共查询到20条相似文献，搜索用时 99 毫秒
1.
A local time-domain transmitting boundary for simulating cylindrical elastic wave propagation in infinite media 总被引：3，自引：0，他引：3
Finite element simulation of the time-dependent wave propagation in infinite media requires enforcing the transmitting boundary to replace the truncated far-field infinite domain so as to model the effect of the wave radiation towards infinity. This paper proposed a novel local time-domain transmitting boundary for simulating the cylindrical elastic wave radiation problem. This boundary is a mechanical model consisting of the spring, dashpot and mass elements, with the auxiliary degrees of freedom introduced, which is dynamically stable and easily implemented into the commercial finite element codes. Numerical analysis of the cylindrical elastic wave radiation problem indicates that the proposed transmitting boundaries with the order N=3 for cylindrical P and SV waves and with the order N=4 for cylindrical SH wave have very high accuracy, even when the artificial boundary at wave source. The proposed transmitting boundary with order N=0 can be applied approximately to the general two-dimensional infinite elastic wave problems that contain the more complex outgoing wave fields at artificial boundary than the cylindrical waves. The plane-strain Lamb problem is analyzed with the acceptable engineering accuracy achieved. On the other hand, the proposed transmitting boundary with higher order can be a tool to localize the temporal convolution that appears in an exact time-domain transmitting boundary for the general infinite wave problems. This potential applicability is mentioned. 相似文献
2.
采用规则网格有限差分方法对二维平面弹性波动方程进行差分离散,得到相应的弹性波动方程的有限差分方程,再将弹性波动方程的差分格式与吸收边界、自由边界的离散形式结合形成弹性波动方程有限差分方程解决问题的主体,将其应用于含方形凹陷半无限非均匀介质的模型中进行数值模拟,得到此离散化模型中不同时刻不同节点的位移值。针对具体算例,运用上述方法结合科学计算软件MATLAB和结果后处理软件DIFEM ISOLINE PLOTER得到不同时刻的水平方向位移等值线图与接收器测量点处的合成位移记录,讨论非均匀介质、吸收边界、方形凹陷等对波动特性的影响。 相似文献
3.
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
4.
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
5.
6.
The scaled boundary finite‐element method is extended to simulate time‐harmonic responses of non‐homogeneous unbounded domains with the elasticity modulus and mass density varying as power functions of spatial coordinates. The unbounded domains and the elasticity matrices are transformed to the scaled boundary coordinates. The scaled boundary finite‐element equation in displacement amplitudes are derived directly from the governing equations of elastodynamics. To enforce the radiation condition at infinity, an asymptotic expansion of the dynamic‐stiffness matrix for high frequency is developed. The dynamic‐stiffness matrix at lower frequency is obtained by numerical integration of ordinary differential equations. Only the boundary is discretized yielding a reduction of the spatial dimension by one. No fundamental solution is required. Material anisotropy is modelled without additional efforts. Examples of two‐ and three‐dimensional non‐homogeneous isotropic and transversely isotropic unbounded domains are presented. The results demonstrate the accuracy and simplicity of the scaled boundary finite‐element method. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
7.
从各向同性介质中波场数值模拟的褶积微分算子法出发,推导出了各向异性双相介质中波场传播数值计算的褶积新算法.将常见的二阶微分Biot波动方程用等效的一阶速度—应力双曲方程表示,其中未知的波场向量包括固相和流体的速度分量和应力分量,由此对方程的时间项使用交错网格差分方法计算,而对空间项则采用褶积微分算法进行求解.对各向异性双相介质在单层介质模型和双层介质模型中的波场特征进行了研究.研究的结果显示,在两层介质分界面上当地震波产生反射时能观测到两类纵波和横波,并且在衰减系数大的介质里慢纵波很难见到. 相似文献
8.
时域高阶双渐近透射边界能够同时模拟层状介质中行波和快衰波的传播,具有很高的计算精度和计算效率.本文将高阶双渐近透射边界推广应用到多层层状地基系统弹性波传播问题的模拟,采用广义特征值分解分析该透射边界的数值稳定性,通过移谱法消除导致数值不稳定的虚假模态.将高阶双渐近透射边界以超单元的形式直接嵌入到近场有限元方程,建立了有限元-高阶双渐近透射边界时域耦合分析模型,并将其应用到重力坝-层状地基动力相互作用分析.数值算例分析结果表明,该时域耦合分析模型具有很高的精度和计算效率,适用于实际重力坝工程的地震响应分析. 相似文献
9.
In this paper, a novel semi-analytical method, called Decoupled Equations Method (DEM), is presented for modeling of elastic wave propagation in the semi-infinite two-dimensional (2D) media which are involved surface topography. In the DEM, only the boundaries of the problem are discretized by specific subparametric elements, in which special shape functions as well as higher-order Chebyshev mapping functions are implemented. For the shape functions, Kronecker Delta property is satisfied for displacement function. Moreover, the first derivatives of displacement function with respect to the tangential coordinates on the boundaries are assigned to zero at any given node. Employing the weighted residual method and using Clenshaw–Curtis numerical integration, coefficient matrices of the system of equations are transformed into diagonal ones, which leads to a set of decoupled partial differential equations. To evaluate the accuracy of the DEM in the solution of scattering problem of plane waves, cylindrical topographical features of arbitrary shapes are solved. The obtained results present excellent agreement with the analytical solutions and the results from other numerical methods. 相似文献
10.
介绍了完美匹配层(PML)人工边界可以吸收不同频率和任意角度入射波的原理以及PML人工边界的构造方法. 在此基础上，将PML人工边界应用于地震波动数值模拟的速度应力混合有限元格式中，探讨了PML应用的可行性，并通过数值试验研究了PML人工边界的反射率，比较了PML人工边界与多次透射公式(MTF)人工边界应用于体波和面波模拟中数值反射的差异，对两种边界的透射效果进行了分析. 结果表明， 尽管数值离散后PML人工边界不再保持完美匹配特性，但PML人工边界在近场波动数值模拟中可获得比MTF人工边界更为理想的吸收效果，在角点透射、大角度掠射情形下尤为明显；PML人工边界在混合有限元格式的数值算法中，未见失稳等不良反应，比MTF人工边界有更好的稳定性；在合理选择参数的情况下，PML人工边界的运算量可接受. 相似文献
11.
12.
Based on the u–p formulation of Biot equation with an assumption of zero permeability coefficient, a high-order transmitting boundary is derived for cylindrical elastic wave propagation in infinite saturated porous media. By this transmitting boundary the total stresses on the truncated boundaries of a numerical model, such as a finite element model, are replaced by a set of spring, dashpot and mass elements, with some additionally introduced auxiliary degrees of freedom. The transmitting boundaries are incorporated into the DIANA SWANDYNE II program and an unconditionally stable implicit time integration algorithm is adopted. Despite the assumption made in the derivation of the transmitting boundary, numerical examples show that it can provide highly accurate results for cylindrical elastic wave propagation problems in infinite saturated porous medium in case the u–p formulation is applicable. Although the direct applications of the proposed transmitting boundary to general two dimensional wave problems in infinite saturated porous media are not highly accurate, acceptable accuracy can still be achieved by placing the transmitting boundary at relatively large distance from the wave source. 相似文献
13.
The theory of perfectly matched layer (PML) artificial boundary condition (ABC), which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construc- tion process of PML boundary based on elastodynamic partial differential equation (PDE) system is developed. Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investi- gated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula (MTF) boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in corner and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computa- tional efficiency of PML boundary is only a little lower than MTF boundary. 相似文献
14.
The strong coupling of applied stress and pore fluid pressure, known as poroelasticity, is relevant to a number of applied problems arising in hydrogeology and reservoir engineering. The standard theory of poroelastic behavior in a homogeneous, isotropic, elastic porous medium saturated by a viscous, compressible fluid is due to Biot, who derived a pair of coupled partial differential equations that accurately predict the existence of two independent dilatational (compressional) wave motions, corresponding to in-phase and out-of-phase displacements of the solid and fluid phases, respectively. The Biot equations can be decoupled exactly after Fourier transformation to the frequency domain, but the resulting pair of Helmholtz equations cannot be converted to partial differential equations in the time domain and, therefore, closed-form analytical solutions of these equations in space and time variables cannot be obtained. In this paper we show that the decoupled Helmholtz equations can in fact be transformed to two independent partial differential equations in the time domain if the wave excitation frequency is very small as compared to a critical frequency equal to the kinematic viscosity of the pore fluid divided by the permeability of the porous medium. The partial differential equations found are a propagating wave equation and a dissipative wave equation, for which closed-form solutions are known under a variety of initial and boundary conditions. Numerical calculations indicate that the magnitude of the critical frequency for representative sedimentary materials containing either water or a nonaqueous phase liquid is in the kHz–MHz range, which is generally above the seismic band of frequencies. Therefore, the two partial differential equations obtained should be accurate for modeling elastic wave phenomena in fluid-saturated porous media under typical low-frequency conditions applicable to hydrogeological problems. 相似文献
15.
Numerical simulation in coupled elastic and poroelastic media is important in oil and gas exploration. However, the interface between elastic and poroelastic media is a challenge to handle. In order to deal with the coupled model, the first-order velocity–stress wave equations are used to unify the elastic and poroelastic wave equations. In addition, an arbitrary high-order discontinuous Galerkin method is used to simulate the wave propagation in coupled elastic–poroelastic media, which achieves same order accuracy in time and space domain simultaneously. The interfaces between the two media are explicitly tackled by the Godunov numerical flux. The proposed forms of numerical flux can be used efficiently and conveniently to simulate the wave propagation at the interfaces of the coupled model and handle the absorbing boundary conditions properly. Numerical results on coupled elastic–poroelastic media with straight and curved interfaces are compared with those from a software that is based on finite element method and the interfaces are handled by boundary conditions, demonstrating the feasibility of the proposed scheme in dealing with coupled elastic–poroelastic media. In addition, the proposed method is used to simulate a more complex coupled model. The numerical results show that the proposed method is feasible to simulate the wave propagation in such a media and is easy to implement. 相似文献
16.
多次透射公式实用形式稳定性分析 总被引：1，自引：1，他引：0
景立平 《地震工程与工程振动》2004,24(4):20-24
本文以二维出平面波动方程为例,利用数值方法研究了多次透射公式的实用形式的稳定问题,结果表明：多次透射公式的实用形式与波动方程的集中质量显式有限元结合,不但存在零频漂移,而且同样存在高频振荡失稳,而与中心差分方法结合仅存在零频漂移失稳。 相似文献
17.
常见弹性波动理论的建立是基于介质均匀这一基本假设,实际介质的非均匀性非常普遍.为研究连续介质中波的传播特征,本文从弹性力学中建立弹性波动方程的三个基本方程出发,考虑连续介质弹性参数的空变特征,建立非均匀介质的弹性波动方程,利用Alkhalifah声学近似思想建立位移表征的纵波波动方程,利用本征值问题求解方法建立标量波频率-波数域传播算子,从而建立描述纵波传播的标量波方程,其中波函数为纵波位移的散度,不同于均匀介质标量波方程的波函数为位移势.随后推导含PML边界波动方程差分格式并建立不同模型数值模拟进行数值试算,与均匀假设标量波方程和变密度方程对比证明本方法的准确性和稳定性. 相似文献
18.
An efficient method for modelling the propagation of elastic waves in unbounded domains is developed. It is applicable to soil–structure interaction problems involving scalar and vector waves, unbounded domains of arbitrary geometry and anisotropic soil. The scaled boundary finite element method is employed to derive a novel equation for the displacement unit-impulse response matrix on the soil–structure interface. The proposed method is based on a piecewise linear approximation of the first derivative of the displacement unit-impulse response matrix and on the introduction of an extrapolation parameter in order to improve the numerical stability. In combination, these two ideas allow for the choice of significantly larger time steps compared to conventional methods, and thus lead to increased efficiency. As the displacement unit-impulse response approaches zero, the convolution integral representing the force–displacement relationship can be truncated. After the truncation the computational effort only increases linearly with time. Thus, a considerable reduction of computational effort is achieved in a time domain analysis. Numerical examples demonstrate the accuracy and high efficiency of the new method for two-dimensional soil–structure interaction problems. 相似文献
19.
The scaled boundary finite‐element method has been developed for the dynamic analysis of unbounded domains. In this method only the boundary is discretized resulting in a reduction of the spatial dimension by one. Like the finite‐element method no fundamental solution is required. This paper extends the scaled boundary finite‐element method to simulate the transient response of non‐homogeneous unbounded domains with the elasticity modulus and mass density varying as power functions of spatial coordinates. To reduce the number of degrees of freedom and the computational cost, the technique of reduced set of base functions is applied. The scaled boundary finite‐element equation for an unbounded domain is reformulated in generalized coordinates. The resulting acceleration unit‐impulse response matrix is obtained and assembled with the equation of motion of standard finite elements. Numerical examples of non‐homogeneous isotropic and transversely isotropic unbounded domains demonstrate the accuracy of the scaled boundary finite‐element method. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
20.
瞬变电磁法的三维有限元正演通常采用齐次边界条件,为满足该边界条件,需要构建较大尺寸的模型,这降低了正演问题的求解速度.针对该问题,本文采用吸收边界条件代替齐次边界条件,以缩小模型体积,加快正演速度:首先,从时间域麦克斯韦方程组出发,推导了基于库伦规范的矢量势的微分控制方程,结合一阶吸收边界条件推导了相应的的弱形式方程;在此基础上采用一阶四面体矢量单元进行单元分析、Newmark法进行时间离散,实现了瞬变电磁法的快速三维正演.通过均匀半空间模型的解析解,H型地电断面的CR1Dmod解和相应模型有限元解的对比,验证了本文算法的正确性.均匀半空间模型分别采用吸收边界条件和齐次边界条件的正演结果对比表明:吸收边界条件确实可以提高三维正演的精度或者缩小模型尺寸、加快计算速度. 相似文献