A Boundary-Field Formulation for Elastodynamic Scattering
A Boundary-Field Formulation for Elastodynamic Scattering
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DOI：
10.1007/s10659-022-09964-7
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发表时间：
2022-06
影响因子：
2
通讯作者：
G. Hsiao;Tonatiuh S'anchez-Vizuet;W. Wendland
中科院分区：
文献类型：
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作者：
G. Hsiao;Tonatiuh S'anchez-Vizuet;W. Wendland
冲击弹性障碍物的入射弹性动力波被嵌入无限大的弹性介质中。本文的目的是研究随后由弹性障碍物散射并传递到弹性障碍物中的弹性场。应用边界场方程方法，利用障碍物内场方程和外弹性介质中的边界积分方程组，建立了拉普拉斯变换域中的非局部边值问题。对于两种不同的积分表示，在Sobolev空间中建立了NBP解的存在唯一性和稳定性。在时间域上得到了相应的结果。稳定界被转化为可以作为基于卷积求积的数值离散的起点的时间域估计。
An incoming elastodynamic wave impinges on an elastic obstacle is embedded in an infinite elastic medium. The objective of the paper is to examine the subsequent elastic fields scattered by and transmitted into the elastic obstacle. By applying a boundary-field equation method, we are able to formulate a nonlocal boundary problem (NBP) in the Laplace transformed domain, using the field equations inside the obstacle and boundary integral equations in the exterior elastic medium. Existence, uniqueness and stability of the solutions to the NBP are established in Sobolev spaces for two different integral representations. The corresponding results in the time domain are obtained. The stability bounds are translated into time domain estimates that can serve as the starting point for a numerical discretization based on Convolution Quadrature.