Enhanced two-point diagonal quadratic approximation methods for design optimization

Computer Methods in Applied Mechanics and Engineering

Volumn 197, Issue 6-8, 2008, Pages 846-856

  Kim, Jong Rip ^a   Choi, Dong Hoon ^b  

^a Samsung SDI   (South Korea)

^b Hanyang University   (South Korea)

Author keywords

Function approximation; Quadratic approximation; Sequential approximate optimization; Two point approximation

Indexed keywords

APPROXIMATION THEORY; FUNCTIONS; QUADRATIC PROGRAMMING; STRUCTURAL DESIGN;

MECHANICAL SYSTEM OPTIMIZATION; SEQUENTIAL APPROXIMATE OPTIMIZATION; TWO-POINT APPROXIMATION;

OPTIMIZATION;

APPROXIMATION THEORY; FUNCTIONS; OPTIMIZATION; QUADRATIC PROGRAMMING; STRUCTURAL DESIGN;

EID: 36049002527     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2007.09.014     Document Type: Article

References (28)

1. Schmit L.A., and Farshi B. Some approximation concepts for structural synthesis. AIAA J. 12 (1974) 692-699
2. Schmit L.A., and Miura H. A new structural analysis/synthesis capability - ACCESS 1. AIAA J. 14 (1976) 661-671
3. Schmit L.A., and Fleury C. Structural synthesis by combining approximation concepts and dual methods. AIAA J. 18 (1980) 1252-1260
4. Haftka R.T., Nachlas J.A., Watson I.T., Rizzo T., and Desai R. Two-point constraint approximation in structural optimization. Comput. Meth. Appl. Mech. Engrg. 60 (1987) 289-301
5. Fleury C., and Braibant V. Structural optimization: a new dual method using mixed variables information. Int. J. Numer. Meth. Engrg. 23 (1986) 409-428
6. Starnes Jr. J.H., and Haftka R.T. Preliminary design of composite wings for buckling, stress and displacement constraints. J. Air Craft 16 (1979) 564-570
7. Svanberg K. Method of moving asymptotes: a new method for structural optimization. Int. J. Numer. Meth. Engrg. 24 (1987) 359-373
8. Chickermane H., and Gea H.C. Structural optimization using a new local approximation method. Int. J. Numer. Meth. Engrg. 39 (1996) 829-846
9. Fadel G.M., Riley M.F., and Barthelemy J.F.M. Two point exponential approximation method for structural optimization. Struct. Opt. 2 (1990) 117-124
10. Wang L.P., and Grandhi R.V. Efficient safety index calculation for structural reliability analysis. Comput. Struct. 52 (1994) 103-111
11. Wang L.P., and Grandhi R.V. Improved two-point function approximation for design optimization. AIAA J. 33 (1995) 1720-1727
12. Wang L.P., and Grandhi R.V. Multipoint approximations: comparisons using structural size, configuration and shape design. Struct. Opt. 12 (1996) 177-185
13. Wang L.P., Grandhi R.V., and Canfield R.A. Multivariate hermite approximation for design optimization. Int. J. Numer. Meth. Engrg. 39 (1996) 787-803
14. Xu S., and Grandhi R.V. Effective two-point function approximation for design optimization. AIAA J. 36 (1998) 2269-2275
15. Prasad B. Explicit constraint approximation forms in structural optimization. part 1; analysis and projections. Comput. Meth. Appl. Mech. Engrg. 40 (1983) 1-26
16. Salajegheh E. Optimum design of plate structures using three-point approximation. Struct. Opt. 13 (1997) 142-147
17. Sui Y.K. The Advances of Modeling Transformation Optimization and Synthesis (1998), Dalian University of Technology Press, Dalian
18. Xu G., Yamazaki K., and Cheng G.D. A new two-point approximation approach for structural optimization. Struct. Multidisciplinary Opt. 20 (2000) 22-28
19. Xu G., Yamazaki K., and Cheng G.D. A new three-point approximation approach for design optimization problems. Int. J. Numer. Meth. Engrg. 50 (2001) 869-884
20. Groenwold A.A., Etman L.F.P., Snyman J.A., and Rooda J.E. Incomplete series expansion for function approximation. Struct. Multidisciplinary Opt. 34 (2007) 21-40
21. J. Rasmussen, Accumulated approximations: a new method for structural optimization, in: Proceedings of the 3rd Air Force/NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization, San Francisco, CA, September 24-26, 1990, pp. 253-258.
22. Rasmussen J. Nonlinear programming by cumulative approximation refinement. Struct. Opt. 15 (1998) 1-7
23. Xu S., and Grandhi R.V. Multipoint approximation development: thermal structural optimization case study. Int. J. Numer. Meth. Engrg. 48 (2000) 1151-1164
24. Kim M.-S., Kim J.-R., Jeon J.-Y., and Choi D.-H. Efficient mechanical system optimization using two-point diagonal approximation in the nonlinear intervening variable space. J. KSME 15 (2001) 1257-1267
25. Vanderplaats G.N. Numerical Optimization Techniques for Engineering with Applications (1984), McGraw-Hill, New York
26. G.N. Vanderplaats, DOT Users Manual, version 4.20, VR& D Inc., 1995.
27. Rosen J.B., and Suzuki S. Construction of nonlinear programming test problem. Commun. Assoc. Comput. Machin. 8 (1965) 113
28. J.M. Gregory, MSC/NASTRAN Design Sensitivity and Optimization: User's Guide version 68, The MacNeal-Schwendler Corporation.