Efficient Meshfree Formulation for Metal Forming Simulations

2000 ◽  
Vol 123 (4) ◽  
pp. 462-467 ◽  
Author(s):  
Sangpil Yoon ◽  
Cheng-Tang Wu ◽  
Hui-Ping Wang ◽  
Jiun-Shyan Chen
Keyword(s):  
Computational Efficiency ◽  
Metal Forming ◽  
Integration Method ◽  
Galerkin Approximation ◽  
Meshfree Methods ◽  
Nodal Integration ◽  
Strain Smoothing ◽  
Forming Analysis ◽  
Forming Simulations ◽  
Integration Constraint

A stabilized conforming (SC) nodal integration method is developed for elastoplastic contact analysis of metal forming processes. In this approach, strain smoothing stabilization is introduced to eliminate spatial instability in collocation meshfree methods. The gradient matrix associated with strain smoothing satisfies the integration constraint (IC) of linear exactness in the Galerkin approximation. Strain smoothing formulation and numerical procedures for history-dependent problems are introduced. Applications to metal forming analysis are presented, with the results demonstrating a significant improvement in computational efficiency without loss of accuracy.

Efficient Meshfree Formulation for Metal Forming Simulations

2000 ◽  
Author(s):  
J. S. Chen ◽  
C. T. Wu ◽  
H. P. Wang ◽  
S. Yoon
Keyword(s):  
Computational Efficiency ◽  
Metal Forming ◽  
Integration Method ◽  
Galerkin Approximation ◽  
Meshfree Methods ◽  
Nodal Integration ◽  
Strain Smoothing ◽  
Forming Analysis ◽  
Forming Simulations ◽  
Integration Constraint

Abstract A stabilized conforming (SC) nodal integration method is developed for elastoplastic contact analysis of metal forming processes. In this approach, strain smoothing stabilization is introduced to eliminate spatial instability in Galerkin meshfree methods using nodal integration. The gradient matrix associated with strain smoothing satisfies the integration constraint (IC) of linear exactness in the Galerkin approximation. Strain smoothing formulation and numerical procedures for history-dependent problems are introduced. Applications to metal forming analysis are presented, with the results demonstrating a significant improvement in computational efficiency without loss of accuracy.

A Boundary Enhancement for the Stabilized Conforming Nodal Integration of Galerkin Meshfree Methods

2015 ◽  
Vol 12 (02) ◽  
pp. 1550009 ◽  
Author(s):  
Dongdong Wang ◽  
Ming Sun ◽  
Pinkang Xie
Keyword(s):  
Transformation Method ◽  
Meshfree Methods ◽  
Shape Functions ◽  
Problem Domain ◽  
Nodal Integration ◽  
Support Size ◽  
Galerkin Meshfree ◽  
Integration Constraint ◽  
Linear Field ◽  
Stabilized Conforming Nodal Integration

The stabilized conforming nodal integration (SCNI) has been successfully developed for Galerkin meshfree methods based upon the linear exactness requirement. In this study, it is shown that for a given problem domain, when the support of the meshfree shape functions associated with the interior nodes do not cover the essential boundary, the linear exactness can be perfectly achieved by the standard SCNI formulation. On the other hand, when the essential boundary lies in the support of the meshfree shape functions of the interior nodes, a linear field may not be exactly obtained with the original SCNI formulation where the essential boundary conditions are enforced via the nodally exact transformation method, and the error even becomes more pronounced with the increase of support size. To resolve this issue, a flux term associated with the essential boundary is recovered in the variational formulation and it turns out to be proper to keep this term since the meshfree shape functions of interior nodes usually do not vanish on the boundary. Consequently the original SCNI integration constraint is revised and the stiffness matrix is enhanced by an additional stiffness contribution from the flux integration along the essential boundary. It is demonstrated that the proposed enhanced formulation is capable of exactly reproducing linear fields regardless of the support sizes. Moreover, several benchmark examples reveal that the present SCNI formulation with boundary enhancement yields better accuracy compared with the original SCNI approach, particularly for meshfree discretizations with larger support sizes.

Metal Forming Analysis

2001 ◽  
Author(s):  
R. H. Wagoner ◽  
J.-L. Chenot
Keyword(s):  
Metal Forming ◽  
Forming Analysis

Meshless TL and UL Approaches for Large Deformation Analysis

2010 ◽  
Vol 139-141 ◽  
pp. 893-896 ◽  
Author(s):  
Yuan Tong Gu
Keyword(s):  
Large Deformation ◽  
Computational Efficiency ◽  
Metal Forming ◽  
Weak Form ◽  
Superior Performance ◽  
Deformation Analysis ◽  
Large Deformation Analysis ◽  
Updated Lagrangian ◽  
Local Weak Form ◽  
Large Deformation Problems

To accurately and effectively simulate large deformation is one of the major challenges in numerical modeling of metal forming. In this paper, an adaptive local meshless formulation based on the meshless shape functions and the local weak-form is developed for the large deformation analysis. Total Lagrangian (TL) and the Updated Lagrangian (UL) approaches are used and thoroughly compared each other in computational efficiency and accuracy. It has been found that the developed meshless technique provides a superior performance to the conventional FEM in dealing with large deformation problems for metal forming. In addition, the TL has better computational efficiency than the UL. However, the adaptive analysis is much more efficient using in the UL approach than using in the TL approach.

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