Green's functions and boundary element method for a magneto-electro-elastic half-plane

2005 ◽  
Vol 20 (2) ◽  
pp. 259-264
Author(s):  
Aimin Jiang ◽  
Haojiang Ding
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Half Plane ◽  
Green's Functions ◽  
Green’S Functions ◽  
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.

scholarly journals Monte Carlo method for determination and analysis damage to the power system

Doklady BGUIR ◽  
2021 ◽  
Vol 19 (1) ◽  
pp. 21-29
Author(s):  
D. E. Marmysh ◽  
U. I. Babaed
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Boundary Element Method ◽  
Power System ◽  
Boundary Element ◽  
Half Space ◽  
Half Plane ◽  
Monte Carlo Methods ◽  
Mechanics Of Solids ◽  
Element Method

The purpose of the work, the results of which are presented within the framework of the article, was to develop algorithms for calculating the damage to a solid or a system of solids based on the Monte Carlo method and the analytical boundary element method. The analytical boundary element method was used to calculate and analyze the stress-strain state of a solid under the distributed surface load. Based on indicators of the stress state, the algorithms for numerically assessing the dangerous volume and integral damage using the Monte Carlo methods, have been developed. Based on the pattern of distribution of stress fields, the technique of determining the area for randomly generating integration nodes is described. General recommendations have been developed for determining the boundaries of a subdomain containing a dangerous volume. Based on the features of the Monte Carlo methods, a numerical assessment of the indicators of damage of continuous media for a different number of integration nodes was carried out. Methods and algorithms were used to calculate the dangerous volume and integral damage in the plane and spatial cases for the two most common laws of the distribution of surface forces in the contact mechanics of solids: in case of contact interaction of two non-conformal bodies (Hertz problem) and when a non deformable rigid stamp is pressed into elastic half-plane or half-space. The scientific novelty of the work is to combine analytical and numerical approaches for the quantitative assessment of damage indicators of the power system. As a result the quantitative indicators of the dangerous volume (in the flat case - the dangerous area) and the integral damage of the half-plane and half-space related to the value of the applied load are obtained.

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