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.

1.
George
,
P. L.
,
Hecht
,
F.
, and
Salte
,
E.
, 1991, “
Automatic Mesh Generator with Specified Boundary
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
92
, pp.
269
328
.
2.
Shephard
,
M. S.
, and
Georges
,
M. K.
, 1991, “
Automatic Three-Dimensional Mesh Generation by the Finite Octree Technique
,”
Int. J. Numer. Methods Eng.
0029-5981,
32
, pp.
709
749
.
4.
Lai
,
M.
,
Benzley
,
S.
, and
White
,
D. R.
, 1999, “
Automated Hexahedral Mesh Generation by Generalized Multiple Source to Multiple Target Sweeping
,”
2nd Symposium on Trends in Unstructured Mesh Generation
,
University of Colorado
, Boulder.
5.
Thompson
,
J. F.
,
Soni
,
B.
, and
Weatherill
,
N.
, 1999,
Handbook of Grid Generation
,
CRC Press
, Cleveland.
6.
Tristano
,
J.
,
Chen
,
Z.
,
Hancq
,
D.
, and
Kwok.
,
W.
, 2003, “
Fully Automatic Adaptive Mesh Refinement Integrated into the Solution Process
,”
Proceedings of the 12th International Meshing Roundtable
.
7.
Zhu
,
J. Z.
, and
Zienkiewicz
,
O. C.
, 1988, “
Adaptive Techniques in the Finite Element Method
,”
Commun. Appl. Numer. Methods
0748-8025,
4
, pp.
197
204
.
8.
Kang
,
E.
, and
Haghighi
,
K.
, 1992, “
Knowledge-Based a-priori Approach to Mesh Generation in Thermal Problems
,”
Int. J. Numer. Methods Eng.
0029-5981,
35
, pp.
915
937
.
9.
Kang
,
E.
, and
Haghighi
,
K.
, 1995, “
Intelligent Finite Element Mesh Generation
,”
Eng. Comput.
0177-0667,
11
, pp.
70
82
.
10.
Desaleux
,
T.
, and
Fouet
,
J.
, 1986, “
Expert Systems for Automatic Meshing
,”
Proceedings of. International Conference on Reliable Mechanical Engineering Analysis
, pp.
503
514
.
11.
Blacker
,
T. D.
,
Stepheson
,
M. B.
,
Mitchiner
,
J. L.
,
Phillips
,
L. R.
, and
Lin
,
Y. T.
, 1988, “
Automated Quadrilateral Mesh Generator: A Knowledge System Approach
,” ASME paper, 88-WA/CIE-4.
12.
Yagawa
,
G. S.
,
Yoshimura
,
N.
,
Soneda
, and
Nakao
,
K.
, 1990, “
Automatic Two and Three Dimensional Mesh Generation Based on Fuzzy Knowledge Processing Technique
,”
Proceedings of the 1990 ASME International Computers in Engineering Conference
, pp.
107
114
.
13.
Takahshi
,
H.
, and
Shimizu
,
H.
, 1991, “
A General Purpose Automatic Mesh Generation using Shape Recognition Technique
,”
Proceedings of the 1991 ASME International Computers in Engineering Conference
, pp.
519
526
.
14.
Young
,
Z.
, and
Grosse
,
I. R.
, 1990, “
A Rule-Based Computational System for Automatic Finite Element Modeling
,”
Proceedings of the 1990 ASME International Computers in Engineering Conference
, pp.
87
94
.
15.
Yagawa
,
G. S.
,
Yoshimura
,
N.
,
Soneda
, and
Nakao
,
K.
, 1992, “
Automatic Two- and Three-Dimensional Mesh Generation Based on Fuzzy Knowledge Processing Technique
,”
Comput. Mech.
0178-7675,
9
, pp.
333
346
.
16.
Yagawa
,
G.
,
Yoshimura
,
S.
, and
Nakao
,
K.
, 1995, “
Automatic Mesh Generation of Complex Geometries Based on Fuzzy Knowledge Processing and Computational Geometry
,”
Integrated Computer-Aided Engineering
,
2
(
4
), pp.
265
280
.
17.
Zadeh
,
A.
, 1975, “
The Concept of a Linguistic Variable and Its Application to Approximating Reasoning I, II, III
,”
J. Inf. Sci.
0165-5515,
8
, pp
199
249
, pp. 301–357;
Zadeh
,
A.
, 1975
J. Inf. Sci.
0165-5515
9
, pp.
43
80
.
18.
Zadeh
,
A.
, 1989, “
Knowledge Representation in Fuzzy Logic
,”
IEEE Trans. Knowl. Data Eng.
1041-4347
1
(
1
), pp.
89
100
.
19.
Kwok
,
W.
,
Haghighi
,
K.
, and
Kang
,
E.
, 1995, “
An Efficient Data Structure for the Advancing-Front Triangular Mesh Generation Technique
,”
Commun. Numer. Methods Eng.
1069-8299,
11
, pp.
465
473
.
20.
Kwok
,
W.
, 1995, “
A Fuzzy Logic Knowledge-Based System for Finite Element Mesh Generation and Analysis
,” Ph.D. thesis, Purdue University.
21.
Oñate
,
E.
, and
Bugeda
,
G.
, 1993, “
A Study of Mesh Optimality Criteria in Adaptive Finite Element Analysis
,”
Eng. Comput.
0264-4401,
10
, pp.
307
321
.
22.
Kandel
,
A.
, 1986,
Fuzzy Mathematical Techniques with Applications
,
Addison-Wesley
, Reading, MA.
23.
Klir
,
J. G.
, and
Folger
,
T. A.
, 1988,
Fuzzy Sets, Uncertainty and Information
,
Prentice Hall
, Englewood Cliffs, NJ.
24.
Zimmermann
,
H. J.
, 1991,
Fuzzy Set Theory and Its Applications
,
Kluwer Academic
, Boston.
25.
Peterson
,
R. E.
, 1974,
Stress Concentration Factors
,
Wiley
, NY.
26.
Mizumoto
,
M.
, 1982, “
Comparison of Fuzzy Reasoning Methods
,”
Fuzzy Sets Syst.
0165-0114,
8
, pp.
253
283
.
27.
Mizumoto
,
M.
, 1985, “
Extended Fuzzy Reasoning
,” in
Approximate Reasoning in Expert Systems
,
M. M.
Gupta
,
A.
Kandel
,
W.
Bandler
, and
J. B.
Kiszka
, eds.,
Elsevier Science
, NY, pp.
71
85
.
28.
Mizumoto
,
M.
, 1988, “
Fuzzy Controls under Various Fuzzy Reasoning Methods
,”
J. Inf. Sci.
0165-5515,
45
,
129
151
.
29.
Fukami
,
S
,
Mizumoto
,
M.
, and
Tanaka
,
K.
, 1980, “
Some Considerations on Fuzzy Conditional Inference
,”
Fuzzy Sets Syst.
0165-0114,
4
, pp.
243
273
.
30.
Lee
,
C. C.
, 1990, “
Fuzzy Logic in Control Systems: Fuzzy Logic Controller—Part I & II
,”
IEEE Trans. Syst. Man Cybern.
0018-9472,
20
(
2
), pp.
404
418
, 419–435.
31.
Lin
,
C. T.
, and
Lee
,
C. S. G.
, 1996,
Neural Fuzzy Systems: A Neuro-Fuzzy Synergism to Intelligent Systems
,
Prentice-Hall
, Englewood Cliffs, NJ.
32.
Kwok
,
W.
, and
Haghighi
,
K.
, 1997, “
On the Design of Initial Mesh and Mesh Quality Measures
,”
The Special Symposium on Trends in Unstructured Mesh Generation
, (
Joint ASME/ASCE/SES Summer Meeting
, Chicago), AMD Vol.
220
, ISBN No. 0-7918 1558-7.
This content is only available via PDF.
You do not currently have access to this content.