Elasto-plastic element-free Galerkin method

2004 ◽  
Vol 33 (3) ◽  
pp. 206-214 ◽  
Author(s):  
M. H. Kargarnovin ◽  
H. E. Toussi ◽  
S. J. Fariborz
Keyword(s):  
Galerkin Method ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Plastic Element ◽  
Element Free

Application of Rigid/Visco-Plastic Element Free Galerkin Method in Three-Dimensional Bulk Metal Forming Processes

2009 ◽  
Vol 419-420 ◽  
pp. 457-460
Author(s):  
Ping Lu ◽  
Xin Wu ◽  
Guo Qun Zhao ◽  
Kai Yong Jiang ◽  
Yan Jin Guan
Keyword(s):  
Galerkin Method ◽  
Metal Forming ◽  
Three Dimensional ◽  
Element Free Galerkin Method ◽  
Bulk Metal ◽  
Bulk Metal Forming ◽  
Finite Element Software ◽  
Element Free Galerkin ◽  
Plastic Element ◽  
Element Free

Combining element free Galerkin method with rigid/visco-plastic flow theory, the paper establishes the three-dimensional rigid/visco-plastic element free Galerkin method, and introduces it to analyze three-dimensional bulk metal forming processes. The velocity field is approximated by MLS method. Employing the incomplete generalized variation principle, stiffness matrix equation and solution formulas are derived. And STL format discrete triangular patches are used to describe the mould cavity. An analysis program for simulating three-dimensional bulk metal forming processes is developed. The program is capable of simulating three-dimensional unsteady bulk metal forming processes with severe deformation and arbitrarily shaped dies. A numerical example is analyzed. Numerical results such as material flow patterns and distributions of the effective stress are obtained. The effectiveness and validity of the proposed method and techniques are demonstrated by comparing with results obtained by using commercial finite element software.

Application of an Element-free Galerkin Method to Water Wave Propagation Problems

2014 ◽  
Vol 60 (1-4) ◽  
pp. 87-105 ◽  
Author(s):  
Ryszard Staroszczyk
Keyword(s):  
Wave Propagation ◽  
Galerkin Method ◽  
Present Model ◽  
Free Surface Elevation ◽  
Element Free Galerkin Method ◽  
Plane Flow ◽  
Element Free Galerkin ◽  
Proposed Model ◽  
Sloping Bed ◽  
Element Free

Abstract The paper is concerned with the problem of gravitational wave propagation in water of variable depth. The problem is solved numerically by applying an element-free Galerkin method. First, the proposed model is validated by comparing its predictions with experimental data for the plane flow in water of uniform depth. Then, as illustrations, results of numerical simulations performed for plane gravity waves propagating through a region with a sloping bed are presented. These results show the evolution of the free-surface elevation, displaying progressive steepening of the wave over the sloping bed, followed by its attenuation in a region of uniform depth. In addition, some of the results of the present model are compared with those obtained earlier by using the conventional finite element method.

Implementing of Displacement Boundary Conditions of Element-Free Galerkin Method and its Applications Used in Fracture Mechanics

2012 ◽  
Vol 629 ◽  
pp. 606-610
Author(s):  
Gang Cheng ◽  
Wei Dong Wang ◽  
Dun Fu Zhang
Keyword(s):  
Boundary Conditions ◽  
Galerkin Method ◽  
Reproducing Kernel ◽  
Particle Method ◽  
Transformation Method ◽  
Computational Method ◽  
Reproducing Kernel Particle Method ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free

The main draw back of the Moving Least Squares (MLS) approximate used in element free Galerkin method (EFGM) is its lack the property of the delta function. To alleviate difficulties in the treatment of essential boundary conditions in EFGM, the local transformation method and the boundary singular weight method, which are used in the reproducing kernel particle method, is combined with the element free Galerkin method. The computational method is given to analyze the stress intensity factors and the numerical simulation of crack propagation of two-dimentional problems of the elastic fracture analysis. The application examples reveal the effectiveness and feasibility of the present methods.

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