利用有限单元伽勒金法反求非线性流情况下砾石层的渗透系数

地下水流问题的数字计算机的应用,现虽处于高度发展阶段,但在采用这种数学物理模型时,首先要知道含水层的导水性能。过去利用水位观察资料或抽水试验资料计算水文地质参数的方法,只能适用于简单的含水体系,由于高度复杂的地质体并且间隙水流为非线性的这类参数如何确定还没有解决,如果利用近期发展起来的有限单元法来反求参数是一种理想的选择,特别是与古典的伽勒金法结合起来,既可简化数学处理过程,并有利于解非线性流问题。古典的伽勒金法原来只能适用于简易的分析域,而且要求介质为均一,但与空间离散的有限单元法结合起来,还便于解非均质而且边界不规则的问题。     

三维塑性极限分析下限法原理及应用

介绍了三维塑性极限分析下限法的基本原理。将计算区域离散为有限个三维空间单元,利用极限分析中的下限定理,借助有限元思想建立数学规划模型,并引入非线性规划的数值方法寻求问题的下限解。以均匀土质边坡的极限荷载作为算例,比较了所得数值解与经典塑性力学理论解,论证了该方法的正确性。     

区域地温场的数学模拟及实例剖析

了解和掌握地壳内部温度场的分布、热流值的变化和地温梯度变化情况不仅对地热理论研究是重要的,而且对地热能的开发利用也是重要的。由于地壳内部各种岩石热物理参数不同,以及研究区域的地质条件一般比较复杂,致使对地温场的研究比较困难,因此更难于作出定量化的评价。然而,近年来飞速发展起来的有限单元法给我们解决上述问题提供了一个极为有力的工具。     

无网格自然单元法在弹塑性分析中的应用

无网格自然单元法在构造位移插值函数时不需要单元的信息,只需要结点的信息,在裂纹扩展模拟、材料非线性分析、几何非线性分析以及三维计算等方面具有广阔的应用前景。阐述了将无网格自然单元法应用于结构弹塑性分析的过程和基本理论,给出了其位移插值函数的构造过程,并将其结果与常规的有限单元法进行对比,证明了该方法用于弹塑性分析的优越性。     

遗传有限单元反演法对理想模型反演的初步研究

一、引言有限单元法是根据边界条件进行应力应变正演计算最常用而又有效的数值方法。在地球动力学研究中,我们常常希望利用测得有限点的应力或应变值等来确定影响应力应变分布的动力机制,这就是地球动力学问题的反演。在线弹性有限元反演中,可以利用叠加原理获得力学方程组,解该方程组即可得到反演结果。但利用叠加原理反演的物理量种类有限,尤其该方法不能推广到非线性有限单元模型;另外,既使在边界力的反演中,由于观测资料的欠缺,使得叠加原理得到的常     

一种三维位移反分析的有限单元法

论述了一种三维位移反分析的有限单元法，包括对初始地应力参数的直接求解法，以及对其他力学特征参数的优化求解法，二者结合起来可应用于地下工程施工过程中的全部反分析工作。     

基于有限元法对深基坑围护桩水平位移的分析

利用有限单元法,通过有限元程序来进行模拟计算。将所研究问题假定为平面应变问题;岩土体为理想弹塑性模型,采用平面四节点等参单元,遵循适于岩土的Drucker—Prager屈服准则;桩与岩土体之间通过设置接触单元来模拟基坑围护桩桩与岩土体的相互作用,重点分析建筑物与基坑的不同距离、基坑围护桩的刚度变化和围护桩底端土体物理力学参数变化时基坑开挖对围护桩变形的影响。     

滑坡稳定性分析与安全系数取值研究

在地质灾害中,滑坡灾害分布最广、发生频率最高、危害最大,是我国地质灾害防治的主要对象。滑坡研究的主要任务之一是稳定性分析。论文针对三板溪水电站进水口滑坡和水布垭水电站大岩淌滑坡,分别采用刚体极限平衡法、块体单元法、有限单元法对稳定安全系数和条间推力分布曲线进行分析和比较,研究各种方法的差异和计算精度,以及各种方法稳定安全系数的取值标准,希望为水利水电工程边坡设计规范有关有限单元法、块体单元法条目的编写和相应的允许安全系数取值标准的制定提供一定的参考。研究结果表明:①块体单元法计算的安全系数与刚体极限平衡法计算的安全系数可以采用相同的取值标准,而有限单元法计算的安全系数取值标准可适当降低;②块体单元法计算的条间水平推力、条间剪切力与刚体极限平衡法(尤其是Sarma法)计算的条间水平推力、条间剪切力非常相近,有限单元法计算的条间水平推力、条间剪切力较小;③分析方法、力学模型与参数取值应与安全系数取值标准相匹配。     

下限分析有限单元法的非线性规划求解

下限分析有限单元法将下限定理这一数学变分问题转化为一个数学规划问题,克服了人为构造可静应力场的困难,在实际工程中具有广阔的应用前景。通过有限元离散得到的非线性下限规划模型中包含大量的优化变量与约束条件,常规优化算法难以求解。为此,在分析非线性下限规划模型自身特点的基础上,引入可行弧技术和Wolfe非精确搜索技术改进其优化求解效率。算例分析表明,基于可行弧技术和Wolfe非精确搜索技术,下限分析有限单元法优化求解程序的收敛速度和步长搜索效率得到明显的提升,并且其数值稳定性良好、计算精度较高,可以较好地适应实际工程问题的计算。     

基于刚体平动运动单元的上限有限元研究

刚性块体极限分析上限法常应用于岩土工程稳定性研究,然而应用时需假定刚性块体破坏模式并递推繁琐的几何关系。为此,提出一种适应性更广的基于非线性规划模型的刚体平动运动单元上限有限元法,并解决了其优化模型初始值的确定问题。通过引入有限单元思想,将计算区域离散成刚体单元,同时以单元速度和节点坐标作为决策变量,由上限定理建立非线性规划模型获得上限解。利用编制的上限有限元程序进行边坡和浅埋隧道稳定性算例验证,表明运动单元上限有限元法能调整速度间断线至较优方位,所得破坏模式特征鲜明,上限解精度高,可广泛应用于边坡、隧道等稳定性分析研究。     

岩体稳定性的极限分析方法——刚体-弹塑性夹层模型

本文提出一种适用于块状岩体结构的计算模型——刚体-弹塑性夹层模型,它根据岩体的实际结构将岩体离散成刚性元(岩块)和弹塑性夹层(软弱结构面)。本文还在此基础上提出了用有限元定量评价岩体稳定性的另外一种方法——极限分析法,给出了衡量岩体稳定性的相应指标——极限乘子。     

An edge-based smoothed point interpolation method for elasto-plastic coupled hydro-mechanical analysis of saturated porous media

An edge-based smoothed point interpolation method is adopted for coupled hydro-mechanical analysis of saturated porous media with elasto-plastic behaviour. A novel approach for the evaluation of the coupling matrix of the porous media is adopted. Stress integration is performed using the substepping method, and the modified Newton-Raphson approach is utilised to address the nonlinearities arising from the elasto-plastic constitutive model used in the formulation. Numerical examples are studied and the results are compared with analytical solutions and those obtained from the conventional finite element method (FEM) to evaluate the performance of the proposed model.     

An improved accelerated initial stress procedure for elasto-plastic finite element analysis

The most flexible and generally applicable methods for elasto-plastic analysis are those based on an incremental-iterative form of the initial stress approach, but such methods often exhibit slow convergence. The acceleration procedure known as the alpha-constant stiffness method is reconsidered and some modifications are proposed. The principal difference in the present approach lies in the use of a single acceleration parameter, rather than a diagonal matrix of acceleration coefficients. The new scheme shows a significant improvement in numerical stability and converges three times faster than the standard initial stress method. Some practical aspects associated with the method are discussed and a number of applications are presented.     

边坡岩体滑动稳定的动力学分析

在地震或爆破等强烈振动影响下边坡岩体往往产生块体滑动。这种失稳的动力学特性迄今尚未获得应有的研究。 在大部分现有的文献中都采用惯性力原理,将动力问题化为静力问题解决。这种常规的准动态分析,只考虑最大振动加速度,使问题过于简化而偏于保守。少数文献中探讨了动力问题,但也未考虑动荷载的全波形,所以未能解决块体滑动的真正的动力学问题。     

汉中梁山小壳动物化石发现及地层意义

梁山位于陕西省汉中市附近,属西南地台的北部边缘。1979年,我系陈润业教授带领学生在梁山大南沟实习,于下寒武统郭家坝组底部,厚度不到1米的含海绿石土黄色灰质砂岩及灰白色砂质灰岩中,首次发现了小壳动物化石(图1),并提出了梁山地区有相当于梅树村期沉积的可能性。     

Extended Finite Element Method for the Analysis of Discontinuities in Rock Masses

The strength and deformability of rock mass primarily depend on the condition of joints and their spacing and partially on the engineering properties of rock matrix. Till today, numerical analysis of discontinuities e.g. joint, fault, shear plane and others is conducted placing an interface element in between two adjacent rock matrix elements. However, the applicability of interface elements is limited in rock mechanics problems having multiple discontinuities due to its inherent numerical difficulties often leading to non-convergent solution. Recent developments in extended finite element method (XFEM) having strong discontinuity imbedded within a regular element provide an opportunity to analyze discrete discontinuities in rock masses without any numerical difficulties. This concept is based on partition of unity principle and can be used for cohesive rock joints. This paper summarizes the mathematical frameworks for the implementation of strong discontinuities in 3 and 6 nodded triangular elements and also provides numerical examples of the application of XFEM in one and two dimensional problems with single and multiple discontinuities.     

一种解析正圆锥状褶皱和复杂环带的方法——三点法

圆锥状褶皱是与圆柱状褶皱几何特征不同但又有一定联系的构造,在自然界并不少见,不仅可以出现于圆柱状褶皱的尾端,而且常见于多期构造变形迭加的地区。作者在辽宁省鞍本地区进行变质岩构造解析时,也遇到了多个不同尺度的圆锥状褶皱。     

Evaluate the performance of an accelerated initial stiffness method in three dimensional finite element analysis

Newton’s method is a commonly used algorithm for elasto-plastic finite element analysis and has three common variations: the full Newton–Raphson method, the modified Newton–Raphson method and the initial stiffness method. The Newton–Raphson methods can converge to the solution in a small number of iterations when the system is stable; however, the methods can be quite computationally expensive in some types of problems, for example where the tangent stiffness matrix is unsymmetric or the plasticity is highly localized. The initial stiffness method is robust in those cases but requires a larger number of iterations. This prompted the formulation of many acceleration techniques in literature. In this paper, those techniques will be briefly discussed. This will be followed by the development of a modified acceleration technique for the initial stiffness method. The performance of the modified accelerated initial stiffness method will be examined in elasto-plastic analyses, using both direct and iterative matrix solvers. The results will be compared – in terms of the required number of iterations and the computation time – with an existing accelerated initial stiffness method, the non-accelerated initial stiffness method and the Newton–Raphson tangent stiffness method.     

根据岩石应力-应变曲线组分析岩石变形破坏的数值方法

在研究岩石变形破坏时,现在采取的弹塑性分析,多是根据岩石在不同的应力状态下的典型破坏现象,提出强度理论(破坏准则),进而在导出岩石的本构关系基础上进行分析计算的。一般说来,岩石在不同应力状态下,基本破坏形式可分下面三类:(1)脆性拉伸破坏,(2)剪切破坏,(3)塑性流动破坏。这三种破坏类型,基本上可以归结为流动和断裂(拉断和剪断)两种破坏形式。     

The analysis of finite elasto-plastic consolidation

A theoretical formulation and a numerical solution method are proposed for the problem of the time dependent consolidation of an elasto-plastic soil subject to finite deformations. The soil is assumed to be a two-phase material with a skeleton which may yield according to a general yield criterion with plastic flow governed by a general flow law, and whose pore fluid flows according to Darcy's Law. Governing equations are cast in a rate form and constitutive laws are expressed in a frame indifferent manner. The method of analysis is illustrated by several examples of practical interest for both a soil with an elastic skeleton and a soil with an elasto-plastic skeleton which obeys a Morh–Coulomb yield criterion and a non-associated flow law.