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本文在弹性动力学问题的有限单元解的基础上,提出了一种弹性波偏移的新方法--有限单元法弹性波偏移。本方法不仅能使反射纵波得到偏移,而且能同时对反射纵波和反射横波进行偏移。 用本方法已对一种层状模型成功地进行了检验。说明了它对反射纵波和转换横波同时向下延拓和偏移是稳定的,所得到的偏移结果是令人满意的。 相似文献
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基于双相各向异性介质模型,首先推导了双相各向异性介质中弹性波传播的动力学方程及其Galerkin变分方程和有限元运动方程,然后给出了孔隙弹性波方程的有限元数值解法以及二维双相PTL介质中波场模拟的人为吸收边界条件. 最后,利用本文给出的有限元方法对双相PTL介质和双相各向同性介质中的弹性波传播进行了数值模拟. 结果表明:有限元方法和吸收边界条件有效、可行,在理想相界条件下,不论是从固体位移,还是从流体位移的波场快照都能看到明显的慢速拟P波;在黏滞相界情况下,能否观察到慢速拟P波,与含流体地层介质的耗散性质有关.对实际含流体介质,从流体位移分量的波场快照比从固体位移波场快照更容易观察到慢速拟P波. 相似文献
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本文对声波与弹性波方程进行有限元法离散,构造有限元法频散关系的一般特征值问题,分析了时间离散格式为中心差分的三角网格有限元法声波与弹性波模拟的频散特性. 比较了三种质量矩阵即分布式质量矩阵、集中质量矩阵和混合质量矩阵对有限元法频散的影响;选取四种典型三角网格,分析了混合质量矩阵有限元（MFEM）频散的方向各向异性;数值频散、方向各向异性随插值阶数的增加逐渐减弱,当空间为三阶插值时,频散主要表现为随采样率的变化而几乎无明显方向各向异性, 其频散幅值也较小. 控制其他影响因素不变的情况下,研究了不同波速比介质中弹性波的数值频散. 最后给出了三角网格MFEM的数值耗散性. 相似文献
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有限元网格中波动的频散与稳定性的一种改进方法 总被引：1，自引：0，他引：1
本文采用含有频率的高阶位移函数,由二维波动方程导出了波在有限元网格中传播的频散关系,利用这一关系给出了波动的稳定条件。理论分析和数值计算结果表明,文中的有限元方法明显地改善了有限元网格中波动的频散性和稳定性。 相似文献
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Analysis of ground vibrations due to underground trains by 2.5D finite/infinite element approach 总被引：1，自引：1，他引：0
The 2.5D finite/infinite element approach is adopted to study wave propagation problems caused by underground moving trains.
The irregularities of the near field, including the tunnel structure and parts of the soil, are modeled by the finite elements,
and the wave propagation properties of the far field extending to infinity are modeled by the infinite elements. One particular
feature of the 2.5D approach is that it enables the computation of the three-dimensional response of the half-space, taking
into account the load-moving effect, using only a two-dimensional profile. Although the 2.5D finite/infinite element approach
shows a great advantage in studying the wave propagation caused by moving trains, attention should be given to the calculation
aspects, such as the rules for mesh establishment, in order to avoid producing inaccurate or erroneous results. In this paper,
some essential points for consideration in analysis are highlighted, along with techniques to enhance the speed of the calculations.
All these observations should prove useful in making the 2.5D finite/infinite element approach an effective one. 相似文献
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Based on Biot theory of two-phase anisotropic media and Hamilton theory about dynamic problem,finite element equations of elastic wave propagation in two-phase anisotopic media are derived in this paper.Numerical solution of finite element equations is given.Finally,properties of elastic wave propagation are observed and analyzed through FEM modeling. 相似文献
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Transient analysis of 1D inhomogeneous media by dynamic inhomogeneous finite element method 总被引：1，自引：1，他引：0
The dynamic inhomogeneous finite element method is studied for use in the transient analysis of one dimensional inhomogeneous media. The general formula of the inhomogeneous consistent mass matrix is established based on the shape function. In order to research the advantages of this method, it is compared with the general finite element method. A linear bar element is chosen for the discretization tests of material parameters with two fictitious distributions. And, a numerical example is solved to observe the differences in the results between these two methods. Some characteristics of the dynamic inhomogeneous finite element method that demonstrate its advantages are obtained through comparison with the general finite element method. It is found that the method can be used to solve elastic wave motion problems with a large element scale and a large number of iteration steps. 相似文献
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Mutsuto Kawahara 《Advances in water resources》1982,5(4):195-207
This paper presents a finite element method for the analysis of nearshore current, which is mainly induced by surface waves. The analysis is divided into two parts, i.e., the analysis of wave and the analysis of currents. The basic equations are conservation of wave number, wave energy, momentum and continuity. The first two are for wave analysis and the last two for the current analysis. The wave angle is determined from the conservation law of wave number. Using the resulting wave angle and the conservation of wave energy, the distribution of wave height is derived. The radiation stress is derived from the wave angle and height. The nearshore current flow is obtained from the conservations of momentum and continuity including the radiation stress. All the numerical procedures are based on the finite element method. For the analysis of the wave angle and wave height, the incremental iteration method and logarithmic function formulation are employed. For the analysis of the current flow, the stream function formulation is used. From the numerical computations, it is seen that the finite element method presented in this paper is very valuable in practical applications. The method is applied to the analysis of the nearshore current flow of Twan Bay in Japan. 相似文献
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利用结构力学与最优控制的模拟理论,研究弹性波在层状介质中传播的数值计算方法. 将弹性波传播问题导向哈密顿(Hamilton)体系,在哈密顿体系中,推导出一种新的半解析单元,称之为动力-部分杂交元,由此导出一套哈密顿体系下的半解析数值计算方法. 本文给出了该方法在层状正交各向异性材料介质的弹性波传播问题的数值算例,分析了一定频率的弹性波在层状介质中传播时的位移、应力的模式. 计算结果展现了Hamilton体系和辛几何在弹性波传播问题研究的应用前景. 相似文献
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A number of temporal procedures for solving the long-wave surface water equations using the finite element method in space are presented and analyzed. The analysis determines the stability of the schemes and the error in wave amplitude and phase that can be expected. The computational efficiency of the various methods is also discussed. The results ofthis analysis indicate types of errors that might be manifested in finite element surface water modeling using the different schemes. 相似文献
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波动问题有限元离散后会引起数值误差, 数值频散的本质就是数值误差传播引起的非物理解. 数值频散不仅没有实际意义, 而且还会影响对真实波动现象的认识. 为厘清有限元三角网格中波动数值频散的影响因素, 本文推导了集中质量矩阵和一致质量矩阵的频散函数, 同时给出了组合质量矩阵的频散函数, 并对不同质量矩阵的数值频散进行了对比研究. 理论分析和数值计算结果表明: 有限元三角网格中波动的数值频散受网格布局、 波传播方向、 单元网格纵横比以及质量矩阵的影响; 一致质量矩阵的数值频散比集中质量矩阵更易受到波传播方向的影响; 不合理的三角网格单元会对数值相速度(数值频散)产生不良影响; 正三角网格中波动的数值频散几乎不受波传播方向的影响; 一致质量矩阵与集中质量矩阵的线性组合能够有效地压制数值频散. 相似文献
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基于可分离小波理论,由一维Daubechies尺度函数的张量积构造二维Daubechies小波基,并将它作为GPR波动方程求解的插值函数,导出了二维Daubechies小波有限元GPR方程离散格式;通过引入转换矩阵,实现小波系数空间与雷达场值之间转换.引入自由度凝聚技术,有效解决了小波有限元求解中小波单元内部自由度过多的问题,节约了计算量并方便与传统有限元法耦合.然后,详细阐述了Daubechies小波有限元联系系数计算方法,有效解决了小波有限元求解偏微分方程的难点与核心问题.最后,以两个典型GPR模型为例,对比了Daubechies小波有限元与传统有限元的雷达正演剖面图与单道波形图,结果表明:在相同的剖分方式及节点数目条件下,Daubechies小波有限元的紧支性与正交性一定程度上提高了求解效率,它与有限元法求解结果能较好地吻合,验证了Daubechies小波有限元算法的正确性. 相似文献
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在地震动数值模拟方法中,谱元法和有限元法是应用较广泛的两种方法。基于经典的Lamb问题模型,首先推导给出地表竖向位移的解析解答。然后分别利用常用的四阶谱元法和线性有限元法,模拟了地表脉冲力源作用下模型的位移响应。考虑有意义的最短波长内的采样点个数及单元高宽比的变化,对比了两种方法的模拟精度;结果表明:对于谱元法,观测点与波源之间需至少包含两个网格,在此条件下,最短波长内包含一个网格（最短波长内5个采样点）时,数值解与解析解的误差小于1%,已达很高的精度;对于有限元法,最短波长内需包含10个网格时才能达到这一精度。此外,在满足网格尺寸要求的前提下,单元水平向与垂直向尺寸的比值在1∶1到5∶1的范围内时,谱元法和有限元法的模拟精度均变化不大。因此,单位波长内采样点个数相同时,谱元法的模拟精度比有限元法高的多,同时,在一定范围内两种方法的模拟结果对于宽高比的变化不敏感。 相似文献
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间断Galerkin有限元法（DG-FEM）作为一种有效的高阶有限元法受到了国内外学者的广泛关注.本文基于任意高阶间断Galerkin有限元法对弹性波方程进行空间离散,并将离散后所得的非齐次线性常微分方程系统齐次化,最后结合针对齐次问题的强稳定性保持龙格库塔（SSP Runge-Kutta）算法,将DG-FEM推广至时间任意高阶精度.另外,借鉴近最佳匹配层（NPML）的思想,基于复频移（CFS）拉伸坐标变换推导了一种新的PML吸收边界条件（简称为CFS-NPML）,该CFS-NPML能够与DG-FEM算法很好地结合,形成有效的起伏地表地震波传播数值模拟技术.数值试验结果表明,DG-FEM具有高阶精度,可以适应任意复杂起伏地表和复杂构造情况下的弹性波传播数值模拟.同时,CFS-NPML对包括面波等震相的人为边界反射都具有良好的吸收效果. 相似文献
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This paper presents a time-dependent semi-analytical artificial boundary for numerically simulating elastic wave propagation problems in a two-dimensional homogeneous half space. A polygonal boundary is considered in the half space to truncate the semi-infinite domain, with an appropriate boundary condition imposed. Using the concept of the scaled boundary finite element method, the wave equation of the truncated semi-infinite domain is represented by the partial differential equation of non-constant coefficients. The resulting partial differential equation has only one spatial coordinate variable and time variable. Through introducing a few auxiliary functions at the truncated boundary, the resulting partial differential equations are further transformed into linear time-dependent equations. This allows an artificial boundary to be derived from the time-dependent equations. The proposed artificial boundary is local in time, global at the truncated boundary and semi-analytical in the finite element sense. Compared with the scaled boundary finite element method, the main advantage in using the proposed artificial boundary is that the requirement for solving a matrix form of Lyapunov equation to obtain the unit-impulse response matrix is avoided, so that computer efforts are significantly reduced. The related numerical results from some typical examples have demonstrated that the proposed artificial boundary is of high accuracy in dealing with time-dependent elastic wave propagation in two-dimensional homogeneous semi-infinite domains. 相似文献
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就大型近场波动的高效数值模拟而言,稳定实现高阶人工边界是一个尚未圆满解决的问题.本文针对使用多次透射公式的SH波动集中质量有限元模拟,依据GKS定理的群速度解释,进一步阐明了人工边界与内域离散格式耦合所导致高频失稳的机理,即两者支持群速度指向内域的外行高频平面谐波,波动能量自发地从人工边界进入內域,从而导致失稳,而这类谐波是由集中质量有限元离散引入的.本文提出了消除此种耦合失稳的一种方法:通过修改有限元刚度阵来改变内域离散格式,并保证修改格式的精度不低于原有格式的精度.理论分析和数值实验表明此法能稳定实现透射边界.本文研究结果具有推广应用前景. 相似文献
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Analytical and numerical solutions for wave propagation in water-saturated porous layered half-space
J. Tabatabaie Yazdi S. Valliappan Chongbin Zhao 《Soil Dynamics and Earthquake Engineering》1994,13(4)
A fluid-saturated one-layer continuum underlain by a rigid half-space is considered. An exact solution is developed in frequency domain for analyzing disturbance induced by a strip footing located at the surface with vertical harmonic excitation. Since the analytical solution can be used only for very simple conditions, a finite element model has been developed also and compared with the exact solution. It is shown that finite element results are in close agreement with the results which have been obtained by a transformation technique. The proposed finite element scheme can take into account the complex geometry and inhomogeneity for practical problems. Besides this, the analytical results exhibit the overall characteristic of wave propagation in porous media and will provide a representative test problem which can be used for a quantitative evaluation of the accuracy of various numerical solution methods. 相似文献