Welding Heat Transfer Analysis Using Element Free Galerkin Method

2011 ◽  
Vol 410 ◽  
pp. 298-301 ◽  
Author(s):  
Raj Das ◽  
K.S. Bhattacharjee ◽  
S. Rao
Keyword(s):  
Heat Transfer ◽  
Arc Welding ◽  
Heat Transfer Analysis ◽  
The Finite Element Method ◽  
Element Free Galerkin Method ◽  
High Deformation ◽  
New Class ◽  
Element Free Galerkin ◽  
Mesh Less ◽  
Element Free

Mesh-less methods belong to a new class of numerical methods in computational mechanics and offer several advantages over the conventional mesh-based methods. They enable modelling of processes involving high deformation, severe discontinuities (e.g. fracture) and multiple physical processes. These types of situations are usually encountered in arc welding, rendering its modelling suitable via mesh-less methods. In this paper, a mesh-less Element Free Galerkin (EFG) method has been developed to model the heat transfer during welding. The results predicted by the EFG method are found to be in close agreement with those obtained by the finite element method and those observed in welding experiments. This demonstrates the effectiveness and utilities of the EFG method for modelling and understanding the heat transfer processes in arc welding.

Multiscale Element–Free Galerkin Method with Penalty for 2D Burgers’ Equation

2013 ◽  
Vol 62 (3) ◽  
Author(s):  
Siaw Ching Liew ◽  
Su Hoe Yeak
Keyword(s):  
Meshless Method ◽  
Burgers Equation ◽  
Basis Functions ◽  
Polynomial Basis ◽  
The Finite Element Method ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Kronecker Delta ◽  
Local Enrichment ◽  
Element Free

In this paper, a new numerical method which is based on the coupling between multiscale method and meshless method with penalty is developed for 2D Burgers’ equation. The advantage of meshless method over the finite element method (FEM) is that remeshing process is not required. This is because the meshless method approximation is constructed entirely in terms of a set of nodes. Since the moving least squares (MLS) shape function does not satisfy the Kronecker delta property, so penalty method is adopted to enforce the essential boundary conditions in this paper. In order to obtain the fine scale approximation, the local enrichment basis is applied. The local enrichment basis may adopt the polynomial basis functions or any other analytical basis functions. Here, the polynomial basis functions are chosen as local enrichment basis. This multiscale meshless method with penalty will provide a more accurate result especially in the critical region which requires higher accuracy. It is believed that this proposed method is an attractive approach for solving more general problems which involve large deformation.

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