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Yu-Jia Hu Yuan-Yuan Zhu Chang-Jun Cheng 《International Journal of Solids and Structures》2009,46(7-8):1667-1675
Based on the Porous Media Theory (PMT), a mathematical model of space-axisymmetrical problems for incompressible fluid-saturated visco-elastic porous media is presented in the case of small deformation, in which the differential-type constitutive relation is applied to describe the mechanical characteristics of solid skeleton. The differential quadrature method (DQM) and the second-order backward difference scheme are used to discretize the governing equations on the spatial and temporal domains, respectively, and a method is proposed to deal with the singularity conditions at points located on the symmetry axis. As application, the dynamic behavior of a column of fluid-saturated elastic porous media is analyzed firstly. The obtained results are compared with the analytical results in the existing literature, they are comparatively accordant, which means that the model and method presented in this paper are correct, and the obtained results are reliable. Further, the dynamic response of a space-axisymmetrical body of fluid-saturated visco-elastic porous media is analyzed, in which the material characteristic of the solid skeleton is described by Burgers model with four parameters. 相似文献
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一维流体饱和粘弹性多孔介质层的动力响应 总被引:3,自引:1,他引:2
本文研究了不可压流体饱和粘弹性多孔介质层的一维动力响应问题。基于粘弹性理论和多孔介质理论,在流相和固相微观不可压、固相骨架服从粘弹性积分型本构关系和小变形的假定下,建立了不可压流体饱和粘弹性多孔介质层一维动力响应的数学模型,利用Laplace变换,求得了原初边值问题在变换空间中的解析解,并利用Laplace逆变换的Crump数值反演方法,得到原动力响应问题的数值解。数值研究了饱和标准线性粘弹性多孔介质层的动力响应,分析了固相位移、渗流速度、孔隙压力及固相有效应力等的响应特征。结果表明,与不可压流体饱和弹性多孔介质相同,不可压流体饱和粘弹性多孔介质中亦只存在一个纵波,并且固相骨架的粘性对动力行为有显著的影响。 相似文献
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基于饱和多孔介质理论,在固相和液相微观不可压,固相骨架小变形且满足线性粘弹性积分型本构关系的假定下,建立了流体饱和粘弹性多孔介质动力响应的若干Gurtin型变分原理,包括Hu-Washizu变分原理.利用所建立的变分原理,导出了流体饱和粘弹性多孔介质动力响应无网格数值模拟的离散控制方程,此方程是一个关于时间的对称微分方程组,便于分析计算.作为数值例子,研究了流体饱和粘弹性多孔柱体的一维动力响应,数值结果揭示了流体饱和粘弹性多孔柱体中波的传播特性以及固相粘性的影响. 相似文献
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梯度饱和土瞬态响应分析 总被引:1,自引:1,他引:0
基于Biot多孔介质理论,建立了饱和土体在动载荷作用下的一维回传射线矩阵法的计算列式,其中考虑了土体的非均匀性、惯性、黏滞以及固体颗粒和流体的可压缩性.利用计算结果与已有结果相比较,二者相吻合,验证了算法的正确性.作为数值算例,考虑饱和土的物理力学性质沿深度方向按幂函数连续变化,利用数值Laplace逆变换求解了在冲击性载荷作用下的位移,应力和孔隙压力等物理量的瞬态响应,重点分析讨论了材料非均匀性对饱和土介质动力特性的影响. 相似文献
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An elastic fluid-saturated porous medium is modeled as a bundle of parallel cylindrical tubes aligned in a direction parallel to the fluid movement. The pore space is filled with viscous compressible liquid. A cell model and the theory of transient pipe flow are used to derive one-dimensional governing equations in such media. All macroscopic constants in these equations are defined by the individual material constants of the fluid and solid. The interaction force includes an additional term not found in Biot's theory. 相似文献
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固体火箭发动机药柱粘弹性材料除具有弹塑性特性,还具有粘滞性,这一特性使得材料变形具有明显的时间效应,本构关系复杂,进行动态力学分析时,动态模量难以有效拟合.本文提出了一种基于(Levenberg-Marquardt, L-M)算法的复数神经网络拟合粘弹性材料动态模量的方法.通过广义Maxwell模型推导得到材料的动态模量表达式,以此构造未定网络参数为复数的神经网络,从而提供了一种输入、输出样本均为复数的神经网络解决方法.将实数L-M训练算法进行改进,衍生到复数领域,提出复数L-M训练算法.通过粘弹性材料实验,将实验数据时温等效转换,获得复数神经网络的训练及测试样本.通过对神经网络进行训练,实现粘弹性材料动态模量的高精度拟合.数值算例表明,与传统神经网络拟合方法相比,所提方法在训练速度和泛化能力方面都有其优越性. 相似文献
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为了深入研究液饱和多孔介质中应力波的传播,提出了三维两相细观计算模型.基于此模型。应用Galerkin余量法并计及流-固耦合界面的耦合效应,利用直接耦合的技术,开发了三维流-固混合显式动力有限元计算程序.在此基础上对冲击载荷作用下液饱和多孔介质中三维应力波的传播现象进行了数值模拟,并详细讨论了孔隙率,孔隙形状等因素对应力波传播主导波形的影响. 相似文献
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混沌运动能在一定的范围内按自身的规律不重复地遍历所有状态。利用这个特点 ,本文将混沌运动引入到双相介质参数反问题的研究中。首先利用边界元方法实现了由介质参数到地表位移的非线性映射 ,然后通过建立合成位移与实测位移的相关函数将参数识别问题归结为优化问题 ,最后利用混沌运动指导优化搜索求得介质参数。算例结果表明了混沌搜索方法用于双相介质参数反演问题的可行性和有效性 相似文献
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According to generalized characteristic theory, a characteristic analysis for stress wave propagation in transversely isotropic fluid-saturated porous media was performed. The characteristic differential equations and compatibility relations along bicharacteristics were deduced and the analytical expressions for wave surfaces were obtained. The characteristic and shapes of the velocity surfaces and wave surfaces in the transversely isotropic fluid-saturated porous media were discussed in detail. The results also show that the characteristic equations for stress waves in pure solids are particular cases of the characteristic equations for fluid-saturated porous media. 相似文献
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Energy focusing is found on the wave fronts of slow waves, which is a new propagation characteristic for slow waves in fluid-saturated
porous materials. The material parameters, as well as the propagation directions, are chosen as the control parameters. Combined
with the two axial variables, the influence of the anisotropy of the solid skeleton and pore fluid parameters on the propagation
characteristic of slow waves in anisotropic fluid-saturated porous materials is discussed. The correspondence between the
focusing on the wave fronts and the contours of zero Gaussian curvature on the slowness surface is explored. The development
of the focusing patterns is investigated and the distinct trends in the energy flux focusing structures are revealed. This
is helpful in further understanding the roles of the pore fluid in the damage of the fluid-saturated porous media. 相似文献
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The quasi-static equations of motion are studied for bi-laminated fluid-saturated porous media within the framework of non-phenomenological mixture theories. The flow-deformation coupled behavior of the media is governed by Biot's theory for which all constituents are considered compressible. The asymptotic analysis for a periodic microstructure with multiple scales, developed by Hegemier and Murakami, is adopted to obtain the equations of equilibrium and mass conservation in a binary saturated porous medium. The multiscale analysis appears to be advantageous for dealing with consolidation phenomena because it is capable of transforming a coupled, transient problem into two decoupled, steady-state ones. Various models with different degrees of approximation are generated, and among them a theory for saturated rocks with a single joint system is described. Mixture properties are expressed explicitly in terms of characteristics of intact and joint material. The most distinctive feature of this model comes from the fact that some cross terms, that have not been included in previous models, appear in the constitutive equations for fluid mass change and fluid flux. These cross terms are physically understood because they simply take into account effects occurring on the local level: the deformation-flow coupled phenomenon, the stress continuity and displacement compatibility conditions. These novel results may have far-reaching consequences for future theoretical modeling and experimental programs in two-phase fluid-filled porous media. 相似文献
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Low-Frequency Asymptotic Analysis of Seismic Reflection from a Fluid-Saturated Medium 总被引:1,自引:0,他引:1
D. B. Silin V. A. Korneev G. M. Goloshubin T. W. Patzek 《Transport in Porous Media》2006,62(3):283-305
Reflection of a seismic wave from a plane interface between two elastic media does not depend on the frequency. If one of
the media is poroelastic and fluid-saturated, then the reflection becomes frequency-dependent. This paper presents a low-frequency
asymptotic formula for the reflection of seismic plane p-wave from a fluid-saturated porous medium. The obtained asymptotic
scaling of the frequency-dependent component of the reflection coefficient shows that it is asymptotically proportional to
the square root of the product of the reservoir fluid mobility and the frequency of the signal. The dependence of this scaling
on the dynamic Darcy’s law relaxation time is investigated as well. Derivation of the main equations of the theory of poroelasticity
from the dynamic filtration theory reveals that this relaxation time is proportional to Biot’s tortuosity parameter. 相似文献
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基于多孔介质理论,在固相骨架和孔隙流体微观不可压,固相骨架小变形且满足线性粘弹性积分型本构关系的假定下,利用卷积积分的性质,本文首先建立了以固相骨架位移、孔隙流体相对速度和孔隙流体压力为宗量的流体饱和粘弹性多孔介质固结问题的一个Gurtin型变分原理.其次,利用Lagrange乘子法解除相关的变分约束条件,建立了流体饱和粘弹性多孔介质固结问题的若干广义Gurtin型变分原理,包括第三类的Hu-Washizu型变分原理.最后,简单讨论了等价初边值问题的相应变分原理.这些Gurtin型变分原理的建立不仅丰富了饱和粘弹性多孔介质的相关理论,而且为相关数值模拟方法,如有限元法、无网格法等的建立奠定了理论基础. 相似文献
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Nonlinear equations for wave propagation through dry or fluid-saturated porous elastic media are derived using a variational formulation. The method presented is very similar to the approach of Bedford and Drumheller, including microinertia terms for local density fluctuations of fluid and solid. One major difference is the choice of a Lagrangian (rather than Eulerian) reference frame locked to the solid constituent. This choice of reference frame is preferable for porous solids and also allows direct comparison to Biot's theories of nonlinear and semilinear rheology of porous solids. 相似文献
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Effects of Mineral Dissolution Ratios on Chemical-Dissolution Front Instability in Fluid-Saturated Porous Media 总被引:1,自引:0,他引:1
The main purpose of this article is to investigate, both theoretically and computationally, the effects of mineral dissolution
ratios on the different respects of chemical-dissolution front instability problems in fluid-saturated porous media. In order
to get a better understanding of how the mineral dissolution ratio affects the propagation and evolution of a planar chemical-dissolution
front in an infinite space consisting of a fluid-saturated porous medium, the theoretical analysis method is used to derive
the generous solution to the propagation speed of the planar chemical-dissolution front, while the computational simulation
method is employed to simulate the detailed evolution process when the planar chemical-dissolution front is evolved into complicated
morphologies at the supercritical Zhao numbers. The related theoretical results reveal that the mineral dissolution ratio plays an important role in controlling
the propagation speed of a planar chemical-dissolution front in the fluid-saturated porous medium. An increase in the value
of the mineral dissolution ratio can result in a remarkable decrease in the value of the propagation speed of a planar chemical-dissolution
front. On the other hand, the related computational simulation results demonstrate that the mineral dissolution ratio has
a considerable influence on the evolution pattern of a planar chemical-dissolution front during its propagation in the fluid-saturated
porous medium. An increase in the mineral dissolution ratio can reduce the likelihood for a planar chemical-dissolution front
to evolve from the initial planar shape into different morphologies within the fluid-saturated porous medium of finite size. 相似文献
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首先引入状态向量,将直角坐标系下横观各向同性饱和土的Biot波动方程转化为一组状态方程,然后基于双重Fourier变换,求解了状态方程,得到传递矩阵.进而利用传递矩阵,并结合饱和地基的边界条件、排水条件及层间接触和连续条件,求解了横观各向同性饱和层状地基的稳态动力响应问题. 相似文献