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A Fuzzy Logic Knowledge-Based Approach for Finite Element Mesh Generation and Analysis

[+] Author and Article Information
W. Kwok

 Ansys, Inc. Southpointe, 275 Technology Drive, Canonsburg, PA 15317wa.kwok@ansys.com

K. Haghighi

Department of Engineering Education, Purdue University, West Lafayette, IN 47907haghighi@purdue.edu

J. Comput. Inf. Sci. Eng 5(4), 317-329 (Jul 05, 2004) (13 pages) doi:10.1115/1.2052807 History: Revised July 05, 2004; Received September 29, 2004

A fuzzy logic knowledge-based approach, FUZZYMESH , for finite element mesh generation and analysis is presented. The proposed approach initiates the adaptive process with a high quality initial mesh that is more refined around the critical points/regions in the problem domain. In order to create high quality initial meshes, the heuristic knowledge, past experience, common sense, and ad hoc methods of finite element specialists are incorporated into the knowledge base of the fuzzy system. Using the linguistic variable concept and approximate reasoning techniques, the fuzzy system makes expert decisions about the initial mesh design by considering the geometric information, as well as the boundary and loading conditions. The decision process includes the determination of priority of critical points/regions and the prediction of mesh sizes for them. According to the mesh size information, a near-optimal initial mesh is created with an automatic mesh generator that is based on the advancing front mesh generation technique. The performance of the proposed approach was measured and evaluated in terms of efficiency and accuracy. The evaluation included comparison between the results of a code based on the proposed fuzzy logic knowledge-based approach, FUZZYMESH , and the conventional approach, which starts the finite element analysis with different meshes, by solving various problems. The global as well as local errors of different solutions were examined and compared. The CPU times for different approaches to achieve a particular accuracy were also measured and compared. The results showed that due to better quality of initial meshes, FUZZYMESH results in lower levels and more accurate error estimates. In turn, the proposed approach is able to solve the problem with a more accurate solution at less cost.

Copyright © 2005 by American Society of Mechanical Engineers
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References

Figures

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Figure 4

The schematic diagram of the preprocessor and the fuzzy inference system

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Figure 6

The hierarchical structure of a linguistic variable STRESS INTENSITY

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Figure 7

A flat tension bar with a notch

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Figure 8

Schematic representation of fuzzy partitions

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Figure 9

Schematic representation of fuzzy reasoning with Rc

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Figure 10

The relationships between priorities, stresses, and mesh sizes

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Figure 11

The schematic diagram of example 1

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Figure 12

The initial (a) and the final mesh (b) with FUZZYMESH approach

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Figure 13

A uniform initial mesh (a) and the final adaptive mesh (b) with conventional approach I

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Figure 14

A uniform initial mesh (a) and the final adaptive mesh (b) with conventional approach II

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Figure 15

A uniform initial mesh (a) and the final adaptive mesh (b) with conventional approach III

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Figure 16

Relative percentage error η vs DOFs

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Figure 17

The schematic diagram of example 2

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Figure 18

The initial mesh (a) and the final mesh (b) with FUZZYMESH approach

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Figure 19

A uniform initial mesh (a) and the final adaptive mesh (b) with conventional approach I

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Figure 20

A uniform initial mesh (a) and the final adaptive mesh (b) with conventional approach II

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Figure 21

A uniform initial mesh (a) and the final adaptive mesh (c) with conventional approach III

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Figure 22

Relative percentage error η vs DOFs

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Figure 23

The schematic diagram of example 3

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Figure 24

The initial mesh (a) and the final mesh (b) with FUZZYMESH approach

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Figure 1

Fuzzy expert system for finite element mesh generation and adaptive analysis, FUZZYMESH

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Figure 2

The schematic diagram of the fuzzy expert system

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Figure 3

Identification of potential critical points/regions

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