论文标题
弹性散射的边界场公式
A boundary-field formulation for elastodynamic scattering
论文作者
论文摘要
撞击弹性障碍物上的传入弹性动力波嵌入无限的弹性介质中。本文的目的是检查散布并传播到弹性障碍物的随后的弹性场。通过应用边界场方程方法，我们可以使用外部弹性介质中的障碍物和边界积分方程来制定拉普拉斯变换域中的非本地边界问题（NBP）。解决方案对NBP的存在，独特性和稳定性是在Sobolev空间中建立的，用于两个不同的积分表示。获得时域中的相应结果。稳定性界限被转化为时域估计值，该估计值可以作为基于卷积正交数值数字离散化的起点。
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.
