Element‐free Galerkin method for contact problems in metal forming analysis

2001 ◽  
Vol 18 (1/2) ◽  
pp. 62-78 ◽  
Author(s):  
Guangyao Li ◽  
Ted Belytschko
Keyword(s):  
Galerkin Method ◽  
Metal Forming ◽  
Contact Problems ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Forming Analysis ◽  
Element Free

Releasing Algorithm for Volumetric Locking in Metal Forming Process Simulation Based on Element-Free Galerkin Method

2008 ◽  
Vol 575-578 ◽  
pp. 356-366
Author(s):  
Yan Jin Guan ◽  
Xin Wu ◽  
Guo Qun Zhao ◽  
Ping Lu
Keyword(s):  
Strain Rate ◽  
Galerkin Method ◽  
Metal Forming ◽  
Volumetric Strain ◽  
Pressure Oscillation ◽  
Element Free Galerkin Method ◽  
Volumetric Locking ◽  
Element Free Galerkin ◽  
Simulation Based ◽  
Element Free

The meshless methods effectively deal with large material distortion simulation. Based on the rigid (visco)plastic material model, the element-free Galerkin method (EFGM) is introduced to simulate the metal forming processes. Aiming at the volume locking and pressure oscillation during EFGM analysis, a volumetric strain rate mapping method is proposed based on pressure projection method. The releasing algorithm is established by modifying the volumetric strain rate in the functional equation. The volumetric strain rate calculated according to velocity field is mapped onto a lower-order space to reduce the number of independent discrete constrain equations. The numerical example shows that the releasing algorithm can effectively eliminate the volumetric locking and pressure oscillation without the expense of employing large support size in the rigid-plastic meshless method.

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.

An element‐free Galerkin method for metal forming simulations

2009 ◽  
Vol 26 (4) ◽  
pp. 327-346 ◽  
Author(s):  
Rodrigo Rossi ◽  
Marcelo Krajnc Alves ◽  
Hazim Ali Al‐Qureshi
Keyword(s):  
Galerkin Method ◽  
Metal Forming ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Forming Simulations ◽  
Element Free

scholarly journals Element-Free Galerkin Method Based on Block-Pulse Wavelets Integration for Solving Fourth-Order Obstacle Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Muhammad Azam ◽  
Khalid Parvez ◽  
Muhammad Omair
Keyword(s):  
Galerkin Method ◽  
Fourth Order ◽  
Computational Cost ◽  
Contact Problems ◽  
Weight Functions ◽  
Test Problems ◽  
Element Free Galerkin Method ◽  
Element Free Galerkin ◽  
Element Free ◽  
Technique Comparison

We introduce improved element-free Galerkin method based on block pulse wavelet integration for numerical approximations to the solution of a system of fourth-order boundary-value problems associated with obstacle, unilateral, and contact problems. Moving least squares (MLS) approach is used to construct shape functions with optimized weight functions and basis. Numerical results for test problems are presented in this article to elaborate the pertinent features for the proposed technique. Comparison with existing techniques shows that our proposed method based on integration technique provides better approximation at reduced computational cost.

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.

Sign in / Sign up

Export Citation Format

Share Document