scholarly journals Dynamic Green’s functions of a buried point load with applications to drainage

2013 ◽  
Author(s):  
B. Y. Ding ◽  
L. J. Zhu
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Point Load ◽  
Buried Point

Green’s Functions for a Point Load and Dislocation in an Annular Region

1991 ◽  
Vol 58 (4) ◽  
pp. 954-959 ◽  
Author(s):  
R. E. Worden ◽  
L. M. Keer
Keyword(s):  
Analytic Continuation ◽  
Rigid Inclusion ◽  
Green's Functions ◽  
Green’S Functions ◽  
Point Load ◽  
Annular Region ◽  
Two Dimensional

This paper contains an analysis of a two-dimensional annular region whose inner boundary is that of either a hole or a perfectly bonded, rigid inclusion. Fast-converging Green’s functions for a point load or a dislocation on the annulus are determined using analytic continuation across the boundaries of the annulus.

Deformation of a spherical, viscoelastic, and incompressible Earth for a point load with periodic time change

2020 ◽  
Vol 222 (3) ◽  
pp. 1909-1922 ◽  
Author(s):  
He Tang ◽  
Jie Dong ◽  
Lan Zhang ◽  
Wenke Sun
Keyword(s):  
Green's Functions ◽  
Green’S Functions ◽  
Point Load ◽  
Point Sources ◽  
Earth Model ◽  
Surface Mass ◽  
Planetary Scale ◽  
Periodic Loading ◽  
Love Numbers ◽  
Analytical Time

SUMMARY Planetary-scale mass redistributions occur on Earth for certain spatiotemporal periods, and these surface mass changes excite the global periodic loading deformations of a viscoelastic Earth. However, the characteristics of periodic viscoelastic deformations have not been well investigated even in a simple earth model. In this study, we derive the semi-analytical Green's functions (fully analytical Love numbers) for long-standing point sources with given periods using a modified asymptotic scheme in a homogeneous Maxwell spherical earth model. Here, the asymptotic scheme is needed in order to obtain accurate semi-analytical time-dependent Green's functions. The amplitudes and phases of the Green's functions may be biased if only the series summations of the Love numbers are used because the influence of viscoelasticity is degree-dependent. We compare the viscoelastic and elastic periodic Green's functions with different material viscosities and loading periods and investigate the amplitude increase percentage and phase delay of the periodic displacement and geoid change. For example, our analysis revealed that the viscosity increases the amplitude by 40–120 per cent and delays the phase approximately −100° to 60° for the displacement and geoid change when bearing a 10-yr loading period, assuming a viscosity of 1018 Pa s and a shear modulus 4 × 1010 Pa.

Green’s functions in non-local three-dimensional linear elasticity

2009 ◽  
Vol 465 (2111) ◽  
pp. 3463-3487 ◽  
Author(s):  
Olaf Weckner ◽  
Gerd Brunk ◽  
Michael A. Epton ◽  
Stewart A. Silling ◽  
Ebrahim Askari
Keyword(s):  
Green's Functions ◽  
Fourier Transforms ◽  
Green’S Functions ◽  
Three Dimensional ◽  
Point Load ◽  
Three Dimensions ◽  
Weak Formulation ◽  
Element Discretization ◽  
Linear Elastic Body ◽  
Non Local

In this paper, we compare small deformations in an infinite linear elastic body due to the presence of point loads within the classical, local formulation to the corresponding deformations in the peridynamic, non-local formulation. Owing to the linearity of the problem, the response to a point load can be used to obtain the response to general body force loading functions by superposition. Using Laplace and Fourier transforms, we thus obtain an integral representation for the three-dimensional peridynamic solution with the help of Green’s functions. We illustrate this new theoretical result by dynamic and static examples in one and three dimensions. In addition to this main result, we also derive the non-local three-dimensional jump conditions, as well as the weak formulation of peridynamics together with the associated finite element discretization.

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