饱和多孔介质中动力渗流耦合分析的Biot-Cosserat连续体模型与应变局部化有限元模拟

提出了适用于饱和多孔介质中应变局部化分析及动力渗流耦合分析的Biot-Cosserat连续体模型。基于饱和多孔介质动力渗流耦合分析的Biot理论,将固体骨架看作Cosserat连续体,并考虑旋转惯性,建立了饱和多孔介质动力渗流耦合分析的Biot-Cosserat连续体模型。基于Galerkin加权余量法,对所发展的模型推导了以固体骨架广义位移(包含旋转)及孔隙水压力为基本未知量的有限元公式。利用所发展的数值模型,对包含压力相关弹塑性固体骨架材料的饱和多孔介质进行了动力渗流耦合分析与应变局部化有限元模拟,结果表明,所发展的两相饱和多孔介质动力渗流耦合分析的Biot-Cosserat连续体模型能保持饱和两相介质应变局部化问题的适定性及模拟饱和多孔介质中由应变软化引起的应变局部化现象的有效性。     

各向异性双重孔隙介质的应力与油水两相渗流耦合理论模型

针对天然裂缝性油藏的特性,建立了描述双重孔隙介质中油水两相流体流动特性的流固耦合理论模型。该模型不仅考虑了渗透率的各向异性,而且考虑了岩石固体骨架变形的各向异性。渗流方程是依据双重孔隙的概念建立起来的,而固体骨架变形控制方程则是根据Biot 的等温、线性孔隙弹性理论建立起来的。同时,给出了横向各向同性及结构各向异性、固体材料各向同性时的双重孔隙介质的应力与油水两相渗流耦合理论模型。对该模型进行了简化,并将其简化后模型与单相流的各项同性和各向异性双重孔隙介质流固耦合理论模型进行了比较。     

基于连续损伤的岩石渗流有限元分析

该文基于连续损伤力学,建立了含损伤的岩石渗流模型,研究岩石损伤破坏并分析其渗流特性。该文采用Weibull分布函数来模拟岩石弹性模量和强度的非均质特性,利用Biot本构关系建立含孔隙结构的弹性变形方程,结合Drucker-Prager强度准则、统计强度理论和连续损伤理论推导出岩石连续损伤演化控制方程及其定解条件,进而采用有限元法对其求解。该文给出的数值算例结果表明所提出的含损伤渗流模型适用于研究岩石的渗流特性,分析结果与实验数据吻合较好,且该求解方法可以对岩石体积压裂、岩层弱面进行可靠、有效的数值分析。     

一种渗流吸水诱发岩体强度弱化的有限体积数值计算方法

传统的渗流数值计算方法难以较真实地描述岩石材料性能劣化和渗透性演化机制。该文提出了一种渗流吸水诱发岩体强度弱化的有限体积数值计算方法。利用高斯散度定理采用有限体积法求解水在岩体中的渗流过程及岩体的变形破坏过程,建立了基质吸水引起岩体模量及强度弱化的理论模型及相应的数学表述。基于考虑吸水弱化算法的各向同性孔隙渗流模型,模拟了低、高两种边界流体压力下某粉砂岩试样的吸水软化过程和不同吸水时间下试样的单轴压缩过程。数值算例表明：边界流体压力越高,试样达到整体饱和状态的时间越快;渗流初期以自由水渗流填充孔隙为主,渗流后期以孔隙内自由水向基质吸水的转化为主;边界流体压力对渗流速率具有明显控制作用,但对基质吸水速度无影响;随着吸水时间的增加,试样的强度（黏聚力、内摩擦角）逐渐减小至残余值,得到的基质吸水含量随时间变化的数值解与理论解基本一致,表明了数值算法的计算精度,可以用于隧道突水、围岩稳定性等实际岩体工程问题的渗流-应力耦合效应分析。     

双变量耦合作用对非饱和岩土波动特性的影响研究

为了研究双变量耦合效应对非饱和岩土波动特性的影响,假定固、液和气材料之间以及它们与骨架之间的力学特性均相互解耦。以Bishop平均应力和修正吸力为骨架的双应力变量,以骨架应变和饱和度为骨架的双应变变量,从小应变变形的多孔介质工程力学出发建立了非饱和多孔岩土的波动控制方程。利用不同双变量建立的线弹性本构方程相互一致的性质,建立了波动方程模型参数和常规室内试验土工参数之间的换算关系。新波动方程的刚度矩阵具有对称性,因而满足弹性力学互易定律。利用新波动方程获得了非饱和岩土三个压缩波和一个剪切波的波速计算公式。数值分析研究结果表明,双变量的耦合效应对剪切波波速无影响,对P2波和P3波的影响可以忽略不计。在饱和度较小时对P1波波速有明显影响。耦合效应越大,对P1波波速的影响越明显,但其影响程度随着饱和度的增大迅速减小。     

流体固体动力耦合分析的有限元法

应用有限元法探讨了流体、固体接触界面由无限接触点对组成,并以接触点对的瞬态接触内力作为待定变量的流体固体动力耦合模型的数值求解方法.分析了流体、固体域插值函数的特点,用二维八节点等参元及流固接触面上的接触点对单元,对流固耦合系统进行了离散化处理;并采用变分原理推导了反映流体固体动力相互作用机理的接触约束矩阵(或称动力耦合矩阵),建立了有限元控制方程,给出了完整的数值计算方法, 研编了动力耦合系统的分析程序.数值计算结果与经典理论解误差很小,验证了动力耦合模型和有限元求解方法的正确性及其较高的计算精度.     

土体冻融过程中水、热、力三场耦合本构问题及数值分析

根据传热学、渗流理论及冻土力学提出了带相变的温度场、水分场和应力场耦合问题的数学力学模型及其控制方程。利用自行开发的程序进行数值模拟,加入我们推出的本构关系和所建立的数学力学模型,通过对冻土路基水分场、温度场、应力场三场的数值计算结果分析,得到了准确、详尽的符合实际的温度场与应力场、位移场、应变场耦合的计算结果。     

楔形体匀速和自由落体水弹性砰击的半解析法求解EI北大核心CSCD

针对二维弹性楔形体入水过程的流固耦合问题,提出一种基于耦合Wagner理论和模态叠加法的半解析解方法。结构湿表面的速度势基于Wagner理论求解并考虑了结构弹性影响。砰击压力根据伯努利方程求解,为提高求解精度考虑了伯努利方程中速度平方项。通过平均弹性速度修正模型推导出附加质量和阻尼矩阵,将其代入固体动力学方程从而建立统一的流固耦合方程,耦合方程通过基于隐式的Newmark-β算法实现求解。通过计算楔形体垂直恒速和自由落体入水两种运动状态,并与基于半解析、数值和试验的文献结果进行了对比,验证了所提理论的可靠性。     

率相关饱和多孔介质动力响应的数值分析

在基于混合物理论的多孔介质模型的基础上,将固体相视为弹粘塑性体,建立了饱和多孔介质的弹粘塑性模型。模型的基本思想是在无粘弹塑性本构关系中引入-时间参数,使固体骨架具备了粘性效应。利用Galerkin加权残值法推导得到了罚有限元格式,并采用Newmark预估校正法求解率相关饱和多孔介质的非线性有限元动力方程,此算法可以很...     

颈动脉粥样硬化斑块模型的谱元法计算

本文考虑人体颈动脉粥样硬化斑块的力学建模及其数值计算.颈动脉粥样硬化斑块的动力学行为由控制血液流动的不可压缩Navier-Stokes方程和控制动脉形变的弹性方程耦合描述,因此完整的硬化斑块模型是一组三维流体/固体耦合方程,其数学理论和数值计算都面临极大的困难.但在一定的假设条件下,该问题可简化为一个弹性力学方程.本文考虑粥样硬化斑块简化模型的数值计算问题.我们构造了一个针对模型简化方程的有效算法,即基于空间方向上的谱元离散和时间方向的Newmark格式的计算方法.分析显示前者对光滑解具有指数收敛性,而后者具有二阶收敛精度并且在特定的参数条件下无条件稳定.论文不仅讨论了连续问题以及半离散问题的稳定性,而且给出了全离散格式的最优误差估计.最后通过数值模拟验证了所提算法的有效性和理论分析结果,并对一些具有实际背景参数的模型问题进行了模拟.     

Parallel 3-d simulations for porous media models in soil mechanics

 Numerical simulations in 3-d for porous media models in soil mechanics are a difficult task for the engineering modelling as well as for the numerical realization. Here, we present a general numerical scheme for the simulation of two-phase models in combination with an abstract material model via the stress response with a specialized parallel saddle point solver. Therefore, we give a brief introduction into the theoretical background of the Theory of Porous Media and constitute a two-phase model consisting of a porous solid skeleton saturated by a viscous pore-fluid. The material behaviour of the skeleton is assumed to be elasto-viscoplastic. The governing equations are transfered to a weak formulation suitable for the application of the finite element method. Introducing an abstract formulation in terms of the stress response, we define a clear interface between the assembling process and the parallel solver modules. We demonstrate the efficiency of this approach by challenging numerical experiments realized on the Linux Cluster in Chemnitz. Received 15 February 2002 / Accepted 12 April 2002     

饱和软粘土中沉桩后桩周土体固结分析

假定沉桩过程是一个平面应变圆孔扩张问题, 采用了修正剑桥模型, 给出了软粘土中沉桩过程后初始时刻超孔隙水压力沿桩径分布的解析函数, 并与Cao 等人的数值解以及Gibson 提出的公式进行了比较。根据土骨架的弹性位移特性以及水流的连续性条件, 得到了桩周土体固结的控制方程。运用分离变量法并结合边界条件以及初始条件得到了桩周土中超孔隙水压力消散的级数解答, 该解答可以作为孔压静力触探反求固结系数的一个理论依据。通过2 个算例分析了土体的应力历史以及刚度对桩侧超静孔压消散的影响;算例分析表明, 随着超固结比的增大, 归一化后的塑性区半径以及桩侧超孔隙水压力均在减小;桩侧的超静孔压消散前期较快, 后期较慢。     

A discussion on high-frequency wave energy behavior in viscoelastic media

A time-varying energy equation is proposed for general high-frequency elastoacoustic waves. Derivations are presented through a wave approach and transport theory. The assumption of uncorrelated waves is adopted in the wave approach and leads to a second-order partial differential equation. A similar process is also mathematically verified in the derivation by means of transport theory. Both derivations allow a simplified energy-based equation to be formulated. This simplified formulation can be of real interest in many engineering applications. Precisely, the recent mathematical results obtained for the high-frequency asymptotic of hyperbolic partial differential equations are used to ease the derivation. Some developments are introduced to extend the classic transport theory for bounded elastoacoustic systems with damping. It is shown that the behavior of high-frequency elastoacoustic energy, being diffusive or wavefront, depends on the correlation lengths of the inhomogeneities of media. The proposed energy equation is mathematically different from the equation applied in the conventional approaches, which are used extensively in recent study of time-varying energy in medium- and high-frequency domains, such as transient statistical energy analysis (SEA) or the time-varying conductivity approach.     

An extended finite element method for fluid flow in partially saturated porous media with weak discontinuities; the convergence analysis of local enrichment strategies

In this paper, a numerical model is developed for the fully coupled analysis of deforming porous media containing weak discontinuities which interact with the flow of two immiscible, compressible wetting and non-wetting pore fluids. The governing equations involving the coupled solid skeleton deformation and two-phase fluid flow in partially saturated porous media are derived within the framework of the generalized Biot theory. The solid phase displacement, the wetting phase pressure and the capillary pressure are taken as the primary variables of the three-phase formulation. The other variables are incorporated into the model via the experimentally determined functions that specify the relationship between the hydraulic properties of the porous medium, i.e. saturation, permeability and capillary pressure. The spatial discretization by making use of the extended finite element method (XFEM) and the time domain discretization by employing the generalized Newmark scheme yield the final system of fully coupled non-linear equations, which is solved using an iterative solution procedure. Numerical convergence analysis is carried out to study the approximation error and convergence rate of several enrichment strategies for bimaterial multiphase problems exhibiting a weak discontinuity in the displacement field across the material interface. It is confirmed that the problems which arise in the blending elements can have a significant effect on the accuracy and convergence rate of the solution.     

基于混合有限体积/有限元法的喷管辐射传递求解研究

针对三维不规则非灰吸收介质的辐射传递问题,提出用混合有限体积侑限元法对其求解.在直角坐标系下,详细推导了混合有限体积/有限元法的计算过程;并结合向量和矩阵运算的相关理论,给出一种能够耦合边界条件的有限元方程的总体合成方法.以姿控推进器喷管扩张段和其内部的吸收介质之间的辐射传递为求解对象,采用该方法得到喷口的光谱辐射亮度...     

Transient gas flow through porous media

The problem of transient, one-dimensional flow of an ideal gas through a deformable porous layer is considered. Due to the assumption of small displacement gradients, the mathematical model leads to a formulation in terms of a nonlinear partial differential equation familiar in gas flow theory. For the limiting case of zero surface pressure analytic short time and long time solutions are presented. These are matched at an intermediate value of time giving an accurate approximate solution. The general case of non-zero surface pressure is treated numerically using Galerkin's method. The analytical character of the early time solution is discussed for this general case.     

Numerical method of inertance tube pulse tube refrigerator

A nodal analysis method for simulating inertance tube pulse tube refrigerators is introduced. The energy equation, continuity equation, momentum equation of gas, energy equation of solid are included in this model. Boundary condition can be easily changed to enable the numerical program calculate thermal acoustic engines, inertance tube pulse tube refrigerators, double inlet pulse tube refrigerators, and others. Implicit control volume method is used to solve these equations. In order to increase the calculation speed, the continuity equation is changed to pressure equation with ideal gas assumption, and merged with momentum equation. Then the algebraic equation group from continuity and momentum equation becomes one group. With this numerical method, an example calculation of a large scale inertance tube pulse tube refrigerator is shown.     

A Galerkin/least‐squares finite element formulation for consolidation

A Galerkin/least‐squares (GLS) finite element formulation for problem of consolidation of fully saturated two‐phase media is presented. The elimination of spurious pressure oscillations appearing at the early stage of consolidation for standard Galerkin finite elements with equal interpolation order for both displacements and pressures is the goal of the approach. It will be shown that the least‐squares term, based exclusively on the residuum of the fluid flow continuity equation, added to the standard Galerkin formulation enhances its stability and can fully eliminate pressure oscillations. A reasonably simple framework designed for derivation of one‐dimensional as well as multi‐dimensional estimates of the stabilization factor is proposed and then verified. The formulation is validated on one‐dimensional and then on two‐dimensional, linear and non‐linear test problems. The effect of the fluid incompressibility as well as compressibility will be taken into account and investigated. Copyright © 2001 John Wiley & Sons Ltd.     

A mixed-penalty finite element formulation of the linear biphasic theory for soft tissues

Hydrated soft tissues of the human musculoskeletal system can be represented by a continuum theory of mixtures involving intrinsically incompressible solid and incompressible inviscid fluid phases. This paper describes the development of a mixed-penalty formulation for this biphasic system and the application of the formulation to the development of an axisymmetric, six-node, triangular finite element. In this formulation, the continuity equation of the mixture is replaced by a penalty form of this equation which is introduced along with the momentum equation and mechanical boundary condition for each phase into a weighted residual form. The resulting weak form is expressed in terms of the solid phase displacements (and velocities), fluid phase velocities and pressure. After interpolation, the pressure unknowns can be eliminated at the element level, and a first order coupled system of equations is obtained for the motion of the solid and fluid phases. The formulation is applied to a six-node isoparametric element with a linear pressure field. The element performance is compared with that of the direct penalty form of the six-node biphasic element in which the pressure is eliminated in the governing equations prior to construction of the weak form, and selective reduced integration is used on the penalty term. The mixed-penalty formulation is found to be superior in terms of tendency to lock and sensitivity to mesh distortion. A number of example problems for which analytic solutions exist are used to validate the performance of the element.