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     

Structural dynamic responses analysis applying differential quadrature method

INTRODUCTION The differential quadrature method (DQM) was proposed by Bellman and Casti as an analogous ex- tension of the quadrature method for integrals (Bellman and Casti, 1971; Bellman et al., 1972). It can be essentially expressed as the values of the de- rivatives at each grid point as weighted linear sums approximately of the function values at all grid points within the domain under consideration. As a distinct numerical solution technique to obtain the initial and/or boundary …     

用非规则节点解偏微分方程的局部微分求积法

In the conventional differential quadrature (DQ) method the functional values along a mesh line are used toapproximate derivatives and its application is limited to regular regions. In this paper, a local differential quadrature (LDQ)method was developed by using irregular distributed nodes, where any spatial derivative at a nodal point is approximatedby a linear weighted sum of the functional values of nodes in the local physical domain. The weighting coefficients in thenew approach are determined by the quadrature rule with the aid of nodal interpolation. Since the proposed method directlyapproximates the derivative, it can be consistently well applied to linear and nonlinear problems and the mesh-free feature isstill kept. Numerical examples are provided to validate the LDQ method.     

混合型微分求积法对求解联立的二维不可压Navier-Stokes方程和热方程的应用

1　Introduction　Variousnumericaltechniques,suchasthefinitedifferencemethodandfiniteelementsmethod ,havebeenusedinthepasttosolvetheincompressibleflowproblemnumerically .Usually ,thesemethodsrequirealargenumberofdiscretizedpointsinthecomputa tionaldomainforaccurateresults .Becausetheinfor mationonallgridpointsisusedtofitderivativesatgrid pointsinthedifferential quadrature (DQ )method ,itisenoughtouseonlyfewgridpointstoob tainhigh accuracynumericalsolutions .Therefore ,thenumberofgridpointscanb…     

Study on one-dimensional consolidation of soil under cyclic loading and with varied compressibility

This paper presents a semi-analytical method to solve one dimensional consolidation problem by taking consideration of varied compressibility of soil under cyclic loading. In the method, soil stratum is divided equally into n layers while load and consolidation time are also divided into small parts and time intervals accordingly. The problem of one-dimensional consolidation of soil stratum under cyclic loading can then be dealt with at each time interval as one-dimensional linear consolidation of multi-layered soils under constant loading. The compression or rebounding of each soil layer can be judged by the effective stress of the layer. When the effective stress is larger than that in the last time interval, the soil layer is compressed, and when it is smaller, the soil layer rebounds. Thus, appropriate compressibility can be chosen and the consolidation of the layered system can be analyzed by the available analytical linear consolidation theory. Based on the semi-analytical method, a computer progra     

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…     

强夯法加固地基的应用实践

强夯法是近些年出现的突破原来压实原理的一种地基处理方法,以石家庄大学(石电大)学生宿舍楼地基处理工程为基础,通过对有关数据的分析,探讨了其在提高地基承载力、消除地基土湿陷性方面的应用.     

考虑剪切效应弹性板弯曲问题的DQ分析方法

A differential quadrature (DQ) method for orthotropic plates was proposed based on Reddy' s theory of plates with the effects of the higher-order transverse shear deformations. Wang-Bert's DQ approach was also further extended to handle the boundary conditions of plates. The computational convergence was studied, and the numerical results were obtained for different grid spacings and compared with the existing results. The results show that the DQ method is fairly reliable and effective.     

Study on one-dimensional consolidation of saturated soil with semi-pervious boundaries and under cyclic loading

The variation of effective stress ratio of stratfied soil with semi-pervious boundaries and under cyclic loading was analyzed on the basis of Terzagh's one-dimensional consolidation assumptions. A solution by Laplace Transform was obtained for the case when the soil was under time-varied loading. With numerical inversion of Laplace Transform, some useful results were obtained for several kinds of commonly encountered loadings. The results can be meaningful in engineering practice. Project supported by the National Natural Science Foundation of China (No. 59908012) and Fok Ying Tung Education Fundation (No. 81067), Education Ministry of China.     

Study on one-dimensional consolidation of saturated soil with semi-pirviovs boundaries and under cyclic loading

The variation of effective stress ratio of stratfied soil with semi-pervious boundaries and under cyclic loading was analyzed on the basis of Terzaghi's one-dimensional consolidation assumptions. A solution by Laplace Transform was obtained for the case when the soil was under time-varied loading. With numerical inversion of Laplace Transform, some useful results were obtained for several kinds of commonly encountered loadings. The results can be meaningful in engineering practice.     

微分求积法求解不可压二阶粘弹性流体和热迁移模型中的稳态流动

1IntroductionAlthoughthe computation of the fluid mechanics hasgreat development during the last decades,due to themodel in nonlinear fluid mechanics is very complicat-ed,the more efficient techniques for solvingthis prob-lemstill attract the interest of many researchers.Thedifferential quadrature method(DQM)introduced byBell man,et al.[1,2]is an efficient numerical methodfor solving partial differential equations.In recentyears,the DQMhas been widely used for solving theproblems of enginee…     

空间相关的多点多维地震动合成方法

基于谱方法的随机场理论,借助功率谱密度函数来描述地震动随机场,同时考虑不同点、不同向地震动分量间的相关性,分别采用Clough-Penzien模型和屈铁军-王君杰相干模型来描述平稳自功率谱和平稳互功率谱,建立了空间相关的多点多维地震动合成方法。采用Matlab R2010b编制生成程序,并以某445m大跨度拱桥场地条件为例,生成空间相关的多点多维地震动时域样本,并将该时域样本的功率谱密度函数与目标功率谱密度函数进行对比。结果表明:模拟结果与目标值吻合较好,按照上述方法生成的多点多维地震时域样本满足要求。     

高陡岩土边坡有限元分析

本文以高陡岩土边坡实测资料为研究对象,遵循资料收集—现场调研—模型建立—程序设计—工程分析的研究思路,采用有限元强度折减数值分析方法,通过前后处理软件,综合考虑土性参数和边坡边界条件的变化,从计算结果中分析边坡的位移,变形及其塑性发展趋势和安全系数。     

Study on One—Dimensional Model of Traffic Flow with Stochastic Deceleration via Lattice Boltzmann Method

One-dimensional traffic model was studied with the consideration of stochastic deceleration by using the lattice Boltzmannmethod.The evolution equation for vehicle density was derived,which has the form of the Burgers equation exhibiting the effect of viscosity corresponding to the deceleration.The simulation with the model shows that the variation of vehicle density in space tends to a periodic one,which implies the existence of kinematic waves in the 1D traffic flow and coincides with theoretical prediction.     

一类由一维概率密度函数构造多维概率密度函数的方法

将文献[1]给出的由一维连续型随机变量的概率密度函数构造二维连续型随机变量的概率密度函数的方法,推广为由一维连续型随机变量的概率密度函数构造三维连续型随机变量的概率密度函数的情况,并作了证明和举例说明.说明利用本文的方法构造多维概率密度函数,其方法简单易行.     

Stress analysis of anisotropic thick laminates in cylindrical bending using a semi-analytical approach

Semi-analytical elasticity solutions for bending of angle-ply laminates in cylindrical bending are presented using the state-space-based differential quadrature method (SSDQM). Partial differential state equation is derived from the basic equations of elasticity based on the state space concept. Then, the differential quadrature (DQ) technique is introduced to discretize the longitu- dinal domain of the plate so that a series of ordinary differential state equations are obtained at the discrete points. Meanwhile, the edge constrained conditions are handled directly using the stress and displacement components without the Saint-Venant principle. The thickness domain is solved analytically based on the state space formalism along with the continuity conditions at interfaces. The present method is validated by comparing the results to the exact solutions of Pagano’s problem. Numerical results for fully clamped thick laminates are presented, and the influences of ply angle on stress distributions are discussed.     

小原子系统基态能量的自洽场计算

利用Hartree-Fock自洽场方法计算了碳、氮、氧原子以及碳元素的各价离子的基态能量，并与实验结果进行了比较。其计算过程展示了自洽场方法的基本特征，因而有助于理解此类方法。     

二次系统焦点量的新算法

二次系统的细焦点的最高阶数为3，这是一个熟知的结果．但文[1]给出上述结论却花了大量的篇幅．作者用Lienard方程的方法，重新计算了n=0时二次系统的焦点量，得到了相同的结论，并大大节省了篇幅．     

电位法测定水中硫酸盐的研究

提出了用离子选择电极电位法测定硫酸盐的新方法.在最佳条件下,电极电位与硫酸盐浓度在1×10-5～1×10-2mol/L之间有良好线性关系,检测下限为6.3×10-6/mol/L.该方法简便准确,已用于水中硫酸盐测定,结果满意.     

二阶延迟微分方程Runge-Kutta方法的稳定性

研究二阶延迟微分方程Runge-Kutta方法的稳定性.首先,引入新变量,将二阶延迟微分方程化为一阶方程组.然后,应用Runge-Kuta 方法于一阶方程组,给出了Runge-Kutta稳定的充分条件,进而得到了二阶延迟微分方程Runge-Kutta方法稳定的充分条件.最后,通过数值试验验证所得结论的正确性.