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1.
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 相似文献
2.
Transient response of a spherical cavity with a partially sealed shell embedded in viscoelastic saturated soil 总被引：1，自引：0，他引：1
INTRODUCTION The propagation of stress-waves in an elasticmedium containing a cavity that are due to arbitrarydynamic loading applied on the cavity is of greatimportance in the fields of seismology, geophysicalprospecting, underground tunnels and deeply buriedpipelines, particularly as a model of an earthquakesource. Ben-Menahem and Cisternas (1963) devel-oped the theory for the dynamic response of an elastichalf-space medium to an explosion spherical cavity.Norwood and Miklowitz (… 相似文献
3.
用Matlab求解系统的状态方程,可用仿真函数、迭代计算和拉氏变换方法得到其数值解、解析解和波形图。用lsim仿真函数求系统响应的数值解;迭代法用来求解离散系统状态方程,连续系统状态方程通过离散化后也可用迭代法;连续系统状态方程采用拉氏变换可得到解析结果。通过实例分析,展现了Matlab在系统状态变量分析方面的优越性,不仅使系统状态方程的计算变得简单,而且可得到可视化的结果。 相似文献
4.
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. 相似文献
5.
吴专保 《岳阳职业技术学院学报》2007,22(2):69-72
x方向采用有限元法,t方向用拉普拉斯的数值逆,求解一个偏积分微分方程的数值解,简便易行,而且该方法选择适当的求导阶数n可以达到所要求的精度。 相似文献
6.
本介绍了一维波动方程Cauchy问题解的表达式的另一种推导方法，并简单考虑了其解的存在条件．首先用Fourier变换、Laplace变换及其它们的相关性质，获得了与参考献一致的解的表达式，然后通过比较这两种不同的推导方法，可知本所述的推导方法具有过程简单、浅显易懂等优点． 相似文献
7.
8.
利用分离变量法,Laplace变换及广义Mittage-Leffler函数,给出了有限区间上分数阶扩散-波方程混合问题的精确解． 相似文献
9.
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. 相似文献
10.
Delta function is an important function in mathematics and physics. In this paper, the Laplace transforms of δ(t)and δ(t-τ)have been discussed in detail. After the Laplace transform of δ(t)is analyzed, the author has found that three aspects should be taken into account, i.e. τ→0+, τ→0- andτ=0; and it is the same with the Laplace transform of δ(t-τ). Then the results of the Laplace transform of Delta function have been obtained in a rigorous and comprehensive sense. 相似文献
11.
ARUN K. MITRA 《European Journal of Engineering Education》1990,15(1):67-74
The particular solution yp (t) of a linear non-homogeneous differential equation with constant coefficients can be expressed in term of a convolution integral, namely, yp(t)=g(t)?T(t), where t(t) is the nonhomogeneous (forcing) term and g(t) is the Green's function for the associated differential operator. g(t) is also the Laplace inverse of the transfer function T(s) = l/P(s), P(s) being the characteristic polynomial of the differential operator. Owing to its versatile application, mathematical sophistication and elegance, and its simplicity, it is suggested, that the Green's function method be introduced while teaching Laplace transform, in a manner described in this article. Some simple results on convolution integrals involving discontinuous functions have been shown to be useful for computing the particular solution when the forcing function r(t) is discontinuous. An attempt has been made to justify the proposed method through a number of simple examples. 相似文献
12.
Newton’s theory of gravitation solvedmany problems of celestialmechanics but led to some major problems, one of which was that it gave rise to a serious paradox discussed in this article. The paradox has a number of manifestations one of which is presented here. It should be remembered that the root cause of all these paradoxes is fundamentally the same. Laplace attempted an ad hoc solution. However, it could not be mathematically demonstrated that his proposal solves the difficulty. In this article, it is shown that his suggestion removes the problem. A physical phenomenon that can justify Laplace’s suggestion is also mentioned briefly. This article also poses an interesting mathematical problem that can be attempted by interested readers. The computational solution is presented here. 相似文献
13.
申洪 《赣南师范学院学报》1988,(Z1)
本文是用连分式求解离散Master方程。我们仅限于考虑一个自变量的情况,并让转移速率W(n+2,n)≠0,W(n-2,n)=0。利用Laplace变换和逆变换,我们求出了这种限制下的两“粒子”跳跃离散Master方程的与时间有关的严格解,它服从一些循环关系。 相似文献
14.
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 相似文献
15.
In this study, ground vibrations due to dynamic loadings from trains moving in subway tunnels were investigated using a 2.5D finite element model of an underground tunnel and surrounding soil interactions. In our model, wave propagation in the infinitely extended ground is dealt with using a simple, yet efficient gradually damped artificial boundary. Based on the assumption of invariant geometry and material distribution in the tunnel??s direction, the Fourier transform of the spatial dimension in this direction is applied to represent the waves in terms of the wave-number. Finite element discretization is employed in the cross-section perpendicular to the tunnel direction and the governing equations are solved for every discrete wave-number. The 3D ground responses are calculated from the wave-number expansion by employing the inverse Fourier transform. The accuracy of the proposed analysis method is verified by a semi-analytical solution of a rectangular load moving inside a soil stratum. A case study of subway train induced ground vibration is presented and the dependency of wave attenuation at the ground surface on the vibration frequency of the moving load is discussed. 相似文献
16.
考虑热源和外部环境对圆柱体三维传热模型和温度场分布的影响,建立了基于半导体制冷的圆柱体三维传热模型,利用变量分离法和拉普拉斯变换法,导出了其三维温度场的封闭解析解．通过数值计算和编程仿真,给出相应的仿真结果,分析了半导体制冷片的位置变化对圆柱体三维温度场的影响特性．为进一步分析圆柱体三维温度场及其应用提供理论依据． 相似文献
17.
胡轶 《太原大学教育学院学报》2007,25(2):88-91
通过研究Laplace变换在初值问题中的应用,且拟解决线性微分方程的初值问题。我们知道Laplace变换求解初值问题比其他方法条件宽泛方便。用Laplace变换法可把原函数所遵从的常系数微分方程变成像函数所遵从的代数方程来进行求解;把偏微分方程变成常系数微分方程,然后进行求解。 相似文献
18.
胡轶 《太原教育学院学报》2007,(2)
通过研究Laplace变换在初值问题中的应用,且拟解决线性微分方程的初值问题。我们知道Laplace变换求解初值问题比其他方法条件宽泛方便。用Laplace变换法可把原函数所遵从的常系数微分方程变成像函数所遵从的代数方程来进行求解;把偏微分方程变成常系数微分方程,然后进行求解。 相似文献
19.
钱学明 《绵阳师范学院学报》2007,26(5):19-24
将含参变量的广义积分取拉普拉斯变换,再通过拉普拉斯逆变换来求解广义积分。并且当其中参变量取某些特殊值时,还可求得其对应的实变量的广义积分的值。该方法简便易行,能够顺利地求解一些通行的《数学分析》教材中很难甚至无法解出的含参变量的广义积分。 相似文献
20.
拉普拉斯变换及其应用 总被引：1，自引：0，他引：1
王振芳 《雁北师范学院学报》2001,17(6):48-49
该文论述了运用拉普拉斯变换将微分方程转化为代数方程.同样,用拉氏逆变换,可求出微分方程的解. 相似文献