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.

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.

A Three-Dimensional Boundary Element Approach for Transient Anisotropic Viscoelastic Problems

2016 ◽  
Vol 685 ◽  
pp. 267-271 ◽  
Author(s):  
Leonid Igumnov ◽  
I.P. Маrkov ◽  
A.V. Amenitsky
Keyword(s):  
Boundary Element ◽  
Correspondence Principle ◽  
Three Dimensional ◽  
Fundamental Solutions ◽  
Anisotropic Elasticity ◽  
Element Formulation ◽  
Dimensional Boundary ◽  
Element Approach ◽  
Anisotropic Elastic ◽  
Material Solution

This paper presents a three-dimensional direct boundary element approach for solving transient problems of linear anisotropic elasticity and viscoelasticity. In order to take advantage of the correspondence principle between viscoelasticity and elasticity the formulation is given in the Laplace domain. Anisotropic viscoelastic fundamental solutions are obtained using the correspondence principle and anisotropic elastic Green’s functions. The standard linear solid model is used to represent the mechanical behavior of viscoelastic material. Solution in time domain is calculated via numerical inversion by modified Durbin’s method. Numerical example is provided to validate the proposed boundary element formulation.

Computation of Green’s tensor integrals for three‐dimensional electromagnetic problems using fast Hankel transforms

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1754-1759 ◽  
Author(s):  
Walter L. Anderson
Keyword(s):  
Half Space ◽  
Three Dimensional ◽  
Hankel Transform ◽  
Electromagnetic Modeling ◽  
Electromagnetic Problems ◽  
Hankel Transforms ◽  
Homogeneous Half Space ◽  
Green's Tensor ◽  
Green’S Tensor ◽  
The Many

A new method is presented that rapidly evaluates the many Green’s tensor integrals encountered in three‐dimensional electromagnetic modeling using an integral equation. Application of a fast Hankel transform (FHT) algorithm (Anderson, 1982) is the basis for the new solution, where efficient and accurate computation of Hankel transforms are obtained by related and lagged convolutions (linear digital filtering). The FHT algorithm is briefly reviewed and compared to earlier convolution algorithms written by the author. The homogeneous and layered half‐space cases for the Green’s tensor integrals are presented in a form so that the FHT can be easily applied in practice. Computer timing runs comparing the FHT to conventional direct convolution methods are discussed, where the FHT’s performance was about 6 times faster for a homogeneous half‐space, and about 108 times faster for a five‐layer half‐space. Subsequent interpolation after the FHT is called is required to compute specific values of the tensor integrals at selected transform arguments; however, due to the relatively small lagged convolution interval used (same as the digital filter’s), a simple and fast interpolation is sufficient (e.g., by cubic splines).

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