Optimal shape of a heavy compressed column

Structural and Multidisciplinary Optimization

Volumn 28, Issue 6, 2004, Pages 388-396

  Atanackovic, T M ^a   Glavardanov, V B ^a  

^a UNIVERSITY OF NOVI SAD   (Serbia)

Author keywords

Optimal shape; Pontryagin's principle

Indexed keywords

BOUNDARY VALUE PROBLEMS; COMPACTION; DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; INTEGRATION; LAGRANGE MULTIPLIERS; MAXIMUM PRINCIPLE; NUMERICAL METHODS; OPTIMIZATION;

NUMERICAL INTEGRATION; OPTIMAL SHAPE; PONTRYAGIN'S MINIMUM PRINCIPLES (PMP); VARIATIONAL PRINCIPLES;

COLUMNS (STRUCTURAL);

EID: 10644272871     PISSN: 1615147X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00158-004-0457-1     Document Type: Article

References (18)

1. Alekseev, V.M.; Tihomirov, V.M.; Fomin, S.V. 1979: Optimal Control. Moscow: Nauka (in Russian)
2. Antman, S.S. 1995: Nonlinear Problems of Elasticity. Berlin Heidelberg New York: Springer
3. Atanackovic, T.M. 1997: Stability theory of elastic rods. River Edge, New Jersey: World Scientific
4. Atanackovic, T.M. (in press): On the Optimal Shape of a Compressed Rotating Rod. Meccanica
5. Chow, S.-N.; Hale, J.K. 1982: Methods of Bifurcation Theory. Berlin Heidelberg New York: Springer
6. Clausen, T. 1851: Über die Form architektonischer Säulen. Bull cl, physico math Acad St Pétersbourg 9, 369-380
7. Cox, S.J. 1992: The Shape of the ideal Column. The Mathematical Intelligencer 14, 16-24
8. Cox, S.J.; McCarthy, C.M. 1998:, The shape of the tallest column. S1AM J Math Anal 29, 547-554
9. Keller, J. 1960: The shape of the strongest column. Arch Rat Mech Anal 5, 275-285
10. Tadjbakhsh, I.; Keller, J.B. 1962: Strongest Columns and Isoperimetric Inequalities for Eigenvalues. J Appl Mech Trans ASME 29, 159-164
11. Keller, J.B.; Niordson, F.I. 1966: The Tallest Column. J Math Mech 16, 433-446
12. Lagrange, J.-L. 1868: Sur la figure des colonnes. In Quveres de Lagrange (edited by M.J.-A. Serret) 2, 125-170, Paris: Gauthier-Villars
13. McCarthy, C.M. 1997: An investigation of the Optimal Design of the Tallest Unloaded Column. Ph.D. thesis, Rice University, Houston, Texas
14. Nuttgens, P. 1999: The Story of Architecture. London:
15. Phaidon Sage, A.P.; White, C.C. 1977: Optimum System Control. New Jersey: Prentice-Hall
16. Seyranian, A.P. 1979: Homogeneous functional and structural optimization problems. Int J Solids Struct 15, 749-759
17. Seyranian, A.P. 2000: The Lagrange Problem on Optimal Column. Preprint No 60, Institute of Mechanics, Moscow State Lomonosov University, Moscow
18. Tabarrok, B.; Cleghorn, W.L. 2000: Application of principle of least action to beam problems. Acta Mechanics 142, 235-243