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Inverse Pre-deformation of Finite Element Mesh for Large Deformation Analysis

[+] Author and Article Information
Arbtip Dheeravongkit

The Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213

Kenji Shimada1

The Department of Mechanical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213shimada@cmu.edu

1

To whom correspondence should be addressed.

J. Comput. Inf. Sci. Eng 5(4), 338-347 (Apr 29, 2005) (10 pages) doi:10.1115/1.2052829 History: Received October 11, 2004; Revised April 29, 2005

The process of finite element analysis that deals with large deformation often produces distorted elements in the later stages of the analysis. These distorted elements lead to analysis problems, such as inaccurate solutions, slow convergence, and premature termination of the analysis. This paper proposes a new mesh generation algorithm to mesh the input part for pure Lagrangian analysis, where our goal is to improve the shape quality of the elements along the analysis process to reduce the number of inverted elements at the later stage, and to decrease the possibility of premature termination of the analysis. One pre-analysis is required to collect geometric and stress information in the analysis. The proposed method then uses the deformed-shape boundary known from the pre-analysis, finds the optimal node locations, considers the stress information to control the mesh sizes, as well as control the mesh directionality, generates meshes on the deformed boundary, and finally, maps the elements back to the undeformed boundary using inverse bilinear mapping. The proposed method has been tested on two forging example problems. The results indicate that the method can improve the shape quality of the elements at the later stage of the analysis, and consequently extend the life of the analysis, thereby reducing the chance of premature analysis termination.

Copyright © 2005 by American Society of Mechanical Engineers
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References

Figures

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Figure 8

Comparing sharp corners of the results of pre-deformed mesh with and without mesh size control

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Figure 9

Comparing the sharp corners of the results of pre-deformed mesh with and without mesh directionality control

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Figure 10

Plots comparing minimum and maximum angles at different die displacements (example 1)

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Figure 11

Finite element analysis of original uniform mesh (a) and uniform sized pre-deformed mesh (b) (example 2)

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Figure 12

Finite element analysis of pre-deformed mesh with size control (a) and pre-deformed mesh with size and directionality controls (b) (example 2)

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Figure 13

Comparing sharp corners of the results of original and pre-deformed meshes (example 2)

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Figure 14

Plots comparing minimum and maximum angles at different die displacements (example 2)

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Figure 15

Plot of angle distribution at die displacement=85% (example 2)

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Figure 1

Examples of large deformation finite element analysis of closed-die forging

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Figure 2

Overview of the proposed method

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Figure 3

Die geometry of example 1

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Figure 7

Finite element analysis of pre-deformed mesh with size control (a) and pre-deformed mesh with size and directionality controls (b) (example 1)

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Figure 4

Inverse bilinear mapping

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Figure 5

Quadrilateral bubble mesh packing and resultant pre-deformed mesh for examples 1 and 2

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Figure 6

Finite element analysis of original uniform mesh (a) and uniform sized pre-deformed mesh (b) (example 1)

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