scholarly journals Equivalence between the Trefftz method and the method of fundamental solutions for Green’s function of concentric spheres using the addition theorem and image concept

2009 ◽  
Author(s):  
J. T. Chen ◽  
H. C. Shieh ◽  
J. J. Tsai ◽  
J. W. Lee
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Fundamental Solutions ◽  
Addition Theorem ◽  
Method Of Fundamental Solutions ◽  
Trefftz Method ◽  
Concentric Spheres

On Fundamental Solutions and Green’s Functions in the Theory of Elastic Plates

1966 ◽  
Vol 33 (1) ◽  
pp. 31-38 ◽  
Author(s):  
A. Kalnins
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Bessel Functions ◽  
Arbitrary Point ◽  
Fundamental Solutions ◽  
Addition Theorem ◽  
Reciprocal Theorem ◽  
Elastic Plates ◽  
Concentrated Load ◽  
The Reciprocal Theorem

This paper is concerned with fundamental solutions of static and dynamic linear inextensional theories of thin elastic plates. It is shown that the appropriate conditions which a fundamental singularity must satisfy at the pole follow from the requirement that the reciprocal theorem is satisfied everywhere in the region occupied by the plate. Furthermore, dynamic Green’s function for a plate bounded by two concentric circular boundaries is derived by means of the addition theorem of Bessel functions. The derived Green’s function represents the response of the plate to a harmonically oscillating normal concentrated load situated at an arbitrary point on the plate.

A Green's Function for the Domain Bounded by Nonconcentric Spheres

2012 ◽  
Vol 80 (1) ◽  
Author(s):  
Jeng-Tzong Chen ◽  
Jia-Wei Lee ◽  
Hung-Chih Shieh
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Fundamental Solutions ◽  
Dirichlet Boundary Conditions ◽  
Method Of Fundamental Solutions ◽  
Circular Cylinders ◽  
Image Method ◽  
Eccentric Annulus ◽  
Function Solution ◽  
Good Agreement

The main result is the analytical derivation of Green's function for the domain bounded by nonconcentric spheres in terms of bispherical coordinates. Both surfaces, inner and outer boundaries, are specified by the Dirichlet boundary conditions. This work can be seen as an extension study for the Green's function of eccentric annulus derived by Heyda (1959, “A Green's Function Solution for the Case of Laminar Incompressible Flow Between Non-Concentric Circular Cylinders,” J. Franklin Inst., 267, pp. 25–34). To verify the solution, a semianalytical solution using the image method and a numerical solution using the method of fundamental solutions (MFS) are utilized for comparisons. Good agreement is made.

Derivation of Green’s function using addition theorem

2009 ◽  
Vol 36 (3) ◽  
pp. 351-363 ◽  
Author(s):  
J.T. Chen ◽  
K.H. Chou ◽  
S.K. Kao
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Addition Theorem

On the accuracy of the addition theorem for a scalar Green's function used in the FMM

2001 ◽  
Vol 31 (6) ◽  
pp. 439-442 ◽  
Author(s):  
Jian-Ying Li ◽  
Le-Wei Li ◽  
Ban-Leong Ooi ◽  
Pang-Shyan Kooi ◽  
Mook-Seng Leong
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Addition Theorem

scholarly journals The Green's Function BEM for Bimaterial Solids Applied to Edge Stress Concentration Problems

2007 ◽  
Vol 1 (2) ◽  
Author(s):  
M. Denda
Keyword(s):  
Stress Concentration ◽  
Green’S Function ◽  
Green's Function ◽  
Free Edge ◽  
Fundamental Solutions ◽  
Singular Stress ◽  
Thin Coatings ◽  
Edge Stress ◽  
Line Force ◽  
Isotropic Solids

A boundary element method (BEM) for bimaterial domains consisting of two isotropic solids bonded perfectly along the straight interface will be developed. We follow the physical interpretation of Somigliana’s identity to represent the displacement in the bimaterial domain by the continuous distributions of the line forces and dislocation dipoles over its boundary. The fundamental solutions used are the Green’s functions for the line force and the dislocation dipole that satisfy the traction and displacement continuity across the interface of two domains. There is no need to model the interface because the required continuity conditions there are automatically satisfied by the Green’s functions. The BEM will be applied to study the edge stress concentration of the bimaterial solids. We calculate the singular stress distribution at the free edge of the interface for various bimaterial configurations and loadings, in particular, for the domain consisting of thin coating over the substratum. Since the Green's function BEM does not require the boundary elements on the interface, it can handle the edge singularity on the interface accurately even for extremely thin coatings. The BEM developed here is not limited to the edge stress concentration problems and can be applied to a broad range of the bimaterial domain problems effectively.

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