力学和声学中超奇异积分方程的直接数值处理
On direct numerical treatment of hypersingular integral equations arising in mechanics and acoustics
摘要：
本文提出了一种处理超奇异积分方程的方法，它在波动力学、弹性力学和流体力学的许多混合边界条件问题中有相关的应用。本工作的主要目标是发展一种有效的直接数值配置法。本文完成了两个例子，从裂纹理论和声学：在线性各向同性弹性介质中的一个单一的裂纹的研究，和平面声波的衍射薄刚性屏幕。
英文摘要：
In this paper we present a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions. The main goal of the present work is the development of an efficient direct numerical collocation method. The paper is completed with two examples taken from crack theory and acoustics: the study of a single crack in a linear isotropic elastic medium, and diffraction of a plane acoustic wave by a thin rigid screen.
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