Generalized Surface Green's Functions for an Elastic Half-Space

被引：0

作者：

Zemskov, A. V. ^{[1
,2
]}

Tarlakovskii, D. V. ^{[1
,2
]}

机构：

[1] Natl Res Univ, Moscow Aviat Inst, Moscow 125993, Russia

[2] Lomonosov Moscow State Univ, Res Inst Mech, Moscow 119192, Russia

来源：

RUSSIAN MATHEMATICS | 2023年 / 67卷 / 04期

基金：

俄罗斯科学基金会;

关键词：

elastic half-space; influence functions; Green's functions; stress functions; generalized functions; point support;

D O I：

10.3103/S1066369X23040084

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

-Using generalized functions, Green's functions for homogeneous elastic isotropic half-planes and half-spaces are constructed. Airy and Maxwell stress functions are used to find Green's functions. One-dimensional and two-dimensional integral Fourier transforms are used to solve the boundary value problems. Taking into account the properties of generalized functions with a point support, singular components of displacement images are distinguished. It is shown that they correspond to the rigid-body displacement. If there are no singular components, then the stresses and di-splacements coincide with the known classical solutions of the Flamant, Boussinesq, and Cerutti problems.

引用

页码：22 / 30

页数：9