A time-stepping scheme based on numerical Green’s functions for the domain boundary element method: The ExGA-DBEM Newmark approach

2011 ◽  
Vol 35 (3) ◽  
pp. 533-542 ◽  
Author(s):  
P. Oyarzún ◽  
F.S. Loureiro ◽  
J.A.M. Carrer ◽  
W.J. Mansur
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Green's Functions ◽  
Green’S Functions ◽  
Domain Boundary ◽  
Time Stepping ◽  
Element Method

Lattice Green’s Functions in Nonlinear Analysis of Defects

2006 ◽  
Vol 74 (4) ◽  
pp. 686-690 ◽  
Author(s):  
S. Haq ◽  
A. B. Movchan ◽  
G. J. Rodin
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Green's Functions ◽  
Model Problem ◽  
Green’S Functions ◽  
Plane Deformation ◽  
Deformation Model ◽  
Linear Region ◽  
Nonlinear Zone ◽  
Element Method

A method for analyzing problems involving defects in lattices is presented. Special attention is paid to problems in which the lattice containing the defect is infinite, and the response in a finite zone adjacent to the defect is nonlinear. It is shown that lattice Green’s functions allow one to reduce such problems to algebraic problems whose size is comparable to that of the nonlinear zone. The proposed method is similar to a hybrid finite-boundary element method in which the interior nonlinear region is treated with a finite element method and the exterior linear region is treated with a boundary element method. Method details are explained using an anti-plane deformation model problem involving a cylindrical vacancy.

APPLICATION OF BOUNDARY ELEMENT METHOD FOR 3D WAVE SCATTERING IN CYLINDERS

2011 ◽  
Vol 08 (01) ◽  
pp. 57-76 ◽  
Author(s):  
H. BAI ◽  
A. H. SHAH
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Wave Scattering ◽  
Green's Functions ◽  
Green’S Functions ◽  
Boundary Integral ◽  
Guided Wave ◽  
Radial Dependence ◽  
Element Method ◽  
Wave Modes

A boundary element method (BEM) is presented to study 3D wave scattering by cracks in a cylinder. Green's functions needed in the kernel of boundary integral equations in BEM are derived with the help of guided wave functions. Guided wave modes in the cylinder are obtained by a semi-analytical finite element (SAFE) method. Green's functions are constructed numerically by superposition of guided wave modes. In this method, the cylinder is discretized in the radial direction into several coaxial circular cylinders (sub-cylinders) and the radial dependence of the displacement in each sub-cylinder is approximated by quadratic interpolation polynomials. A numerical procedure is used here to accurately calculate the Cauchy's principal value (CPV) and weakly singular integrals. The multi-domain technique is employed here to model the crack surface. Numerical results are presented to show the effectiveness of the proposed solution.

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