Numerical manifold method for dynamic nonlinear analysis of saturated porous media

It is well known that the Babuska–Brezzi stability criterion or the Zienkiewicz–Taylor patch test precludes the use of the finite elements with the same low order of interpolation for displacement and pore pressure in the nearly incompressible and undrained cases, unless some stabilization techniques are introduced for dynamic analysis of saturated porous medium where coupling occurs between the displacement of solid skeleton and pore pressure. The numerical manifold method (NMM), where the interpolation of displacement and pressure can be determined independently in an element for the solution of u–p formulation, is derived based on triangular mesh for the requirement of high accurate calculations from practical applications in the dynamic analysis of saturated porous materials. The matrices of equilibrium equations for the second‐order displacement and the first‐order pressure manifold method are given in detail for program coding. By close comparison with widely used finite element method, the NMM presents good stability for the coupling problems, particularly in the nearly incompressible and undrained cases. Numerical examples are given to illustrate the validity and stability of the manifold element developed. Copyright © 2006 John Wiley & Sons, Ltd.     

Fast iterative solution of large undrained soil‐structure interaction problems

In view of rapid developments in iterative solvers, it is timely to re‐examine the merits of using mixed formulation for incompressible problems. This paper presents extensive numerical studies to compare the accuracy of undrained solutions resulting from the standard displacement formulation with a penalty term and the two‐field mixed formulation. The standard displacement and two‐field mixed formulations are solved using both direct and iterative approaches to assess if it is cost‐effective to achieve more accurate solutions. Numerical studies of a simple footing problem show that the mixed formulation is able to solve the incompressible problem ‘exactly’, does not create pressure and stress instabilities, and obviate the need for an ad hoc penalty number. In addition, for large‐scale problems where it is not possible to perform direct solutions entirely within available random access memory, it turns out that the larger system of equations from mixed formulation also can be solved much more efficiently than the smaller system of equations arising from standard formulation by using the symmetric quasi‐minimal residual (SQMR) method with the generalized Jacobi (GJ) preconditioner. Iterative solution by SQMR with GJ preconditioning also is more elegant, faster, and more accurate than the popular Uzawa method. Copyright © 2003 John Wiley & Sons, Ltd.     

岩石变形破坏的熵突变过程与破坏判据

在岩石的变形破坏过程中,当进入不稳定的破裂发展阶段之后,系统不断调整结构抵抗外力的扰动,裂纹向局域集中的有序方向发展,应变能不断耗散,并以应变能的耗散为媒介,使系统与外扰动所追加的负熵流产生能量流通,也使系统熵值和系统的维数逐次降低,这一阶段岩石系统远离平衡态,岩石的破坏是系统熵的突变过程。基于这一认识,并在验证应变能分布与结构块度分布模式的一致性的基础上,推导出包含了结构因素和能量分布的熵表达式;对熵表达式进行平衡分析获得局部突变的分岔集,得到了岩石局部破坏的熵折迭突变破坏准则;同时,探讨了熵表达式所表征的结构有序度的尖点突变性,解出岩石系统的分岔集,这个分岔集就是岩石系统熵突变的整体破坏准则。     

条件平差和间接平差模型应满足的两个等式关系

条件平差和间接平差法是两种最基本的测量数据处理的方法,在整个工科数据处理中得到了广泛应用.但是,实践中,一些工程人员对这两种平差方法的区别与联系并不十分了解.本文基于最小二乘准则解的本质,推导出了条件平差法与间接平差法系数阵和常数项间应满足的两个等式关系,有助于广大工程人员理解这两种测量平差的本质与联系.     

削弱残余误差对多波束测深综合影响的方法研究

提出了一种基于地形变化长波项与短波项相结合的残余误差综合削弱方法。实验验证了该方法的有效性。     

基于CQG2000的吉林省西部地区似大地水准面的建立

针对CQG2000精度无法满足实际工作的情况,提出一种新的重力似大地水准面与GPS水准的拟合方法—残差模型法,利用CQG2000、较密集的GPS水准点,采用残差模型法建立吉林省西部地区似大地水准面模型（JiLin West Quasi-Geoid,JLWQG）。论述建立JLWQG的三角剖分双线性内插算法及其适用性,检测结果表明,JLWQG精度达到了±0.05m,JLWQG在吉林省西部地区基础测绘更新工作中进行了大面积的应用,取得了满意的结果。     

双步抗差估计及其应用

抗差估计是一种可以有效抵制粗差影响的平差方法。但权因子函数的临界值定值问题较为困难,若选取不当,会造成法方程系数阵秩亏或粗差观测值的影响未能完全消除,从而导致平差无法进行或抗差不彻底。针对上述问题提出了一种改进型抗差估计法一双步抗差估计法,并通过对一边角网和一实测GPS向量网进行的试算,验证了双步抗差估计的优越性。     

高精度锥体棱镜的“自差法”检测技术

本文提出一种采用“自差法”检测高精度锥体棱镜的新方法，阐述检测原理与装置，建立检测角度和面形误差的定量判据，并给出一个实例说明其应用。实践表明，“自差法”检测技术对于产品质量的控制，具有快速准确和简便实用等特点。     

等角投影理论和方法综述

等角投影比其它性质投影之研究更为深刻，应用也最为广泛。本文对等角投影的历史发展作了简单回顾，重点对等角投影的数学基础、等角投影的一般公式、等角投影变形量度［８］、具有极值特性的等角投影和探求等角投影的方法等进行了综述。最后提出需要继续研究的若干问题作为等角投影研究展望。     

隧道衬砌厚度不足的健康判据试验研究

针对目前隧道健康诊断指标判据不统一的现状,采用室内相似模型试验,结合实际工程实例,研究了隧道支护结构衬砌减薄状态下围岩与支护结构破坏规律与极限承载能力,得出了隧道支护结构在相应的受力状态下健康状态判据。结果表明：隧道衬砌支护结构的位移特征以拱肩的压入和拱顶的挤出为主,随着拱顶衬砌支护结构减薄量的增加,支护结构衬砌与围岩之间的接触应力逐渐减小,结构的承载能力逐渐下降,隧道拱顶部位的位移增加,其柔性逐渐增大,隧道拱顶内侧被压溃,外侧受到拉力作用而开裂,随后隧道拱腰和边墙出现裂纹,最后逐渐扩展贯通;隧道承载力曲线呈现明显的“S”型,据此可以划分为承载力缓慢退化阶段、快速退化阶段和退化完成阶段,相对应的阶段可以划分为隧道结构的健康等级与级别,为工程应用提供了参考依据