析解,分析了非线性压力解与线性压力解的差异,发现在晚时段其差异可达8%以上．因此在试井长时要考虑二次梯度项的影响．     

再论弹性大挠度问题von Kármán方程与量子本征值问题Schrǒdinger方程的关系

本文是文[1]的继续和改善。利用本文的结果,还可以改善文[2～3]中有关弹性大挠度问题的讨论。在本文中,我们再次对弹性大挠度问题的von Kármán方程进行简化,使它最终成为非线性Schr?dinger方程。其次,在本文中我们对AKNS方程在多维条件下进行了更为对称的拓展。由于非线性Schr?dinger方程与AKNS方程即Dirac方程的可积性条件相联系,因此,弹性大挠度问题可以用逆散射方法求得其精确解,也就是说,它完全成了量子本征值问题。对于正交各向异性大挠度问题,本文也作了推论。     

复合材料多层板壳大挠度非线性问题的迭代解法

在王震鸣等人提出的各向异性多层扁壳的大挠度方程的基础上,提出了复合材料多层板壳大挠度非线性问题的迭代解法。分析了四边简支的复合材料多层矩形扁壳,与小挠度线性理论解析解及有限元非线性解进行了对比。结果表明,载荷较小并发生小挠度时,所得的大挠度解和小挠度解析解非常接近,载荷较大时,所得解和有限元非线性解非常接近。     

Pointwise and L2 bounds in some nonstandard problems for the heat equation

We consider some initial-boundary value problems for the linear and nonlinear heat equation where the gradient of the solution is prescribed on the boundary. Assuming that a solution exists, we obtain bounds for the solution and its gradient by maximum principle arguments or by means of differential and integral inequalities.     

Calculating the Optimum Two-Link Robot Arm with Respect to Movement Time

The use of a projection-iteration method for determining the response time of a nonlinear dynamic system is examined. The method is based on the idea of a finite difference approximation for the corresponding boundary value problem based on the principle of the maximum of a set of finely divided grids, followed by a solution of the grid equations using a shooting approach with the aid of a gradient method.     

关于具有初始挠度的圆薄板的跳跃问题

本文利用江福汝提出的“两变量法”[3][4]与正则摄动法研究了具有初始挠度的圆薄板的跳跃问题[本文中(1.1),(1.2)]。我们得到了这一问题的N阶一致有效渐近解[(1.66),(1.67)]。当初始挠度变为零时,该解变为圆薄板非线性弯曲问题的解[6];如果初始挠度较大而初始挠度与载荷强度符号相反时,载荷强度达到某一值时,将发生跳跃现象。     

Surface effects on nonlinear free vibration of functionally graded nanobeams using nonlocal elasticity

In this paper, to consider all surface effects including surface elasticity, surface stress, and surface density, on the nonlinear free vibration analysis of simply-supported functionally graded Euler–Bernoulli nanobeams using nonlocal elasticity theory, the balance conditions between FG nanobeam bulk and its surfaces are considered to be satisfied assuming a cubic variation for the component of the normal stress through the FG nanobeam thickness. The nonlinear governing equation includes the von Kármán geometric nonlinearity and the material properties change continuously through the thickness of the FG nanobeam according to a power-law distribution of the volume fraction of the constituents. The multiple scale method is employed as an analytical solution for the nonlinear governing equation to obtain the nonlinear natural frequencies of FG nanobeams. The effect of the gradient index, the nanobeam length, thickness to length ratio, mode number, amplitude of deflection to radius of gyration ratio and nonlocal parameter on the frequency ratios of FG nanobeams is investigated.     

Interactions between exotic multi-valued solitons of the (2+1)-dimensional Korteweg-de Vries equation describing shallow water wave

Korteweg-de Vries equation governs the weakly nonlinear long wave whose phase speed reaches a simple maximum of wave with the infinite length in shallow water wave. The exponential-form variable separation solution of (2+1)-dimensional Kortweg-de Vries equation is found via the two-function method, and this solution covers many special combined solutions including sinh-cosh,sin-cos,sech-tanh,csch-coth,sec-tan and csc-cot solutions. From the exponential-form solution with choosing suitable functions, inelastic interactions between special multi-valued solitons with two loops such as anti-bell-shaped, anti-peak-shaped semifoldons and anti-foldon are graphically and analytically studied. By the asymptotic analysis, phase shift and its difference during interactions between multi-valued solitons are analytically given.     

基于非局部应变梯度理论功能梯度纳米板的弯曲和屈曲研究

以纳米机器人等智能器件中的功能梯度纳米板结构为研究对象,基于非局部应变梯度理论,研究了其弯曲和屈曲问题.推导了一般情况下的功能梯度纳米板运动方程,弯曲和屈曲作为其特例可简化而成.分析了非局部尺度参数、材料特征尺度参数、梯度指数、纳米板尺寸等对弯曲挠度和临界屈曲载荷的影响.结果表明:不同高阶连续介质力学理论下的最大挠度都...