Boundary elements for half‐space problems via fundamental solutions: A three‐dimensional analysis

2001 ◽  
Vol 52 (11) ◽  
pp. 1189-1202 ◽  
Author(s):  
J. Liang ◽  
K. M. Liew
Keyword(s):  
Half Space ◽  
Dimensional Analysis ◽  
Three Dimensional ◽  
Boundary Elements ◽  
Fundamental Solutions

Transient fundamental solutions for a transversely isotropic elastic half space

1993 ◽  
Vol 442 (1916) ◽  
pp. 505-531 ◽  
Keyword(s):  
Half Space ◽  
Transient Response ◽  
Analytical Solutions ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Integral Transforms ◽  
Fundamental Solutions ◽  
Elastic Half Space ◽  
Kernel Functions ◽  
Two Dimensional

This paper is concerned with the study of transient response of a transversely isotropic elastic half-space under internal loadings and displacement discontinuities. Governing equations corresponding to two-dimensional and three-dimensional transient wave propagation problems are solved by using Laplace–Fourier integral transforms and Laplace−Hankel integral transforms, respectively. Explicit general solutions for displacements and stresses are presented. Thereafter boundary-value problems corresponding to internal transient loadings and transient displacement discontinuities are solved for both two-dimensional and three-dimensional problems. Explicit analytical solutions for displacements and stresses corresponding to internal loadings and displacement discontinuities are presented. Solutions corresponding to arbitrary loadings and displacement discontinuities can be obtained through the application of standard analytical procedures such as integration and Fourier expansion to the fundamental solutions presented in this article. It is shown that the transient response of a medium can be accurately computed by using a combination of numerical quadrature and a numerical Laplace inversion technique for the evaluation of integrals appearing in the analytical solutions. Comparisons with existing transient solutions for isotropic materials are presented to confirm the accuracy of the present solutions. Selected numerical results for displacements and stresses due to a buried circular patch load are presented to portray some features of the response of a transversely isotropic elastic half-space. The fundamental solutions presented in this paper can be used in the analysis of a variety of transient problems encountered in disciplines such as seismology, earthquake engineering, etc. In addition these fundamental solutions appear as the kernel functions in the boundary integral equation method and in the displacement discontinuity method.

Transient Response of Multiple Rigid Foundations on an Elastic, Homogeneous Half-Space

1994 ◽  
Vol 61 (3) ◽  
pp. 656-663 ◽  
Author(s):  
F. Guan ◽  
M. Novak
Keyword(s):  
Boundary Element ◽  
Half Space ◽  
Transient Response ◽  
Three Dimensional ◽  
Numerical Procedure ◽  
Nonlinear Problems ◽  
Fundamental Solutions ◽  
Dynamic Interaction ◽  
Homogeneous Half Space ◽  
Element Approach

Three-dimensional transient response of both massless and massive multiple, rigid foundations, bonded to an elastic, homogeneous half-space, is investigated to study the effect of dynamic interaction through-soil. The numerical procedure is formulated in terms of the boundary element approach by means of the transient fundamental solutions developed by the authors (1994). This procedure works efficiently for the problem addressed here since the separated foundations are analyzed without discretizing the surface of the half-space outside the contact areas between the half-space and the foundations. It also provides the possibility to study nonlinear problems involved with semi-infinite soils.

Sign in / Sign up

Export Citation Format

Share Document