直角坐标系下黏弹性层状地基动力响应分析

基于直角坐标系下黏弹性力学的基本控制方程,运用Fourier-Laplace积分变换、解耦变换、微分方程组理论和矩阵理论,推导轴对称动荷载及非轴对称动荷载作用时黏弹性地基三维空间问题积分变换域内的解析单元刚度矩阵;根据边界条件和层间连续条件集成总刚度矩阵;求解含有总刚度矩阵方程的代数方程,得到积分变换域内相应问题的解;利用Fourier-Laplace积分逆变换得到真实物理域内的解.编制相应程序计算黏弹性层状地基动力响应与已有解答进行对比,验证了提出方法的正确性.     

层状横观各向同性饱和地基上圆板的非轴对称振动

研究了层状横观各向同性饱和地基上弹性圆板的非轴对称振动问题．首先,通过方位角的Fourier变换,将圆柱坐标系下横观各向同性饱和土的三维动力方程转化为一阶常微分方程组,基于径向Hankel变换,建立问题的状态方程,求解状态方程后得到传递矩阵;其次,利用传递矩阵,结合层状饱和地基的边界条件、排水条件及层间接触和连续条件,给出了任意简谐激振力作用下层状横观各向同性饱和地基动力响应的通解;然后,按混合边值问题建立层状饱和地基上弹性圆板非轴对称振动的对偶积分方程,并将对偶积分方程化为易于数值计算的第二类Fredholm积分方程,并给出了算例．     

弹性半空间地基上四边自由矩形板稳态振动的解析解

采用双重Fourier变换,分析得到弹性半空间地基受竖向稳态荷载作用下的积分变换解．与四边自由矩形板的振动解析解相结合,得出弹性半空间地基上四边自由矩形板稳态振动的解析解．还给出算例及参数影响分析．     

求解层间界面反平面剪切破坏的剪切梁模型(Ⅰ)——基本特性

在反平面剪切载荷及侧压力共同作用下引起的裂纹及裂纹扩展导致的层间界面失效,是岩土工程层间界面及砌体结构中界面层上典型的失效方式.运用弹性力学和断裂力学的理论原理,提出了能够反映上述层间界面断裂失效问题力学特性的剪切梁模型.文中采用具有应力软化特性的“粘性裂纹”(内聚力裂纹)模型来表述层间裂纹前方损伤过程区的本构行为.对通过粘性层结合在一起的两个弹性板,在反平面剪切载荷及侧压力共同作用下的力学行为作了解析分析计算,研究了层间界面裂纹扩展规律.     

复合材料层合剪切圆柱曲板在侧压作用下的后屈曲

基于Reddy高阶剪切变形理论的Kármám-Donnell型非线性壳体方程,给出复合材料层合剪切圆柱曲板在侧压作用下的后屈曲分析。将壳体屈曲的边界层理论推广到复合材料层合剪切圆柱曲板受侧压作用的情况。相应的奇异摄动法,用于确定圆柱曲板的屈曲荷载和后屈曲平衡路径。分析中同时考虑非线性前屈曲变形和初始几何缺陷的影响。数值算例给出完善和非完善,中等厚度正交铺设层合圆柱曲板的后屈曲荷载-挠度曲线。讨论了横向剪切变形,曲板几何参数,铺层数,铺展方式和初始几何缺陷等各种参数变化的影响。     

集中载荷作用下层合厚圆板的轴对称弯曲

从三维弹性力学基本方程出发,建立了横观各向同性层合圆板轴对称弯曲问题的状态方程,并将板面的集中载荷展成付里叶贝塞尔级数,从而给出问题的解析解,此解满足弹性力学全部方程,计及了所有独立的弹性常数,并满足层间连续性条件。     

单箱双室简支箱梁剪切变形及剪力滞双重效应分析

基于各个翼板选取不同的最大剪切转角差为剪力滞广义位移,应用能量变分原理分别推导出了考虑和不考虑剪切变形时单箱双室截面控制微分方程组,结合边界条件给出了箱梁纵向应力和竖向挠度的初参数解,从力学、数学角度上证实了剪切变形和剪力滞效应是两个相对独立的力学行为,进一步阐述了二者对箱梁的影响,即剪切变形对箱梁截面纵向应力无影响,但是对竖向挠度有很大的影响.数值算例表明,利用该文解和数值解分析跨中截面剪力滞系数横向分布规律,二者吻合程度良好,其横向分布规律与单室箱梁类似,唯独不同之处是边腹板处的剪力滞效应比中腹板处的剪力滞效应略微大一些;挠度计算表明,剪切效应使得该箱梁在集中和均布荷载作用下跨中挠度分别增大4.6%和2.7%.     

求解层间界面反平面剪切破坏的剪切梁模型（I）——基本特性

在反平面剪切载荷及侧压力共同作用下引起的裂纹及裂纹扩展导致的层间界面失效,是岩土工程层间界面及砌体结构中界面层上典型的失效方式。运用弹性力学和断裂力学的理论原理,提出了能够反映上述层间界面断裂失效问题力学特性的剪切梁模型。中采用具有应力软化特性的“粘性裂纹”（内聚力裂纹）模型档表述层间裂纹前方损伤过程区的本构行为。对通过粘性层结合在一起的两个弹性板,在反平面剪切载荷及侧压力共同作用下的力学行为作了解析分析计算,研究了层间界面裂纹扩展规律。     

双参数弹性地基上自由边矩形板

本文以迭加法[1]给出在V. Z. Vlazov双参数弹性地基上自由边矩形板的精确解.文中导出了在各种边界条件下的基本解式,迭加这些基本解式,求得了在双参数弹性地基上自由边矩形板的最一般的精确解.它严格满足双参数弹性地基上板的控制微分方程和自由边的边界条件和角点条件.给出了数值结果.计算结果表明:当板的平面尺寸一定,地基深度与板厚度之比H/h=15时,双参数弹性地基与Winkler弹性地基相接近,证明了Winkler地基模式适用于压缩尺寸比较薄的弹性地基.     

双模量复合材料正交迭层矩形厚板的热弯曲问题

本文给出了双模量复合材料迭层板热弯曲的加权残数解。各层都假定为弹性和热弹性的双模量各向异性材料。该模型是建立在Whitney-Pagano迭层板理论和热弹性模型基础上,考虑了沿板厚的剪切应变。所得挠度和中性面位置的结果和精确解非常吻合。     

变弹基模量刚性路面的设计

本对刚性路面设计中所采用的克尔地基理论．考虑了地基反力模量的可变性，所得结果具有一定的理论价值和实际意义。     

基础动力分析的一种半解析、半数值方法

提出了一种基础动力分析的半解析、半数值计算方法．采用Lamb解及其相应的近似公式,建立了基础动反力和位移的关系式．从而可象静力问题那样将基础板分离出来,将板看作上部作用已知载荷,下部作用用挠度表示的地基反力,因此只需要对板进行有限元分析．采用这种方法分析了不同形状、 不同刚度、不同频率下的地基板的振动问题, 而且可以考虑基础埋深的影响．算例分析表明,提出的方法是一种计算简便、精度较高、适用范围广泛的有效数值方法．     

静水压力下钢筋混凝土矩形板的一般解

本将钢筋混凝土矩形板看作是正交各向异性矩形板，利用Navier解法，求得受一般静水压力作用的简支矩形薄板在温克勒弹性地基上的一般挠度表达式，所得结果在某些特殊情况下退化成现今有工程实用价值的一些算式．     

Finite element analysis of pressure vessel using beam on elastic foundation analysis

In this study, we first applied the variation principle to derive a new finite element method (FEM) based on the theory of beam on elastic foundation using line element. The derived FEM was then applied to solve, for the first time, the pressure vessel problems with uniform thickness. Our FEM results, obtained even by using only one line element, agreed exactly with the available closed-form solution, confirming the validity and computing efficiency of our finite element formulation. Moreover, we have applied our new FEM to solve pressure vessel problems with non-uniform thickness where no exact analytical solution is known to exist. The distributions of discontinuity stress in the cylindrical part were obtained. We found that shear force and bending moment were indeed discontinuous at the geometrically discontinuous juncture, due to the bending rigidity and elastic constant change by the non-uniform thickness. Finally, the case of discontinuity stresses in a bimetallic joint was also studied. The locations of maximum shear force and bending moment were found to be affected by the bending rigidity of the material.     

Analysis of fluid storage tanks including foundation-superstructure interaction

An analytical formulation is developed to predict the flexural behavior of a cylindrical liquid storage tank resting on an isotropic elastic soil medium, which is modelled as a half space. The interface between the plate foundation and the soil medium is considered to be smooth and continuous. The plate deflection function is assumed in the form of a power series expansion in terms of the radial coordinate. The procedure accounts for the interactions between the tank wall and the plate foundation, and between the plate foundation and the soil medium. The principle of minimum potential energy is used to evaluate the unknown coefficients appearing in the assumed power series expansion and also the unknown interacting forces at the tank wall-plate foundation junction. Any number of terms can be considered in the assumed deflection function. Analytical expressions are obtained for the plate foundation deflections and radial moment, the contact stress distribution, the tank wall displacements, and the tank wall stress resultants. The results obtained compare well with the finite element analysis of a similar problem. Results of a parametric study are also presented to demonstrate the effect of the various geometric and material parameters on the flexural behavior of the system.     

Forced vibration of curved beams on two-parameter elastic foundation

Forced vibration analysis of curved beams on two-parameter elastic foundation subjected to impulsive loads are investigated. The Timoshenko beam theory is adopted in the derivation of the governing equation. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method. The solutions obtained are transformed to the real space using the Durbin’s numerical inverse Laplace transform method. The static and forced vibration analysis of circular beams on elastic foundation are analyzed through various examples.     

Nonlinear analysis of thin rectangular plates on Winkler–Pasternak elastic foundations by DSC–HDQ methods

This article introduces a coupled methodology for the numerical solution of geometrically nonlinear static and dynamic problem of thin rectangular plates resting on elastic foundation. Winkler–Pasternak two-parameter foundation model is considered. Dynamic analogues Von Karman equations are used. The governing nonlinear partial differential equations of the plate are discretized in space and time domains using the discrete singular convolution (DSC) and harmonic differential quadrature (HDQ) methods, respectively. Two different realizations of singular kernels such as the regularized Shannon’s kernel (RSK) and Lagrange delta (LD) kernel are selected as singular convolution to illustrate the present DSC algorithm. The analysis provides for both clamped and simply supported plates with immovable inplane boundary conditions at the edges. Various types of dynamic loading, namely a step function, a sinusoidal pulse, an N-wave pulse, and a triangular load are investigated and the results are presented graphically. The effects of Winkler and Pasternak foundation parameters, influence of mass of foundation on the response have been investigated. In addition, the influence of damping on the dynamic analysis has been studied. The accuracy of the proposed DSC–HDQ coupled methodology is demonstrated by the numerical examples.     

非均匀弹性地基圆薄板大挠度问题的一般解*

本文在文[1]的基础上提出了一个新的方法可用于求解任意变系数非线性常微分方程组.文中导出了任意轴对称载荷和不同边界条件下的非均匀弹性地基圆薄板大变形的一般解,并给出了收敛于精确解的证明.问题最后可归结为求解一个仅含有三个未知量的非线性代数方程组.该方法和其它方法比较,具有收敛范围大,计算简便迅速等特点.文末给出算例表明内力和位移均可得到满意的结果,验证了本文理论的正确性.     

无拉力Winkler地基上自由边矩形Reissner板的弯曲

本文提出了一种求解无拉力Winkler地基上自由边矩形Reissner板受任意载荷的弯曲问题的解析方法.通过适当设定满足可导条件的Fourier级数加补充项形式的挠度函数和剪力函数,把给定边界条件下的微分方程化成最简形式的无穷代数方程组.对于常规的Winkler地基,可直接求解;而对于无拉力Winkler地基,方程组为一组弱非线性代数方程组.使用迭代法容易得到解.     

弹性地基上自由边矩形厚板

弹性地基上自由边矩形厚板的分栀由于其难度较大,一直没有得到很好的解决.本文采用单三角级数和重三角级数相叠加的方法,求得该问题的精确解.文中所用方法简单明了.所得结果完全满足边界条件并与王克林等[2]的结果完全一致.