层状地基中单桩扭转振动特性分析

采用积分变换和Muki的方法求解了层状地基中单桩的扭转振动问题.在分析过程中,首先对基本控制方程进行Hankel变换,建立了单层地基的初参数解答和刚度矩阵,得到层状地基的递推矩阵;然后利用递推矩阵、边界条件和桩-土变形协调条件建立了层状地基中单桩扭转振动问题的基本积分方程并进行数值求解.文末数值算例给出了退化的层状地基中刚性单桩的扭转变形,其结果与已有经典解答吻合良好.同时,并研究了两层地基中单桩的扭转动力响应,分析了桩-土参数对动力响应的影响,所得结论对工程实践和桩基扭转波检测有一定的指导意义.     

层状地基参数的频域识别

在分析水平层状地基运动特征的基础上, 通过研究地层系统的特征值和特征向量与地层参数之间的关系, 修正测量得到的数据与理论计算结果之间的偏差, 建立了层状地基参数的频域识别方法。并利用大型振动台上的地基模型试验数据, 实施了层状地基的参数识别过程。结果表明, 该方法产生良好的地基参数估计。     

求解双参数层状地基模型的积分变换法

计算弹性地基梁板时，大都采用文克尔地基模型。由于该模型过于简化，不能正确反映土的工程性质，为此本文提出了一种双参数层状地基模型。该模型由一系列的弹性层组成，并对每一层中应力应变分布做了假设。通过积分变换的方法可以求出每一层表面处位移与力之间的关系，进而形成层刚度矩阵。按照有限元法的原理，可把每一层的刚度矩阵凝聚成总体刚度矩阵进行求解。本文模型是V1azov模型的延伸和发展。通过与V1azov模型计算结果的比较，证明本文方法是正确的。并且本文得到了荷载作用于层状模型内部时的解答，为将双参数地基模型用于桩基分析打下了理论基础。     

用薄层法分析层状地基中条形基础的阻抗函数

薄层法是分析和模拟弹性波在层状介质中传播的一种半解析半数值方法,以往薄层法在柱坐标体系中建立求解方程,并通过直角坐标系和柱坐标系的转化关系而得到直角坐标系中的解答,本文从直角坐标直接推导了层状地基在无限长线荷载作用下的计算公式,求解了层状地基在垂直方向和水平方向上无限长线激振荷载作用下薄层法位移基本解.结合容积法得出了层状地基中基础-地基动力相互作用方程及条形基础阻抗函数的计算公式.本文计算了半无限弹性地基以及基岩上覆盖层在无限长简谐线荷载作用下的位移反应,计算了半无限弹性地基以及基岩上覆盖层地基中明置与埋置条形基础的地基阻抗函数.计算结果与已有的研究结果的比较表明两者吻合较好,验证了本文方法的适用性.     

层状地基中埋管地基阻抗函数的分析方法

本文首先利用波函数展开法推导了弹性半空间中埋管的地基轴向阻抗函数计算公式.然后采用层状地基中无限长线激振荷载薄层法基本位移解,结合容积法求解了层状地基中埋管的地基轴向、垂直及水平阻抗函数.分别用两种方法计算了弹性全空间、弹性半空间地基内埋管的地基轴向阻抗函数,两者的计算结果符合良好,验证了用薄层法求解的可行性.本文还利用薄层法分析了弹性半空间内埋管的埋深对地基水平、垂直及轴向阻抗函数的影响;计算了弹性半空间内埋管的轴向刚度系数并与我国及日本的相关规范对比分析;计算分析了上海典型层状地基内地铁隧道的地基阻抗函数.     

成层非饱和地基上矩形基础稳态响应解析研究

采用积分变换法求解非饱和土的控制方程,得到变换域内土体的位移和应力表达式;建立了单层非饱和土体的刚度矩阵,并组装每一层的刚度矩阵,构成了层状地基的总体刚度矩阵;结合地基上下表面的边界条件,推导了层状非饱和地基表面位移的积分形式解答。另外,选取带有补充项的双重余弦级数解作为矩形基础的振型函数,并令其与地表位移按余弦级数展开的表达式相等,建立了矩形基础与地基的协调条件。最后,联立矩形基础的控制方程、边界条件和基础与地基之间的协调条件,求解得到矩形基础的挠度幅值、弯矩幅值以及基底压力幅值。选取已有文献中的非饱和土参数计算,其结果与文献吻合良好,验证了本文方法的正确性。本文进一步研究了单层地基和双层地基上矩形板的动力响应,分析了土体参数对矩形基础动力响应幅值的影响规律。结果表明:地基层厚与基础尺寸之比为5时,地基就可以看作半空间地基;矩形基础的稳态响应随非饱和土的饱和度的增大而减小;渗透率对矩形基础动力响应的影响不明显。     

层状地基轴对称问题的Mindlin解

本文在文献〔１〕的基础上，对层状地基应力和位移的计算方法做了一些创新的工作，首先作者提出求解传矩阵的逆矩阵的简便公式。并在应力、位移的计算上，对荷载作用面上下分别采用二种不同的传递矩阵。加快了计算速度，避免了层状体系计算中常见的溢出问题及大数减大数造成的计算困难。     

层状横观各向同性饱和土的非轴对称动力响应

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Biot非轴对称波动方 程转化为一组一阶常微分方程组. 然后基于径向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. 进而利用传递矩阵,结合饱和层状地基的边界条件、排水条件及层间接触和连续条件,求解 了任意震源力作用下层状横观各向同性饱和地基频域动力响应问题. 时域解可通过频率的Fourier积分得到.     

横观各向同性饱和层状地基的三维稳态动力响应

首先引入状态向量,将直角坐标系下横观各向同性饱和土的Biot波动方程转化为一组状态方程,然后基于双重Fourier变换,求解了状态方程,得到传递矩阵.进而利用传递矩阵,并结合饱和地基的边界条件、排水条件及层间接触和连续条件,求解了横观各向同性饱和层状地基的稳态动力响应问题.     

用薄层法分析层状地基中各种基础的阻抗函数

薄层法是分析和模拟弹性波在层状介质中传播的一种半解析半数值方法.采用薄层单元和傍轴边界分别模拟层状地基和弹性半空间.利用薄层法位移基本解和容积法推导了层状地基中基础-地基动力相互作用方程及块式基础、桩基础和承台群桩基础阻抗函数的统一计算公式.通过计算半无限弹性地基中桩基础、块式基础和二层地基上基础的阻抗函数验证了方法的适用性.进而计算了某实际层状地基中承台群桩基础的阻抗函数,并与试验结果进行对比,两者吻合较好.本文方法可用于分析弹性层状地基中各种基础的阻抗函数.     

Stress intensity factors for a moving cylindrical crack in a nonhomogeneous cylindrical layer in composite materials

Stresses are determined for a finite cylindrical crack that is propagating with a constant velocity in a nonhomogeneous cylindrical elastic layer, sandwiched between an infinite elastic medium and a circular elastic cylinder made from another material. The Galilean transformation is employed to express the wave equations in terms of coordinates that are attached to the moving crack. An internal gas pressure is then applied to the crack surfaces. The solution is derived by dividing the nonhomogeneous interfacial layer into several homogeneous cylindrical layers with different material properties. The boundary conditions are reduced to two pairs of dual integral equations. These equations are solved by expanding the differences in the crack surface displacements into a series of functions that are equal to zero outside the crack. The Schmidt method is then used to solve for the unknown coefficients in the series. Numerical calculations for the stress intensity factors were performed for speeds and composite material combinations.     

非齐次边界条件下轴向运动梁的非线性振动

轴向运动系统的横向非线性振动一直是国内外研究的热点课题之一.目前相关研究大都是针对齐次边界条件的.但是在工程实际中,非齐次边界条件更为常见,而针对非齐次边界条件的研究相对较少.为深入研究非齐次边界条件对轴向运动系统横向非线性振动的影响,本文以轴向变速运动黏弹性Euler梁为例,引入由黏弹性引起的非齐次边界条件,同时还引入由轴向加速度引起的径向变化张力,建立梁横向振动的积分-偏微分型运动方程,并导出了相应的非齐次边界条件.采用直接多尺度法分析了梁的次谐波参数共振.由可解性条件得到了梁的稳态响应,并根据Routh-Hurvitz判据确定了系统稳态响应的稳定性.通过数值例子讨论了黏弹性系数,轴向运动速度,轴向速度脉动幅值和非线性系数对幅频响应的影响,并详细对比分析了非齐次边界条件和齐次边界条件对幅频响应的影响.结果表明:随着黏弹性系数的增大,非齐次边界条件下的零解失稳区域和稳态响应幅值比齐次边界条件下的失稳区域和幅值大,非齐次边界条件对高阶次谐波参数共振的影响更加显著.最后,引入微分求积法来验证直接多尺度法的近似解结果.      

Modeling method for a crack problem of functionally graded materials with arbitrary properties—piecewise-exponential model

A new model, piecewise-exponential model (PE model), is developed to investigate the crack problem of the functionally graded materials (FGMs) with arbitrary properties. In the PE model, the functionally graded material is divided into some nonhomogeneous layers along the gradient direction of the properties, with each layer’s properties varying exponentially. By this way, the real material properties can be approached by a series of exponential functions. Since the real material properties are used on both surfaces of each nonhomogeneous layer, the nature of continuously varying properties of FGMs can be approached accurately. The influences of the local nonhomogeneity on the crack-tip fields can be fully considered. By using the new model, the fracture problem of a functionally graded strip with arbitrary properties and a crack vertical to the free surfaces is studied. The integral transform method, the theory of residues and the theory of singular integral equation are applied. Some representative samples with different kinds of nonhomogeneous properties are analyzed and the corresponding stress intensity factors (SIFs) are presented. It is shown that the PE mode is effective for investigating the crack problems of the FGMs with arbitrary properties.     

极坐标下弹性力学的一个新解答

在极坐标下将Hamilton体系下的分离变量法应用到弹性力学的非齐次边界情况,得到了一个新解答,利用这个新解可以求解一类弹性力学问题。文中给出了具体例子。     

Synchronization of complex networks with nonhomogeneous Markov jump topology

The problem of synchronization of complex networks with nonhomogeneous Markov jump topology and time-varying coupling delay is investigated in this paper. The Markov process in the underlying complex networks is finite piecewise homogeneous, which is a special case of nonhomogeneous Markov process. Based on the Lyapunov functional approach, an exponential stability condition is derived for the error system in terms of the linear matrix inequality method. Based on the condition, the design method of the desired controller is given. An example is given to show the effectiveness of the proposed technique.     

Analysis of vibrations in a nonhomogeneous thermoelastic thin annular disk under dynamic pressure

The forced vibration analysis of nonhomogeneous thermoelastic, isotropic, thin annular disk under periodic and exponential types of axisymmetric dynamic pressures applied on its inner boundary has been performed and analytical benchmark solution has been obtained. The material has been assumed to have inhomogeneity according to a simple power law in the radial coordinate. The present analysis has been worked out in the context of generalized theory of thermoelasticity with one relaxation time. The two coupled partial differential equations have been clubbed and solved by employing Laplace transform technique to obtain the solution for radial displacement and temperature change in the space domain. In order to obtain the solution in physical domain, the inversion of the transform has been carried out by using residue calculus. The radial displacement, radial stress, circumferential stress, and temperature change have been computed numerically for copper material annular disk. The numerically computed results have been presented graphically to demonstrate the effect of two different types of dynamic pressure in reference to homogeneous and nonhomogeneous material disk. The results for homogeneous material disk have been deduced and validated with that available in literature. The closed-form solution obtained here is interesting and allows further parametric studies of nonhomogeneous structures.     

Driving forces and kinking of an oblique crack in bonded nonhomogeneous materials

Summary  Plane elasticity solutions are presented for the problem of an oblique crack in two bonded media. The material model under consideration consists of a homogeneous half-plane with an arbitrarily oriented crack and a nonhomogeneous half-plane. The Fourier integral transform method is employed in conjunction with the coordinate transformations of field variables in the basic elasticity equations. Formulation of the crack problem results in having to solve a system of singular integral equations for arbitrary crack surface tractions. A crack perpendicular to or along the bonded interface between the homogeneous and nonhomogeneous constituents arises as a limiting case. In the numerical results, the values of mixed-mode stress intensity factors are provided for various combinations of relevant geometric and material parameters of the bonded media. Subsequently, the infinitesimal kinks from the tips of a main crack are presumed, with the corresponding local driving forces being evaluated in terms of the stress intensities of the main crack. The criterion of maximum energy release rate is applied with the aim of making some conjectures concerning the likelihood of kinking and the probable kink direction based on the approximation of local homogeneity and brittleness of the crack-tip behavior. Received 25 September 2001; accepted for publication 13 February 2002     

An FE analysis of reinforced subgrade under automobile loading

An FE analysis procedure was presented to predict the behavior of soil-geogrid interaction under automobile loading. The dynamic interactions between the transverse bars, the longitudinal ribs and the soil were simulated by a system consisting of nonlinear springs, dashpots and masses, to study the deformation properties of the reinforced soil. The equivalent stiffness and damping ratios could be determined with the shaking table. The dynamic responses of a reinforce subgrade were analyzed with the 3D finite element approach. This approach is programmed and applied to analyze the soil-geogrid interaction under dynamic loading. The comparative analysis of the response of the reinforced subgrade and that of the subgrade without reinforcement shows that the geogrid placed at the bottom of the base layer may effectively reduce the accumulative plastic deformation due to the cyclic automobile loading.     

Stochastic thermoelastic problem of a functionally graded plate under random temperature load

This study attempts to derive the statistics of temperature and thermal stress in functionally graded material (FGM) plates exposed to random external temperatures. The thermomechanical properties of the FGM plates are assumed to vary arbitrarily only in the plate thickness direction. The external temperatures are expressed as random functions with respect to time. The transient temperature field in the FGM plate is determined by solving a nonhomogeneous heat conduction problem for a multilayered plate with linear nonhomogeneous thermal conductivity and different homogeneous heat capacity in each layer. The autocorrelations and power spectrum densities (PSDs) of temperature and thermal stress are derived analytically. These statistics for FGM plates composed of partially stabilised zirconia (PSZ) and austenitic stainless steel (SUS304) are computed under the condition that the fluctuation in the external temperature can be considered as white noise or a stationary Markov process.