Finite elements, genetic algorithms and β-splines: A combined technique for shape optimization

Finite Elements in Analysis and Design

Volumn 33, Issue 2, 1999, Pages 125-141

  Annicchiarico, W ^a   Cerrolaza, M ^a  

^a UNIVERSIDAD CENTRAL DE VENEZUELA   (Venezuela)

Author keywords

Finite elements; Genetic algorithms; Optimization; splines

Indexed keywords

EID: 0001735495     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-874X(99)00030-X     Document Type: Article

References (23)

1. O.C. Zienkiewicz, J.C. Campbell, Shape optimization and sequential linear programming, in: R.A. Gallagher, O.E. Zienkiewicz (Eds.), Optimum Structural Design, Wiley, New York, 1973, pp. 109-126.
2. C.V. Ramakrishnan, A. Francavilla, Structural shape optimization using penalty functions, J. Struct. Mech. 3 (4) (1975) 403-422.
3. R.J. Yang, D.L. Dewhirst, J.E. Allison, A. Lee, Shape optimization of connecting rod pin end using a generic model, Finite Eelement Anal. Des. 11 (1992) 257-264.
4. K.H. Chang, K.K. Choi, A geometry-based parameterization method for shape design of elastic solids, Mech. Struct. and Mach. 20 (1992) 215-252.
5. D.A. Tortorelli, A Geometric representation scheme suitable for shape optimization, Mech. Struct. Mach. 21 (1993) 95-121.
6. D.A. Tortorelli, J.A. Tomasko, T.E. Morthland, J.A. Dantzig, Optimal designs of non-linear parabolic systems - Part II: variable spatial domain with applications to casting optimization, Comput. Methods. Appl. Mech. Eng. 113 (1994) 157-172.
7. N. Olhoff, E. Lund, J. Rasmussen, Concurrent engineering design optimization in a CAD environment, Special Report 16, Institute of Mechanical Engineering, Aalborg University, 1992.
8. A.D. Belegundu, S.D. Rajan, A shape optimization approach based on natural design variables and shape functions, Comput. Methods. Appl. Mech. Eng. 66 (1988) 87-106.
9. S. Kodiyalam, V. Kumar, P.M. Finnigan, Constructive solid geometry approach to three dimensional structural shape optimization, AIAA J. 30 (1992) 1408-1415.
10. S. Chen, D.A. Tortorelli, Three dimensional shape optimization with variational geometry, Struct. Optim. 13 (1997) 81-94.
11. U. Schramm, W.D. Pilkey, Parameterization of Structural Shape Using Computer Aided Geometric Design Elements, Structural Optimization 93, Proceedings of the World Congress on Optimal Design of Structural Systems, Vol. 1, Río de Janeiro Brazil, 1993, pp. 75-82.
12. O. Othmer, Marriage of CAD, FE and BE, in: C.A. Tanaka, C.A. Brebbia, R. Shaw (Eds.), Advances in Boundary Element Methods in Japan and USA, Comp. Mech. Publications, Boston, MA, 1990.
13. N. Olhoff, M.P. Bendsoe, J. Rasmussen, On CAD-integrated structural topology and design optimization, Comput. Methods. Appl. Mech. Eng. 89 (1991) 259-279.
14. W. Annicchiarico, M. Cerrolaza, Optimization of finite element bidimensional models: An approach based on genetic algorithms, J. Finite Elements Anal. Des. 29 (3-4) (1998) 231-257.
15. J. H. Holland, Adaptation in Natural and Artificial Systems, University of Michigan Press, 1975 and First MIT Press edition, (1992) p. 121 (Chapter 7).
16. D.E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Publishing Company, New York, 1989.
17. L. Davis, Handbook of Genetic Algorithms, Van Nostrand Reinhold, New York, 1991.
18. W. Annicchiarico, M. Cerrolaza, Structural shape optimization using genetic algorithms, in: M. Marchetti, C.A. Brebbia, M.H. Aliabadi (Eds.), Boundary elements XIX, Comp. Mech. Pub., UK, 1997, pp. 399-408.
19. W. Annicchiarico, M. Cerrolaza, A structural optimization approach and software based on genetic algorithms and finite elements, J. Eng. Optim. (1999) in press.
20. A. Brindle, Genetic algorithms for function optimization, Doctoral Dissertation, University of Alberta, Edmonton, 1981.
21. B.A. Barsky, Computer Graphics and Geometric Modeling Using β-Splines, Springer, New York, 1988.
22. R.H. Bartels, J.C. Beatty, B.A. Barsky, An Introduction to Splines for Use in Computer Graphics and Geometry Modeling, Morgan Kaufmann, Los Altos, CA, 1987.
23. K. W. Zumwalt, M. E. M. El-Sayed, Structural shape optimization using cubic β-Splines, Proceedings of Structural Optimization 93, The World Congress on Optimal Design of Structural Systems, Vol. 1, Río de Janeiro Brazil, (1993) pp. 83-90.