An updated Lagrangian method with error estimation and adaptive remeshing for very large deformation elasticity problems

2014 ◽  
Vol 100 (13) ◽  
pp. 1006-1030 ◽  
Author(s):  
S. Léger ◽  
A. Fortin ◽  
C. Tibirna ◽  
M. Fortin
Keyword(s):  
Large Deformation ◽  
Error Estimation ◽  
Lagrangian Method ◽  
Adaptive Remeshing ◽  
Elasticity Problems ◽  
Updated Lagrangian

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.

A STABILIZED PARTICLE METHOD FOR LARGE DEFORMATION DYNAMIC ANALYSIS OF STRUCTURES

2012 ◽  
Vol 12 (04) ◽  
pp. 1250026 ◽  
Author(s):  
H. OSTAD ◽  
S. MOHAMMADI
Keyword(s):  
Large Deformation ◽  
High Frequency ◽  
Cumulative Effect ◽  
Particle Method ◽  
Particle Methods ◽  
Taylor Series Expansions ◽  
Updated Lagrangian Formulation ◽  
High Frequency Vibrations ◽  
Updated Lagrangian ◽  
Large Deformation Problems

The property of free movement of particles allows for most meshless particle methods to be efficiently used for simulation of solid problems involving large deformation as it removes the necessity of remeshing, which is one of the time-consuming parts of the traditional finite element method based on an updated Lagrangian formulation. One of the main sources of instabilities in meshfree particle methods, which approximate the strong form of partial differential equations, is the existence of extra high frequency vibrations. They are induced into the solution due to the use of truncated Taylor series expansions. The cumulative effect of the extra vibrations makes the solution to be polluted by zero energy modes and tensile instabilities. In this paper, the CSPM particle method is used to solve elastodynamic large deformation problems based on an updated Lagrangian procedure. A field smoothing approach, recently proposed for reduction of instabilities that rise from excessive high frequency vibrations, is further extended to large deformation problems. Also, the phenomenon of particles penetration can be prevented without the requirement of any additional artificial damping forces. Another major advantage of the new approach is its generality which allows for its implementation into other particle methods and its application for solving other physical problems. A variety of large deformation problems are solved by the proposed approach and the results are compared with other available results.

Adaptive Large Deformation Viscoplastic Finite Element Analysis

1995 ◽  
Author(s):  
Ravi P. Tetambe ◽  
Sunil S. Saigal
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Large Deformation ◽  
Large Strain ◽  
Two Dimensions ◽  
Triangular Element ◽  
Element Analysis ◽  
Adaptive Remeshing ◽  
L2 Norm ◽  
Norm Error

Abstract The adaptive remeshing and rezoning procedures developed for large deformation finite element analysis using viscoplastic material model are presented in two dimensions. The adaptive procedure is driven by the posteriori error estimation technique. The nonlinear error estimators based on the energy rate norm error and the L2 norm error of incremental total strains are used for error computation. The remeshing algorithm creates new acceptable meshes in the course of the deformation process without any loss of geometric information. The remeshing of the current geometry is achieved using the boundary refinement technique. This technique is observed to be sufficiently accurate in problems where mesh refinement is largely required at the boundary or very close to the boundary of the structure. The rezoning procedure is then used to accurately interpolate the solution variables from the existing mesh to the new adaptively created mesh. The element subdivision approach is used during the rezoning process. The adaptive remeshing and rezoning procedures are developed for 6-node triangular element. These procedures are implemented in the general purpose finite element program, ANSYS [13], and are validated by solving two complex large strain examples. In both examples, these procedures are successful in achieving very high deformation levels in a structure.

Assessment of two a posteriori error estimators for elasticity problems

2008 ◽  
Vol 35 (11) ◽  
pp. 1239-1250
Author(s):  
A. H. ElSheikh ◽  
S. E. Chidiac ◽  
S. Smith
Keyword(s):  
Finite Element ◽  
Error Estimation ◽  
Posteriori Error ◽  
A Posteriori ◽  
A Posteriori Error Estimators ◽  
A Posteriori Error ◽  
Estimation Techniques ◽  
Error Estimators ◽  
Elasticity Problems ◽  
Posteriori Error Estimators

The main focus of this paper is on the evaluation of local a posteriori error estimation techniques for the finite element method (FEM). The standard error estimation techniques are presented for the coupled displacement fields appearing in elasticity problems. The two error estimators, the element residual method (ERM) and Zienkiewicz–Zhu (ZZ) patch recovery technique, are evaluated numerically and then used as drivers for a mesh adaptation process. The results demonstrate the advantages of employing a posteriori error estimators for obtaining finite element solutions with a pre-specified error tolerance. Of the two methods, the ERM is shown to produce adapted meshes that are similar to those adapted by the exact error. Furthermore, the ERM provides higher quality estimates of the error in the global energy norm when compared to the ZZ estimator.

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