SGBEM Analysis of Diffraction of P- and SV-Waves by a Plane Crack in an Infinite Domain

2020 ◽  
Vol 6 (4) ◽  
Author(s):  
Tan-Tung Phan ◽  
Tuan-Kiet Nguyen ◽  
Dinh-Huan Phan ◽  
Anh-Vu Phan
Keyword(s):  
Plane Crack ◽  
Infinite Domain ◽  
P And Sv Waves

Identification of a plane crack in an elastic body by invariant integrals

2008 ◽  
Vol 43 (3) ◽  
pp. 437-452 ◽  
Author(s):  
A. V. Kaptsov ◽  
E. I. Shifrin
Keyword(s):  
Elastic Body ◽  
Plane Crack ◽  
Invariant Integrals

Coupled FEM-BEM Approach for Axisymetrical Heat Transfer Problems

2008 ◽  
Vol 273-276 ◽  
pp. 740-745
Author(s):  
Gennady Mishuris ◽  
Michał Wróbel
Keyword(s):  
Heat Transfer ◽  
Half Space ◽  
Integral Transform ◽  
Transfer Problem ◽  
Mixed Boundary ◽  
Nonlocal Boundary ◽  
Fem Analysis ◽  
Nonlocal Boundary Conditions ◽  
Problem Solution ◽  
Infinite Domain

This work deals with a stationary axisymmetrical heat transfer problem in a combined domain. This domain consists of half-space joined with a bounded cylinder. An important feature of the problem is the possible flux singularity along the edge points of the transmission surface. Domain decomposition is used to separate the subdomains. The solution for an auxiliary mixed boundary value problem in the half space is found analytically by means of Hankel integral transform. This allows us to reduce the main problem in the infinite domain to another problem defined in the bounded subdomain. In turn, the new problem contains a nonlocal boundary conditions along the transmission surface. These conditions incorporate all basic information about the infinite sub-domain (material properties, internal sources etc.). The problem is solved then by means of the Finite Element Method. In fact it might be considered as a coupled FEM-BEM approach. We use standard MATLAB PDE toolbox for the FEM analysis. As it is not possible for this package to introduce directly a non-classical boundary condition, we construct an appropriate iterative procedure and show the fast convergence of the main problem solution. The possible solution singularity is taken into account and the corresponding intensity coefficient of the heat flux is computed with a high accuracy. Numerical examples dealing with heat transfer between closed reservoir (filled with some substance) and the infinite foundation are discussed.

A new Reliable Numerical Algorithm Based on the First Kind of Bessel Functions to Solve Prandtl–Blasius Laminar Viscous Flow over a Semi-Infinite Flat Plate

2012 ◽  
Vol 67 (12) ◽  
pp. 665-673 ◽  
Author(s):  
Kourosh Parand ◽  
Mehran Nikarya ◽  
Jamal Amani Rad ◽  
Fatemeh Baharifard
Keyword(s):  
Viscous Flow ◽  
Flat Plate ◽  
Numerical Algorithm ◽  
Bessel Functions ◽  
Nonlinear Ordinary Differential Equation ◽  
Finite Domain ◽  
Algebraic Equations ◽  
Infinite Domain ◽  
Third Order ◽  
Domain Truncation

In this paper, a new numerical algorithm is introduced to solve the Blasius equation, which is a third-order nonlinear ordinary differential equation arising in the problem of two-dimensional steady state laminar viscous flow over a semi-infinite flat plate. The proposed approach is based on the first kind of Bessel functions collocation method. The first kind of Bessel function is an infinite series, defined on ℝ and is convergent for any x ∊ℝ. In this work, we solve the problem on semi-infinite domain without any domain truncation, variable transformation basis functions or transformation of the domain of the problem to a finite domain. This method reduces the solution of a nonlinear problem to the solution of a system of nonlinear algebraic equations. To illustrate the reliability of this method, we compare the numerical results of the present method with some well-known results in order to show the applicability and efficiency of our method.

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