An optimality criterion for shape optimization in eigenfrequency problems

Structural and Multidisciplinary Optimization

Volumn 29, Issue 6, 2005, Pages 457-469

  Pedersen, P ^a   Pedersen, N L ^b  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

^b AALBORG UNIVERSITY   (Denmark)

Author keywords

Optimality criteria; Parameterization; Plate vibrations; Shape optimization

Indexed keywords

BOUNDARY CONDITIONS; EIGENVALUES AND EIGENFUNCTIONS; FREQUENCIES; KINETIC ENERGY; MATHEMATICAL PROGRAMMING; MOLECULAR VIBRATIONS; NUMERICAL ANALYSIS; OPTIMIZATION;

OPTIMALITY CRITERIA; PARAMETERIZATION; PLATE VIBRATIONS; SHAPE OPTIMIZATION;

FINITE ELEMENT METHOD;

EID: 21144451712     PISSN: 1615147X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00158-004-0499-4     Document Type: Article

References (18)

1. Bathe KJ (1996) Finite element procedures. 2nd edn. Prentice-Hall, NJ, USA
2. Dems K, Mroz Z (1978) Multiparameter structural shape optimization by finite element method. Int J Numer Methods Eng 13:247-263
3. Grandhi R (1993) Structural optimization with frequency constraints - a rewiev. AIAA J 31(12):2296-2303
4. Haslinger J, Neittaanmaki P (1996) Finite element approximation for optimal shape, material and topology design. 2nd edn. Wiley, Chichester, UK
5. Haug EJ, Choi KK, Komkov V (1986) Design sensitivity analysis of structural systems. Academic, Orland, FL, USA
6. Jensen JS, Pedersen NL (2003) On maximal eigenfrequency separation in two-material structures: the Id and 2d scalar cases. DCAMM (687): 1-24 (submitted)
7. Niordson F, Pedersen P (1973-74). A review of optimal structural design. In Thirteenth Int. Congress of Theoretical and Applied Mechanics, 264-278, IUTAM, Moscow, Russia, 148 references
8. Niordson FI (1965) On the optimal design of a vibrating beam. Q Appl Math 23:47-53
9. Olhoff N (1980) Optimal design with respect to structural eigenvalues. In: Rimrott FPJ, Tabarrot B (eds.) IUTAM Congress, 133-149, North-Holland, Canada
10. Pedersen P (1982-83). Design with several eigenvalue constraints by finite elements and linear programming. J Struct Mech 10(3):243-271
11. Pedersen P (1998) Some general optimal design results using anisotropic power law non-linear elasticity. Struct Optim 15:73-80
12. Pedersen P (2000) On optimal shapes in materials and structures. Struct Multidisc Optim 19:169-182
13. Pedersen NL (2004) Optimization of holes in plates for control of eigenfrequencies. Struct Multidisc Optim 28(1): 1-10
14. Prager W, Taylor JE (1968) Problems of optimal structural design. J Appl Mech Trans ASME 35(1):102-106
15. Rozvany GNI (1989) Structural Design via Optimality Criteria. Kluwer, Dordrecht, The Netherlands
16. Svanberg K (1987) The method of moving asymptotes - a new method for structural optimization. Int J Numer Methods Eng 24:359-373
17. Wasiutynski Z (1960) On the congruency of the forming according to the minimum potential energy with that according to equal strength. Bull, de l'Academie Polonaise des Sciences, Serie des Sciences Techniques 8(6):259-268
18. Wittrick WH (1962) Rates of change of eigenvalues, with reference to buckling and vibration problems. J R Aeronaut Soc 66:590-591