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.

scholarly journals An Adaptive Local Meshfree Updated Lagrangian Approach for Large Deformation Analysis of Metal Forming

2010 ◽  
Vol 97-101 ◽  
pp. 2664-2667 ◽  
Author(s):  
Yuan Tong Gu
Keyword(s):  
Large Deformation ◽  
Metal Forming ◽  
Meshfree Methods ◽  
Superior Performance ◽  
Deformation Analysis ◽  
Large Deformation Analysis ◽  
Good Potential ◽  
Updated Lagrangian Approach ◽  
Updated Lagrangian ◽  
Large Deformation Problems

The large deformation analysis is one of major challenges in numerical modelling and simulation of metal forming. Because no mesh is used, the meshfree methods show good potential for the large deformation analysis. In this paper, a local meshfree formulation, based on the local weak-forms and the updated Lagrangian (UL) approach, is developed for the large deformation analysis. To fully employ the advantages of meshfree methods, a simple and effective adaptive technique is proposed, and this procedure is much easier than the re-meshing in FEM. Numerical examples of large deformation analysis are presented to demonstrate the effectiveness of the newly developed nonlinear meshfree approach. It has been found that the developed meshfree technique provides a superior performance to the conventional FEM in dealing with large deformation problems for metal forming.

Application of Meshless Integral Method to Metal Forming

2010 ◽  
Author(s):  
Jianfeng Ma ◽  
Joshua David Summers ◽  
Paul F. Joseph
Keyword(s):  
Integral Equation ◽  
Boundary Conditions ◽  
Large Deformation ◽  
Metal Forming ◽  
Integral Method ◽  
Weak Form ◽  
Boundary Integral ◽  
Deformation Analysis ◽  
Updated Lagrangian ◽  
Lagrange Strain

In this paper, the meshless integral method based on the regularized boundary integral equation [1] is applied to analyze the metal forming processes characteristic with large deformation. Using Green-Naghdi’s theory, the updated Lagrangian governing integral equation is obtained from the weak form of elastoplasticity over a local sub-domain. The meshless function approximation is implemented by using the moving least-squares approximation. In Green-Naghdi’s theory, the Green-Lagrange strain is decomposed into the elastic part and plastic part and a J2 elastoplastic constitutive relation is used to relate the Green-Lagrange strain to the second Piola-Kirchhoff stress. The essential boundary conditions are imposed by a generalized collocation method and the natural boundary conditions are incorporated into the system governing equation and require no special handling. The solution algorithm for large deformation analysis is discussed in detail. Numerical examples show that this method is accurate and robust.

An Incremental Constitutive Relation of Unilateral Contact Friction for Large Deformation Analysis

1985 ◽  
Vol 52 (3) ◽  
pp. 639-648 ◽  
Author(s):  
J.-H. Cheng ◽  
N. Kikuchi
Keyword(s):  
Large Deformation ◽  
Constitutive Relation ◽  
Contact Friction ◽  
Deformation Analysis ◽  
Elastoplastic Material ◽  
Unknown Parameters ◽  
Large Deformation Analysis ◽  
Proposed Model ◽  
Updated Lagrangian Approach ◽  
Updated Lagrangian

An incremental constitutive relation of friction contact is presented for large deformation analysis. After a brief review of published explanations of friction, a model is constructed following the established concepts of plasticity theory. Extensive studies are laid on how the theory closely simulates the nature of friction and how the unknown parameters in the equation are to be determined from the existing experimental results. Possible extensions to allow considerations of temperature and nonlocal effects are discussed. Formulations of a quasistatic boundary value problem based on the updated Lagrangian approach are summarized. The elastoplastic material is assumed to behave according to the generalized Prandtl-Reuss constitutive equation. Finite element methods are employed to solve the problem. Two examples are selected to demonstrate the capability and adequacy of the proposed model.

A Meshless Method Based on the Nonsingular Weight Functions for Elastoplastic Large Deformation Problems

2019 ◽  
Vol 11 (01) ◽  
pp. 1950006 ◽  
Author(s):  
Fengbin Liu ◽  
Qiang Wu ◽  
Yumin Cheng
Keyword(s):  
Large Deformation ◽  
Numerical Solutions ◽  
Weak Form ◽  
Weight Functions ◽  
Computational Accuracy ◽  
Lagrange Formulation ◽  
Element Free Galerkin ◽  
Penalty Factor ◽  
Element Free ◽  
Large Deformation Problems

In this study, based on a nonsingular weight function, the improved element-free Galerkin (IEFG) method is presented for solving elastoplastic large deformation problems. By using the improved interpolating moving least-squares (IMLS) method to form the approximation function, and using Galerkin weak form based on total Lagrange formulation of elastoplastic large deformation problems to form the discretilized equations, which is solved with the Newton–Raphson iteration method, we obtain the formulae of the IEFG method for elastoplastic large deformation problems. In numerical examples, the influences of the penalty factor, scale parameter of influence domain and weight functions on the computational accuracy are analyzed, and the numerical solutions show that the IEFG method for elastoplastic large deformation problems has higher computational efficiency and accuracy.

Large deformation analysis of moderately thick viscoelastic plates

2019 ◽  
Vol 163 ◽  
pp. 146-167 ◽  
Author(s):  
Nasrin Jafari ◽  
Mojtaba Azhari ◽  
Bijan Boroomand
Keyword(s):  
Large Deformation ◽  
Deformation Analysis ◽  
Large Deformation Analysis
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