Application of pontryagin's principle to bimodal optimization problems

Structural and Multidisciplinary Optimization

Volumn 37, Issue 1, 2008, Pages 1-12

  Atanackovic, Teodor M ^a   Seyranian, Alexander P ^b  

^a UNIVERSITY OF NOVI SAD   (Serbia)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Bimodal optimization; Optimal shape; Pontryagin's principle

Indexed keywords

NONLINEAR EQUATIONS; NONLINEAR SYSTEMS;

BIMODAL OPTIMIZATION; BIMODAL OPTIMIZATIONS; FIRST INTEGRALS; NECESSARY OPTIMALITY CONDITIONS; NUMERICAL RESULTS; OPTIMAL COLUMNS; OPTIMAL SHAPE; PONTRYAGIN'S PRINCIPLE; PONTRYAGIN'S PRINCIPLES; SYSTEM OF DIFFERENTIAL EQUATIONS;

OPTIMIZATION;

EID: 55849146681     PISSN: 1615147X     EISSN: 16151488     Source Type: Journal    
DOI: 10.1007/s00158-007-0211-6     Document Type: Article

References (31)

1. Atanackovic TM (1997) Stability theory of elastic rods. World Scientific, River Edge, NJ
2. T. M. Atanackovic 2006 Optimal shape of column with own weight: bi and single modal optimization Meccanica 41 173 196
3. T. M. Atanackovic B. N. Novakovic 2006 Optimal shape of an elastic column on elastic foundation Eur J Mech A/Solids 25 154 165
4. T. M. Atanackovic S. S. Simic 1999 On the optimal shape of Pflüger column Eur J Mech A/Solids 18 903 913
5. J BŁachut M Życzkowski 1984 Bimodal design of clamped-clamped columns under creep conditions Int J Solids Struct 20 571 577
6. T. Clausen 1851 Über die Form architektonischer Säulen Bull. cl. Physico-Math Acad St Pétersbourg 9 369 380
7. S. J. Cox 1992 The shape of the ideal column The Mathematical Intelligencer 14 16 24
8. S. J. Cox M. L. Overton 1992 On the optimal design of columns against buckling SIAM J Math Anal 23 287 325
9. Hale JK (1969) Ordinary differential equations. Wiley, New York
10. Y. V. Egorov 2002 On the Lagrange problem about strongest column C R Acad Sci Paris Ser I 335 997 1002
11. Y. V. Egorov 2003 On the Lagrange problem about the optimal form for circular hollow columns C R Acad Sci Paris Ser Mechanique 331 699 704
12. Y. V. Egorov 2003 On the problem of Lagrange on the optimal form of a column Mathematics-Doklady 392 1 5
13. Y. V. Egorov 2004 On the optimization of higher eigenvalues C R Acad Sci Paris Ser Mechanique 332 673 678
14. Grinev VB, Filippov AP (1979) Optimization of Rods with Respect to Spectrum of Eigenvalues. Naukova Dumka, Kiev (in Russian)
15. J. Keller 1960 The shape of the strongest column Arch Rat Mech Anal 5 275 285
16. J. B. Keller F. I. Niordson 1966 The tallest column J Math Mech 16 433 446
17. Lagrange J-L (1868) Sur la figure des colonnes. In: Serret MJ-A (ed) In Ouveres de Lagrange, vol 2. Gauthier-Villars, Paris, pp 125-170
18. E. F. Masur 1984 Optimal structural design under multiple eigenvalue constraints Int J Solids Struct 20 211 231
19. N. Olhoff F. I. Niordson 1979 Some problems concerning singularities of optimal beams and columns ZAMM 59 3 16 26
20. N. Olhoff S. H. Rasmussen 1977 On the single and bimodal optimum buckling loads of clamped columns Int J Solids Struct 13 605 614
21. Sage AP, White CC (1977) Optimum system control. Prentice-Hall, New Jersey
22. A. P. Seyranian 1979 Homogeneous functionals and structural optimization problems Int J Solids Struct 15 749 759
23. A. P. Seyranian 1983 A solution of a problem of Lagrange Soviet Physics Doklady 28 7 550 551
24. A. P. Seyranian 1984 On a problem of Lagrange Mech Solids (Mekhanika Tverdogo Tela) 19 2 100 111
25. A. P. Seyranian 1995 New solutions to Lagrange's problem Physics-Doklady 40 5 251 253
26. A. P. Seyranian 2003 The Lagrange problem on optimal column Adv Mech (Uspekhi Mekhaniki) 2 45 96
27. A. P. Seyranian O. G. Privalova 2003 The Lagrange problem on an optimal column: old and new results Struct Multidisc Optim 25 1 18
28. A. P. Seyranian E. Lund N. Olhoff 1994 Multiple eigenvalues in structural optimization problems Struct Optim 8 207 227
29. I. Tadjbakhsh J. B. Keller 1962 Strongest columns and isoperimetric inequalities for eigenvalues J Appl Mech (Transactions of ASME) 29 159 164
30. Vujanovic BD, Atanackovic TM (2004) An introduction to modern variational techniques in mechanics and engineering. Birkhäuser, Boston
31. Wang CM, Wang CY, Reddy JN (2005) Exact solutions for buckling of structural members. CRC Press, Boca Raton