On the maximization of the fundamental eigenvalue in topology optimization

Structural and Multidisciplinary Optimization

Volumn 34, Issue 3, 2007, Pages 181-195

  Achtziger, Wolfgang ^a   Kočvara, Michal ^b  

^a TU DORTMUND UNIVERSITY   (Germany)

^b UNIVERSITY OF BIRMINGHAM   (United Kingdom)

Author keywords

Non linear semidefinite programming; Optimization of eigenvalues; Topology optimization; Vibration of structures

Indexed keywords

ALGORITHMS; COMPUTER PROGRAMMING; MATHEMATICAL MODELS; NATURAL FREQUENCIES; OPTIMIZATION; TOPOLOGY;

LINEAR SEMIDEFINITE PROGRAMS; NON-LIPSCHITZEAN BEHAVIOR; OBJECTIVE FUNCTION;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 34547534195     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-007-0117-3     Document Type: Article

References (22)

1. Achtziger W, Kočvara M (2006) Structural topology optimization with eigenvalues. Tech. Rep. No. 315, Institute of Applied Mathematics, University of Dortmund, Germany (to appear in SIAM Journal on Optimization)
2. Achtziger W, Ben-Tal A, Bendsøe M, Zowe J (1992) Equivalent displacement based formulations for maximum strength truss topology design. Impact Comput Sci Eng 4:315-345
3. Ben-Tal A, Nemirovski A (2001) Lectures on modern convex optimization. MPS-SIAM Series on Optimization. SIAM, Philadelphia
4. Bendsøe M, Sigmund O (2002) Topology optimization. Theory, methods and applications. Springer, Heidelberg
5. Bhatia R (1996) Matrix analysis. Springer, New York
6. Bhatia R, Li RC (1996) On perturbations of matrix pencils with real spectra. II. Math Comput 65:637-645
7. Clarke FH (1983) Optimization and nonsmooth analysis. Wiley, New York
8. Gantmacher FR (1959) The theory of matrices, vol 1. Chelsea, New York
9. de Klerk E (2002) Aspects of semidefinite programming. Kluwer, Dordrecht
10. Kočvara M, Stingl M (2003) PENNON-a code for convex nonlinear and semidefinite programming. Optim Methods Softw 18(3):317-333
11. Kočvara M, Stingl M (2006) PENBMI User's Guide. Version 2.1. http://www.penopt.com/
12. Kočvara M, Leibfritz F, Stingl M, Henrion D (2004) A nonlinear SDP algorithm for static output feedback problems in COMPlib. LAAS-CNRS research report no. 04508, LAAS, Toulouse
13. Lewis AS, Overton ML (1996) Eigenvalue optimization. Acta Numer 5:149-190
14. Löfberg J (2004) YALMIP: A toolbox for modeling and optimization in MATLAB. In: Proceedings of the CACSD conference, Taipei, Taiwan. Available from http://control.ee.ethz.ch/~joloef/yalmip.php
15. Luenberger D (1997) Optimization by vector space methods. Wiley, New York
16. Ohsaki M, Fujisawa K, Katoh N, Kanno Y (1999) Semi-definite programming for topology optimization of trusses under multiple eigenvalue constraints. Comp Meth Appl Mech Eng 180:203-217
17. Olhoff N (1980) Optimal design with respect to structural eigenvalues. In: Rimrott F, Tabarott B (eds) Theoretical and applied mechanics, Proc. XVth Int. IUTAM Congress, North-Holland, pp 133-149
18. Olhoff N, Rasmussen SH (1977) On single and bimodal optimum bukling loads of clamped columns. Int J Solids Struct 13:605-614
19. Seyranian AP, Mailybaev AA (2003) Multiparameter stability theory with mechanical applications. World Scientific, Singapore
20. Stewart GW (1979) Perturbation bounds for the definite generalized eigenvalue problem. Linear Algebra Appl 23:69-86
21. Stingl M (2005) On the solution of nonlinear semidefinite programs by augmented lagrangian methods. Ph.D. Thesis, Inst. of Appl. Math., University of Erlangen
22. Zhang T, Law KH, Golub GH (1998) On the homotopy method for perturbed symmetric generalized eigenvalue problems. SIAM J Sci Comput 19:1625-1645