scholarly journals A note on the use of the Companion Solution (Dirichlet Green's function) on meshless boundary element methods

2017 ◽  
Vol 75 ◽  
pp. 57-64 ◽  
Author(s):  
H. Power ◽  
N. Caruso ◽  
M. Portapila
Keyword(s):  
Green’S Function ◽  
Boundary Element ◽  
Green's Function ◽  
Boundary Element Methods ◽  
Companion Solution

Panel Contribution Analysis Based on FEM, BEM and Numerical Green’s Function Approaches

2018 ◽  
Vol 26 (03) ◽  
pp. 1850037
Author(s):  
Kirill Shaposhnikov ◽  
Mads J. Herring Jensen
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Noise Level ◽  
Acoustic Pressure ◽  
Boundary Element Methods ◽  
Numerical Techniques ◽  
Structural Vibrations ◽  
Contribution Analysis ◽  
Pros And Cons ◽  
Acoustic Contribution

The panel acoustic contribution analysis is used to determine the contribution of vibrating panels to the noise level inside closed spaces like a car cabin. The use of numerical techniques makes it possible to rate the panels according to their contributions accounting for the interaction between the structural vibrations and the acoustic pressure at a listening point. We consider the application of the finite and boundary element methods and the numerical Green’s function approaches to the problem and discuss the pros and cons regarding their use. The results show that the numerical Green’s function approach coupled to structure can be effectively used for the panel contribution analysis in situations with multiple panels and few listening points.

On NGF Applications to LBIE Potential and Displacement Discontinuity Analyses

2010 ◽  
Vol 454 ◽  
pp. 127-135 ◽  
Author(s):  
L.S. Miers ◽  
J.C.F. Telles
Keyword(s):  
Integral Equation ◽  
Fracture Mechanics ◽  
Boundary Element ◽  
Boundary Integral Equation ◽  
Green's Function ◽  
Boundary Integral ◽  
Displacement Discontinuity ◽  
Local Boundary ◽  
Local Boundary Integral Equation ◽  
Companion Solution

This work aims at extending the concept of the Numerical Green's Function (NGF), known from boundary element applications to potential and fracture mechanics problems, to the Local Boundary Integral Equation (LBIE) context. As a "companion" solution, the NGF is used to remove the integrals of the main discontinuities over the crack boundary and is to be introduced only for source points whose support touches or contains the actual crack surfaces.

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