Numerical Simulation of Large Deformation Problems by Element Free Galerkin Method

2013 ◽  
Vol 535-536 ◽  
pp. 85-88 ◽  
Author(s):  
Rajesh Kumar ◽  
Indra Vir Singh ◽  
B.K. Mishra ◽  
Akhilendra Singh
Keyword(s):  
Galerkin Method ◽  
Large Deformation ◽  
Crack Problem ◽  
Nonlinear Problems ◽  
Nonlinear Material ◽  
Material Behaviour ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free ◽  
Large Deformation Problems

In large deformation problems, the contribution of nonlinear terms is quite significant. Hence, components/structures involving large deformation must be analysed using non-linear theories. In this paper, element free Galerkin method (EFGM) has been applied to solve large deformation problems using updated Lagrangian approach. Geometrically nonlinear problems have been simulated assuming linear elastic material behaviour. The results obtained by EFGM have been compared with those obtained by FEM and analytical solutions. An elasto-plastic edge crack problem has been solved using nonlinear material behaviour and large deformation kinematics.

Superplastic Deforming Analysis Based on Element Free Galerkin Method

2007 ◽  
Vol 551-552 ◽  
pp. 309-315
Author(s):  
Yu Ying Yang ◽  
Jing Li
Keyword(s):  
Galerkin Method ◽  
Large Deformation ◽  
Variational Principles ◽  
Meshfree Method ◽  
Element Free Galerkin Method ◽  
Mesh Distortion ◽  
Element Free Galerkin ◽  
Incompressible Materials ◽  
Mls Approximation ◽  
Element Free

Superplastic large deformation problems always meet handicaps associated with severe mesh distortion and iterative remeshing when traditional mesh-based numerical approaches are used. To eliminate these difficulties, meshless simulation of element free Galerkin method (EFGM) for rigid-viscoplastic(RVP) model and incompressible materials is built upon the Moving Least Squares (MLS) approximation and modified Markov variational principles. Also, a numerical quadrature that aligns integration cells with the local supports of shape functions is presented to compute integrations involved in the objective functions. Satisfying results of a superplastic upsetting example with very large compression ratio demonstrate the feasibility and accuracy for the meshfree method to simulate superplastic large deformation process.

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