Two-dimensional time domain BEM for scattering of elastic waves in solids of general anisotropy
Two-dimensional time domain BEM for scattering of elastic waves in solids of general anisotropy
复制标题
一般各向异性固体中弹性波散射的二维时域边界元法
DOI：
10.1016/0020-7683(95)00217-0
复制
发表时间：
1996
影响因子：
3.6
通讯作者：
S. Hirose
中科院分区：
文献类型：
--
作者：
C. Wang;J. Achenbach;S. Hirose
提出了一种有效的二维时域边界元法，用于求解一般各向异性固体的弹性动力边界/初值问题。该方法基于Wang和Achenbach(1994)[各向异性固体的弹性动力学基本解]导出的Green函数的积分表达式的使用。地球物理学。[j] .力学与工程学报，1999,8(2):1 - 3。奇异静力部分是弹性静力格林函数，具有相对简单的封闭显式表达式。正则动态部分用单位圆上的线积分表示，其积分具有简单的结构，物理上相当于平面波的叠加。通过格林函数的划分，将奇异弹性动力边界积分方程分解为对应于奇异弹性静力积分方程加正则动力项的项。通过分析计算每个边界元的积分和每个时间步长的时间卷积，减少了计算工作量。因此，只有单位圆上的常规线积分才能用数值方法计算。讨论了弹性波在空腔散射中的应用。通过将数值结果与现有的各向同性固体的解析解进行比较，对该方法进行了验证。本文还得到了弹性波在横向各向同性材料中经圆柱腔散射的数值结果。
An efficient two-dimensional time-domain application of the Boundary Element Method is presented to solve elastodynamic boundary/initial-value problems in solids of general anisotropy. The method is based on the use of integral expressions for the Green's functions derived by Wang and Achenbach (1994) [Elastodynamic fundamental solutions for anisotropic solids. Geophys. J. Int.118, 384–392], and on the partition of these Green's functions into singular static and regular dynamic parts. The singular static parts are the elastostatic Green's functions, which have relatively simple explicit expressions in closed form. The regular dynamic parts are given in terms of line integrals over a unit circle, whose integrands have a simple structure which physically corresponds to a superposition of plane waves. The partition of the Green's functions leads to the decomposition of the singular elastodynamic boundary integral equation into terms corresponding to a singular elastostatic integral equation plus regular dynamic terms. The calculation effort is reduced by analytically evaluating both the integration over each boundary element and the time-convolution over each time-step. As a result only regular line integrals over the unit circle have to be computed numerically. Applications are discussed for scattering of elastic waves by cavities. The method has been checked by comparing numerical results against existing analytical solutions for an isotropic solid. Numerical results for scattering of elastic waves in a transversely isotropic material by a circular cylindrical cavity have also been obtained.