An updated Lagrangian method with error estimation and adaptive remeshing for very large deformation elasticity problems: The three-dimensional case

2016 ◽  
Vol 309 ◽  
pp. 1-18 ◽  
Author(s):  
S. Léger ◽  
A. Pepin
Keyword(s):  
Large Deformation ◽  
Error Estimation ◽  
Three Dimensional ◽  
Lagrangian Method ◽  
Dimensional Case ◽  
Adaptive Remeshing ◽  
Elasticity Problems ◽  
Updated Lagrangian

Effective Convergence Checks for Verifying Finite Element Stresses at Three-Dimensional Stress Concentrations

2018 ◽  
Vol 3 (3) ◽  
Author(s):  
J. R. Beisheim ◽  
G. B. Sinclair ◽  
P. J. Roache
Keyword(s):  
Finite Element ◽  
Error Estimation ◽  
A Posteriori Error Estimates ◽  
Three Dimensional ◽  
Posteriori Error ◽  
Test Problems ◽  
A Posteriori ◽  
Stress Concentrations ◽  
Element Analysis ◽  
A Posteriori Error

Current computational capabilities facilitate the application of finite element analysis (FEA) to three-dimensional geometries to determine peak stresses. The three-dimensional stress concentrations so quantified are useful in practice provided the discretization error attending their determination with finite elements has been sufficiently controlled. Here, we provide some convergence checks and companion a posteriori error estimates that can be used to verify such three-dimensional FEA, and thus enable engineers to control discretization errors. These checks are designed to promote conservative error estimation. They are applied to twelve three-dimensional test problems that have exact solutions for their peak stresses. Error levels in the FEA of these peak stresses are classified in accordance with: 1–5%, satisfactory; 1/5–1%, good; and <1/5%, excellent. The present convergence checks result in 111 error assessments for the test problems. For these 111, errors are assessed as being at the same level as true exact errors on 99 occasions, one level worse for the other 12. Hence, stress error estimation that is largely reasonably accurate (89%), and otherwise modestly conservative (11%).

The Uniform Flexure of an Incomplete Tore

1949 ◽  
Vol 2 (4) ◽  
pp. 469
Author(s):  
W Freiberger ◽  
RCT Smith
Keyword(s):  
General Solution ◽  
Cross Section ◽  
Harmonic Functions ◽  
Rectangular Cross Section ◽  
Three Dimensional ◽  
Elasticity Problems ◽  
Three Dimensional Elasticity ◽  
Derivatives Of ◽  
Special Case

In this paper we discuss the flexure of an incomplete tore in the plane of its circular centre-line. We reduce the problem to the determination of two harmonic functions, subject to boundary conditions on the surface of the tore which involve the first two derivatives of the functions. We point out the relation of this solution to the general solution of three-dimensional elasticity problems. The special case of a narrow rectangular cross-section is solved exactly in Appendix II.

The Boundary Contour Method for Three-Dimensional Linear Elasticity

1996 ◽  
Vol 63 (2) ◽  
pp. 278-286 ◽  
Author(s):  
A. Nagarajan ◽  
S. Mukherjee ◽  
E. Lutz
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Linear Elasticity ◽  
Three Dimensional ◽  
Contour Method ◽  
Boundary Contour ◽  
Boundary Contour Method ◽  
Novel Variant ◽  
Elasticity Problems ◽  
Element Method

This paper presents a novel variant of the boundary element method, here called the boundary contour method, applied to three-dimensional problems of linear elasticity. In this work, the surface integrals on boundary elements of the usual boundary element method are transformed, through an application of Stokes’ theorem, into line integrals on the bounding contours of these elements. Thus, in this formulation, only line integrals have to be numerically evaluated for three-dimensional elasticity problems—even for curved surface elements of arbitrary shape. Numerical results are presented for some three-dimensional problems, and these are compared against analytical solutions.

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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