Solution of a rigid disk on saturated soil considering consolidation and rheology

INTRODUCTION An important problem in foundation engineeringis the determination of the rate of settlement of a raftfoundation placed on a deep clay layer. Gibson andMcNamee (1957), and McNamee and Gibson (1960a;1960b) considered the problem of normal uniformloading applied to the surface of a half-space andshowed that one-dimensional theory gives a markedunderestimate of the rate of settlement. This theorycorresponds to the case of a perfectly flexible footing.However, it is often…     

Nonlinear analytical solution for one-dimensional consolidation of soft soil under cyclic loading

INTRODUCTION Conventional consolidation analysis based on Terzaghi’s one-dimensional theory neglects the non-linearity of soil for the sake of mathematical expediency, which is considered to be one of the theory’s shortcomings. Many researchers have pro-posed one-dimensional (1D) consolidation models where the coefficient of volume compressibility mv, coefficient of permeability kv, and coefficient of consolidation cv, vary with either depth or time. Schiffman (1958), Davis and Raymon…     

带梯度项的p-Laplacian方程正解的Blow-up

研究了RN中一般区域上的一族带非线性梯度项的p-Laplacian方程解的Blow-up性质.通过构造适当的辅助函数,利用特征函数法和不等式技巧,给出了其齐次Dirichlet边值问题的正解产生Blow-up的充分条件,该方法也适用于研究其他带非线性源的退缩非线性抛物方程解的Blow-up问题.     

梯度饱和土层的一维固结度的计算

研究了梯度饱和土层在外荷载下的固结作用,利用Biot理论给出了固结的基本微分方程,一些材料常数假设为指数模型,当梯度系数为零时,退化为一维均匀饱和土层的固结,利用分离变量等方法,得到透水和不透水边界条件下孔隙压力,给出了固结度曲线。当梯度系数不为零时,给出了梯度饱和土在外荷载下的孔隙压力,利用固结度的定义,数值算例出了梯度饱和土层的固结度变化曲线,分析和讨论了梯度系数等对固结度的影响。这些结果对地基下沉量计算和预测有一定的理论价值和意义。     

Computation of one-dimensional consolidation of double layered ground using differential quadrature method

The authors give the solution to the problem of one-dimensional consolidation of double-layered ground with the use of the differential quadrature method. Case studies showed that the computational results for pore-water pressure in soil layer agreed with those of analytical solution; and that in the computational results for the interface of soil layer also agreed with those of the analytical solution except for the small discrepancies during shortly after the start of computation. The advantages of the solution presented in this paper are that compared with the analytical solution, it avoids the cumbersome work in solving the transcendental equation for eigenvalues, and in the case of the Laplace transform solution, it can resolve the precision problem in the numerical solution of long time inverse Laplace transform. Because of the matrix form of the solution in this paper, it is convenient for formulating computational program for engineering practice. The formulas for calculating double-layered ground consolidation may be easily extended to the case of multi-layered soils. Project (No. RC9609) supported by the Zhejiang Provincial Natural Science Foundation of China     

常系数非齐次线性微分方程组求特解的新方法

利用一般多项式与多项式矩阵的升幂综合除法,解决算子多项式矩阵的逆的形式幂级数展开问题,进而得到常系数非齐次线性微分方程组求特解的新方法.     

一类混合型方程的封闭边界值问题的解的研究

混合型方程的封闭边界值问题的解的研究是很有意义的,它与物理现象紧密联系在一起.这篇文章主要研究了在一定的条件下一类混合型方程的闭边界值问题的解的存在性;用的方法是利用函数乘子a-b-c变换,在Sobolev空间里Friedrichs的积分方法.     

估测湿样品空气渗透系数的近似解析解

利用文献[1]的自然降压法测量非饱和材料的空气渗透系数,推出一个估测湿样品空气渗透系数的近似解析解.通过解析方法和数值方法验证解析解的理论值和实验数据吻合.若忽略可预计的误差,在给定条件下,运用自然降压法得到的近似解析解可求湿样品的空气渗透系数.     

Analytical modelling and free vibration analysis of piezoelectric bimorphs

INTRODUCTION Piezoelectric bimorphs (or benders), a special type of piezoelectric device, which can produce flexural deformation significantly larger than the length or thickness deformation of the individual piezoelectric layers, have been widely used as elec- troacoustic transducers, medical devices and micro- robot due to their characteristics of easy miniaturiza- tion, high positioning accuracy, sensitive response, and large displacement (e.g., Shirley and Hampton, 1978; Ha and Kim, 2…     

关于非线性Klein-Gordon方程解的爆破

用特征函数法系统地讨论了非线性Klein—Gordon方程初边值问题在三类边界条件下解的爆破.     

旋转电机磁场计算的数值解析结合法

A numerical-analytical method is applied for the two-dimensional magnetic field computation in rotational electric machines in this paper. The analytical expressions for air gap magnetic field are derived. The pole pairs in the expressions are taken into account so that the solution region can be reduced within one periodic range. The numerical and analytical magnetic field equations are linked with equal vector magnetic potential boundary conditions. The magnetic field of a brushless permanent magnet machine is com-     

Singularly perturbed first-order differential equations with integral boundary condition

In this paper, a kind of singularly perturbed first-order differential equations with integral boundary condition are considered. With the method of boundary layer function and the Banach fixed-point theorem, the uniformly valid asymptotic solution of the original problem is obtained.     

常微分方程中的齐次化原理与Green函数

通过介绍齐次线性微分方程的通解及求非齐次微分方程的特解的一种方法，定义了Green函数。     

非齐次线性方程组的同解类

两个n元有解的非齐次线性方程组同解的根本原因是什么?为了回答这个问题,首先引入线性空间的子空间的陪集概念,然后证明了F~n的陪集的一个重要性质,最后给出了两个n元有解非齐次线性方程组同解的充分必要条件,从而完善了线性方程组的同解性理论。     

椭圆型Boussinesq方程Dirichlet问题解的存在性和唯一性

在关于k,hb,μb的非常弱的假设条件下,在Sobolev空间中证明了非齐次Dirichlet边界条件u=ud(x,y), (x,y)∈(e)Ω下非齐次椭圆型Boussinesq方程-（△）*(K(x,y)(u-hb)（△）u)=f(x,y,u), (x,y)∈Ω的解的唯一性以及齐次椭圆型Boussinesq方程（△）*(K(x,y)(u-hb)（△）u)=0, (x,y)∈Ω的解的存在性,其中Ω为有界多边形域.并给出反例,指出对一给定的f(x,y),非齐次方程-（△）*(K(x,y)(u-hb)（△）u)=f(x,y,u), (x,y)∈Ω的Dirichlet问题是不可解的.     

基于有限差分法的一维输运方程定解问题

许多物理方程的定解问题,如波动方程、输运方程等,或由于其泛定方程比较复杂,或由于边界形状比较复杂,或由于其它原因,往往不具有解析解,或者其解析解不易计算,所以要采用可行的数值解法。有限差分方法就是一种数值解法,它把表示变量连续变化关系的偏微分方程离散为有限个代数方程,然后利用电子计算机求解此线性代数方程组。     

一类抛物型方程混合边值问题弱解的存在性和正则性

对一类抛物型方程的混合边值问题弱解的存在性和正则性进行了讨论．利用Lions定理建立抛物型方程混合边值问题弱解的存在性定理,然后在弱解存在的基础上利用差商方法,通过讨论弱解的导数所属空间来证明弱解的正则性．     

Analytical solutions for a uniformly loaded circular plate with clamped edges

INTRODUCTION The problem of circular plates subjected to auniform load is one of the classical problems in elas-ticity theory,which also is encountered frequently inpractice.Timoshenko and Goodier(1970)presented athree-dimensional solution for uniformly loaded iso-tropic circular plates with simply supported edges.Analytical solutions of isotropic circular plates witheither clamped or simply supported edges subjectedto a uniform load,which were derived based on thinplate theory with Kirch…     

二维抛物型方程非齐次边值问题的高精度差分格式

针对二维非齐次抛物型方程提出了高精度紧致差分格式，本文将把在[2]中二维问题的差分格式在空间方向上提高到四阶，对其进行了收敛性分析，证明其收敛阶为o（△t^2＋hx^4＋hy^4），并采用ADI算法将二维问题降为一阶求解。     

An exact analytical solution for convective heat transfer in rectangular ducts

An exact analytical solution is obtained for convective heat transfer in straight ducts with rectangular cross-sections for the first time. This solution is valid for both H1 and H2 boundary conditions, which are related to fully developed convective heat transfer under constant heat flux at the duct walls. The separation of variables method and various other mathematical techniques are used to find the closed form of the temperature distribution. The local and mean Nusselt numbers are also obtained as functions of the aspect ratio. A new physical constraint is presented to solve the Neumann problem in non-dimensional analysis for the H2 boundary conditions. This is one of the major innovations of the current study. The analytical results indicate a singularity occurs at a critical aspect ratio of 2.4912 when calculating the local and mean Nusselt numbers.