Application of the Laplace transform dual reciprocity boundary element method in the modelling of laser heat treatments

2005 ◽  
Vol 29 (2) ◽  
pp. 126-135 ◽  
Author(s):  
J.M. Amado ◽  
M.J. Tobar ◽  
A. Ramil ◽  
A. Yáñez
Keyword(s):  
Boundary Element Method ◽  
Laplace Transform ◽  
Boundary Element ◽  
Heat Treatments ◽  
Laser Heat ◽  
The Laplace Transform ◽  
Element Method

Boundary element analysis of finite domains under thermal and mechanical shock with the Lord-Shulman theory

2003 ◽  
Vol 38 (1) ◽  
pp. 53-64 ◽  
Author(s):  
P Hosseini-Tehrani ◽  
M. R Eslami
Keyword(s):  
Boundary Element Method ◽  
Laplace Transform ◽  
Boundary Element ◽  
Relaxation Times ◽  
Finite Domain ◽  
Laplace Transform Method ◽  
Transform Method ◽  
Laplace Transform Technique ◽  
The Laplace Transform ◽  
Element Method

A boundary element method based on the Laplace transform technique is developed for transient coupled thermoelasticity problems with relaxation times in a two-dimensional finite domain. The dynamic thermoelastic model of Lord and Shulman (LS) is selected to show how mechanical and thermal energy conversion takes place in a coupled field. The Laplace transform method is applied to the time domain and the resulting equations in the transformed field are discretized using the boundary element method. The nodal dimensionless temperature and displacements in the transformed domain are inverted to obtain the actual physical quantities, using the numerical inversion of the Laplace transform method. The creation and propagation of elastic and thermoelastic waves in a finite domain and their effects on each other are investigated for the first time in this paper. Different relaxation times are chosen to show briefly the events that take place in temperature, displacement and stress fields considering the LS theory. Details of the formulation and numerical implementation are presented.

An Energy Diffusion Model for Interior Acoustics With Structural Coupling Using the Boundary Element Method

2012 ◽  
Author(s):  
Joseph M. Corcoran ◽  
Ricardo A. Burdisso
Keyword(s):  
Boundary Element Method ◽  
Diffusion Equation ◽  
Laplace Transform ◽  
Diffusion Process ◽  
Boundary Element ◽  
Diffusion Model ◽  
Acoustic Energy ◽  
Room Acoustics ◽  
Energy Diffusion ◽  
Element Method

Recently, a new model for the propagation of sound in interior volumes known as the acoustic diffusion equation has been explored as an alternative method for acoustic predictions and analysis. The model uses statistical methods standard in high frequency room acoustics to compute a spatial distribution of acoustic energy over time as a diffusion process. For volumes coupled through a structural partition, the energy consumed by structural vibration and acoustic energy transmitted between volumes has been incorporated through a simple acoustic transmission coefficient. In this paper, a Boundary Element Method (BEM) solution to the simple diffusion model is developed. The integral form of the 3D acoustic diffusion equation for coupled volumes is derived using the Laplace transform and Green’s Second Identity. The solution using the BEM is developed as well as an efficient Laplace transform inversion scheme to obtain both steady state and transient interior acoustic energy. In addition, a fully coupled model where both structural and acoustic energy are computed as a diffusion process is proposed. A simple volume configuration is examined as the diffusion models are analyzed and compared to conventional room acoustics analysis methods. Advantages of the energy diffusion methods over conventional methods, such as computation of energy distributions and accurate transmission from one volume to another, are revealed as the comparisons are made.

Modeling the Dynamics of 3-D Elastic Anisotropic Solids Using Boundary Element Method

2014 ◽  
Vol 1040 ◽  
pp. 633-637 ◽  
Author(s):  
Leonid A. Igumnov ◽  
Ivan Markov ◽  
Yan Yu. Rataushko
Keyword(s):  
Numerical Modeling ◽  
Boundary Element Method ◽  
Laplace Transform ◽  
Boundary Element ◽  
Singular Solutions ◽  
Numerical Inversion ◽  
Computational Results ◽  
Time Step ◽  
Integral Laplace Transform ◽  
Element Method

The numerical modeling problem is solved using a direct formulation of the boundary element method. The integral Laplace transform is used, as well as time-step methods of its numerical inversion. Matrices of fundamental and singular solutions are computed with the help of a combined direct-interpolation approach. The computational results obtained are compared with the results of other authors.

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