二维渗透各向异性多层地基Biot固结分析

从二维渗透各向异性Biot固结问题的基本控制方程出发,对时间t进行Laplace变换,对坐标x进行Fourier变换,构造出Laplace-Fourier变换域内的常微分方程,利用Cayley-Hamilton定理推导出单层地基的传递矩阵。根据传递矩阵的性质,并结合层间连续条件和边界条件,求得了二维渗透各向异性多层地基Biot固结问题在Laplace-Fourier变换域内的解,通过Laplace-Fourier逆变换可求得该问题物理域内的真实解。编制了相应的计算程序,并对数值计算结果进行了比较和分析。计算结果表明:土的渗透各向异性对固结过程中的地表位移有比较显著的影响。     

层状横观各向同性地基与刚性条形基础共同作用分析

运用对偶积分方程来求解刚性条形基础与层状横观各向同性地基的接触问题。从直角坐标系下平面应变问题基本控制方程出发,通过对坐标的Fourier积分变换和Cayley-Hamilton定理推导出单层横观各向同性地基的传递矩阵。将单层地基传递矩阵结合层间连续性条件,推导出层状地基的传递矩阵解。利用刚性条形基础与层状横观各向同性地基接触的混合边值条件,推导出一组对偶积分方程,并应用Jacobi正交多项式将其转化为线性代数方程组,求解得到地基反力。编制了相应的计算程序,其计算结果与已有文献和有限元软件的结果基本吻合,并分析了地基横观各向同性性质与成层性对计算结果的影响。     

横观各向同性层状地基平面应变问题的解析层元解

从横观各向同性平面应变弹性体的基本控制方程出发,通过Fourier积分变换和Cayley-Hamilton定理推导出单层横观各向同性地基的传递矩阵,然后再通过矩阵变换求得单层地基的精确刚度矩阵,即解析层元解;根据有限层法原理组合得到总刚度矩阵,通过求解总刚度矩阵得到横观各向同性层状地基平面应变问题在积分变换域内的解答,应用Fourier逆变换得到物理域内的精确解。编制相应的计算程序,计算结果与有限元软件模拟结果吻合。算例分析表明土的分层特性和横观各向同性性质对土体变形有明显影响。     

解析层元法求解层状横观各向同性地基轴对称问题

提出了一个求解横观各向同性层状地基轴对称问题的解析层元方法。从弹性力学基本方程出发并利用 Hankel 变换,得到横观各向同性单层地基的传递矩阵解,进而推导出单层地基的解析层元刚度矩阵。利用有限元方法组装总体刚度矩阵,通过求解总体刚度矩阵,并采用 Hankel 逆变换的数值积分方法,可求出层状横观各向同性弹性体轴对称问题在物理域内的精确解。刚度矩阵元素中不存在正指数并具有对称的特点,不仅使计算过程简化,还提高了计算精度。最后文中给出了算例来证明推导结果的准确性。     

多层地基轴对称弹性空间问题的解析层元解

从轴对称弹性空间问题的基本控制方程出发,推导出Hankel积分变换域内单层地基的精确刚度矩阵,即解析层元,然后按有限层法组装成多层地基的总体刚度矩阵。通过求解由总体刚度矩阵形成的方程组,得到该问题在Hankel积分变换域内的解,再通过Hankel积分逆变换,得到轴对称荷载作用下多层地基的精确解。编制了相应程序进行计算,通过与已有文献的结果及有限元计算结果比较,证明了所提方法的正确性;通过多层地基模型与均匀地基模型的比较,揭示了两者的差异。天然地基往往呈层状分布,各层土的物理性质差别较大,故与通常采用的均匀地基模型相比,成层地基模型更能真实地分析天然地基在轴对称荷载作用下的位移。     

任意荷载下成层弹性地基的一维固结

针对成层弹性地基模型，运用Ｌａｐｌａｃｅ变换及矩阵传递法求解了任意荷载下成层弹性地基一维固结问题，得到了频域内的通解，通过Ｌａｐｌａｃｅ逆变换，即可计算成层弹性地基在任意荷载下的一维团结。经典的Ｔｅｒｚａｈｉ一维固结理论解是一个特例。此外，结合三层的地基算例，对解进行了探讨，揭示了成层弹性地基的固结特性。     

多层地基上轴对称受荷弹性圆板问题

利用弹性圆板与多层地基表面的竖向位移协调条件与光滑接触条件,再由多层地基应力与位移的传递矩阵解,推导出多层地基上轴对称受荷弹性圆板问题的解析解。在此基础上,编制了相应的程序,并进行了数值计算。计算结果表明,园板刚度对弹性圆板的位移以及圆板中心下的竖向应力有着较大的影响。     

成层地基土中水平受荷桩桩身响应的矩阵传递解

目前关于成层地基土体中水平受荷桩内力与变形的研究相对较少。将成层地基土体假设为均质弹性介质,将桩视为竖向放置的弹性地基梁,同时将桩-土之间的相互作用关系假设为一般形式的三参数地基反力模型,建立桩身响应的微分方程,并采用Laplace变换解得任意土层深度处桩身响应的矩阵传递系数进而得到成层地基土中水平荷载作用下桩身位移、转角、弯矩和剪力的矩阵传递解。相比传统的有限差分法与幂级数法,矩阵传递法求解成层地基土中的水平受荷桩时更加便捷。通过算例对比,验证了矩阵传递法解的正确性。最后进行了桩身响应的参数影响分析,结果表明:桩顶边界条件对桩身变形与内力沿桩身的分布规律影响显著;同时,地基反力模型中的参数0z和n对桩身最大水平位移、最大弯矩的影响较为明显。     

层状地基中单桩的扭转变形分析

研究了扭矩作用下单桩的扭转变形。采用积分变换和传递矩阵方法求解成层土在内部环形荷载作用下的基本解;利用此基本解并考虑桩土位移协调条件,提出了层状地基中单桩扭转变形的半解析方法;通过一匀质地基算例验证了该理论方法的正确性,并给出了双层地基模型的数值分析结果。     

三维渗透各向异性层状地基Biot固结分析

从渗透各向异性三维Biot固结问题的基本控制方程出发,引入中间变量和Laplace-Fourier积分变换,构造出两组变换域内的状态方程,利用Cayley-Hamilton定理得到渗透各向异性单层地基三维Biot固结问题的传递矩阵;根据边界条件和层间连续条件,并结合传递矩阵的性质和Laplace-Fourier逆变换技术,从而求解出渗透各向异性层状地基三维Biot固结问题。此外,编制相应的程序,并将计算结果进行分析和比较,结果表明土体的渗透各向异性性质对固结过程有较显著的影响。     

一类代数方程系统解的存在性

文章中笔者将大量的应用问题归结为一类非线性代数方程系统,如:二阶差分方程、四阶差分方程、偶数阶差分方程等的边值问题,偏差分方程的边值问题;复杂性神经网络稳态方程;微分方程和偏微分方程的离散模型等.并介绍了作者本人与合作者最近研究的关于这类代数系统正解和非退化解的存在结果,值得注意的是关于这类非线性代数方程系统还有大量的问题有待研究.     

厚圆柱扁壳位移型基本方程及控制方程分析

基于考虑横向剪切变形的厚壳位移型基本方程及扁壳基本假定,建立了以5个中面位移为5个独立变量的厚扁壳及厚圆柱扁壳位移型基本方程。对厚圆柱扁壳进行了动力分析,首先引入3个辅助位移函数,同时运用柯西-黎曼条件,将5个二阶微分方程变形为1个二阶和2个四阶过渡微分方程;然后引入另一辅助位移函数,建立其解耦的控制微分方程;最后利用4个辅助位移函数求出5个位移分量。结果表明,厚扁壳的位移型基本方程退化为厚圆柱扁壳及薄圆柱扁壳的位移型方程是正确的,且所推导的方程具有通用性。     

On the fundamental equations of water hammer

The wide spectrum of practical problems that warrant water-hammer modelling has increased the importance of careful formulation of the fundamental equations of water hammer and critical analysis of their assumptions. To this end, this paper reviews the relation between state equations and wave speeds in single as well as multiphase and multicomponent transient flows, formulates the various forms of one- and two-dimensional water-hammer equations and illuminates the assumptions inherent in these equations. The derivation of the one- and two-dimensional water-hammer equations proceeds from the three-dimensional Navier?-?Stokes equations for a compressible fluid. The governing equations for turbulent water-hammer flows are obtained by applying ensemble averaging to the simplified form of the Navier?-?Stokes equations for water-hammer problems. Unlike time averaging, ensemble averaging is applicable to unsteady flows where the time scale of the transient is often much smaller than the time scales of the turbulence. Order of magnitude analysis, physical understanding and recent research findings are used throughout the paper to evaluate the accuracy of the assumptions made in the derivation of the one- and two-dimensional water-hammer equations.     

Dynamic modelling of hydraulic excavator motion using Kane's equations

This paper presents differential equations of motion of a hydraulic excavator in the form of Kane's equations. The equations proposed allow studying the excavator dynamics in the digging, lifting and unloading transport operations. The influence of soil foundation deformability is considered. The detailed presentation of the procedure for determination of generalised forces of hydro-cylinders is given. The equations obtained are compared with the similar ones from the literature.     

A semi-implicit finite element model for natural water bodies

In this work, a semi-implicit model, applied to the shallow water equations, is developed for natural water bodies. In the proposed model, the shallow water equations are integrated in the vertical direction, finite elements are employed in the spatial discretization, and finite differences in the time discretization. The model is based on the uncoupling of the governing equations, in which the expressions of the velocity components, obtained explicitly from the discretized momentum equations, are substituted in the continuity equation. Therefore, there is an uncoupling of the solution; initially the continuity equation is solved, and, in the sequence, the momentum equations are solved. Yet, this uncoupling produces a significant reduction in the number of equations of the resulting systems, when compared to standard coupled systems. This reduction improves substantially the computer performance.     

Fundamental period of irregular moment‐resisting steel frame structures

The determination of the fundamental period of vibration of a structure is essential to earthquake design. Current code equations such as American Society of Civil Engineers Standard (ASCE) 7‐10 provide formulas for the approximate period of moment‐resisting frames (MRFs), which are dependent only on the height of the structure or number of stories. Such a formulation is overly conservative and unable to account for structures with geometric irregularities. This study investigated the fundamental periods of MRFs with varying geometric irregularities. The fundamental periods based on vibration theory for each example were compared with empirical equations, including current code equations as well as equations proposed in recent literature. New equations are proposed for the fundamental periods of MRFs, which take into account vertical and horizontal irregularities. Through statistical comparison, it was found that a three‐variable power model that is able to account for irregularities resulted in a better fit to the Rayleigh data than equations that were dependent on height only. The proposed equations were validated through a comparison of available measured period data for MRFs. They will allow design engineers to quickly estimate the fundamental period of MRF structures by taking into account irregularities. Copyright © 2013 John Wiley & Sons, Ltd.     

火灾区域模型中压力方程的求解

建筑火灾区域模拟的核心有两部分：建立火灾发展过程中各个现象的数学模型；通过求解数学方程式得到室内压力、温度和烟气层高度等火灾参数。后者是进行区域模拟软件编制以及火灾风险评估的核心，尤其是压力方程的求解，压力是求解其它参数的前提。给出了压力方程的求解思路，以单室火灾为例介绍了压力求解的具体方法，验证了计算结果的正确性。     

Physical aspect of flocculation process—II. Contact flocculation

Kinetic equations which describe the process of contact flocculation in solids contact clarifiers were proposed. Decrease of micro-flocs with the contact of high concentration and large diameter well-grown-flocs both in a turbulent flocculation chamber and in a floc blanket of upflow clarifier were discussed.First order equations with the micro-floc concentration were derived theoretically for both types of contact flocculation. By experiments, these kinetic equations were verified and their coefficients were evaluated.Finally, practical equations for the design of micro-floc removal process with the contact of well-grown-flocs both in a turbulent flocculator and in a floc blanket were proposed.     

圆底球面厚扁壳的位移型控制方程及一般解

基于考虑横向剪切变形的厚壳位移型基本方程及扁壳基本假定,建立了以5个中面位移为5个独立变量的厚扁壳位移型基本方程,并由此得到厚扁球壳在正交曲线坐标及极坐标下的位移型基本方程。为了求解圆底球面厚扁壳在极坐标下的位移型基本方程,通过引入4个辅助位移函数,建立其解耦的控制微分方程,最后通过这4个辅助位移函数求出5个位移分量。结果表明,厚扁壳的位移型基本方程退化为厚扁球壳及薄扁球壳的位移型方程是正确的,且所推导方程具有一般性。     

由Helmholtz方程Neumann外问题化归的各种边界积分方程的注记

对由Ｈｅｌｍｈｏｌｔｚ方程Ｎｅｕｍａｎｎ外问题化归的各种边界积分方程进行了讨论。在用Ｈｅｌｍｈｏｌｔｚ表达式导出这些积分方程的过程中，分析了其中一些方程当波数Ｋ是内问题的特征值时没有唯一解这一著名难题产生的原因，并提出了克服这一难题的方法，即检出一个既与原边值问题等价，又对所有波数Ｋ都具有唯一解的直接边界积分方程。