Buckling and post-buckling of extensible rods revisited: A multiple-scale solution

International Journal of Non-Linear Mechanics

Volumn 44, Issue 2, 2009, Pages 200-208

  Mazzilli, Carlos E N ^a  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

Author keywords

Buckling; Elastic instability; Extensible rod; Method of multiple scales; Post buckling

Indexed keywords

NUMERICAL METHODS;

BUCKLING AND POST-BUCKLING; ELASTIC INSTABILITIES; EXTENSIBLE ROD; METHOD OF MULTIPLE SCALE; MULTIPLE SCALE; NUMERICAL INTEGRATIONS; POSTBUCKLING; SLENDERNESS RATIOS;

BUCKLING;

EID: 58549112936     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2008.11.005     Document Type: Article

References (18)

1. L. Euler, Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici latissimo sensu accepti. Additamentum I. De curvis elasticis, Marcum-Michaelem Bousquet, 1744 (in Latin).
2. Timoshenko S.P. History of Strength of Materials (1953), McGraw-Hill, New York
3. Timoshenko S.P., and Gere J.M. Theory of Elastic Stability (1961), McGraw-Hill Kogakusha
4. J. Ratzersdorfer, Flambagem. I Barras Prismáticas, Instituto de Pesquisas Tecnológicas, Publicação 513, São Paulo, 1954 (a revised version in Portuguese of the book Knickfestigkeit von Stäben und Stabwerken, Springer, Vienna, 1936, in German).
5. C. Truesdell, The rational mechanics of flexible or elastic bodies, in: L. Euler Opera Omnia (2), vol. 11(2), Füssli, 1960.
6. W.T. Koiter, On the stability of elastic equilibrium, PhD Thesis, Delft, 1945 (in Dutch; English translation NASA Report TTF-10, 1967).
7. Tompson J.M.T., and Hunt G.W. A General Theory of Elastic Stability (1973), Wiley, New York
8. Antman S.S. The Theory of Rods, Handbuch der Physik vol. VIa/2 (1972), Springer, Berlin pp. 641-703
9. C.E.N. Mazzilli, Euler buckling and the "elastica" revisited: a unified formulation for the five classical cases, Boletim Técnico do Departamento de Engenharia de Estruturas e Fundações, BT-8710, Escola Politécnica da Universidade de São Paulo, 1987 (in Portuguese).
10. C.E.N. Mazzilli, Back to the "elastica" and Euler buckling, in: Proceedings of the VIII Ibero-Latin-American Congress of Computational Methods in Engineering, vol. C, Rio de Janeiro, 1987, pp. 201-218 (in Portuguese).
11. Wang C.Y. Post-buckling of a clamped-simply supported elastica. International Journal of Non-Linear Mechanics 32 6 (1997) 1115-1122
12. Nayfeh A.H., and Mook D.T. Nonlinear Oscillations (1979), Wiley, New York
13. Fu-ru J. Nonlinear analyses for the postbuckling behaviors of annular and circular thin plates. Applied Mathematics and Mechanics 8 9 (1987) 797-813
14. Wadee M.K., and Bassom A.P. Characterization of limiting homoclinic behaviour in a one-dimensional elastic buckling model. Journal of Mechanics and Physics of Solids 48 (2000) 2297-2313
15. P.M. Pimenta, C.E.N. Mazzilli, Minima correctio methodi inveniendi lineas curvas elasticii, Boletim Técnico do Departamento de Engenharia de Estruturas e Fundações, BT-8613, Escola Politécnica da Universidade de São Paulo, 1986 (in Portuguese).
16. Filipich C.P., and Rosales M.B. A further study on the postbuckling of extensible elastic rods. International Journal of Non-Linear Mechanics 35 (2000) 997-1022
17. Sampaio R., and Almeida M.P. Buckling of extensible rods. Revista Brasileira de Ciências Mecânicas 7 (1985) 373-385
18. Magnusson A., Ristinmaa M., and Ljung C. Behaviour of the extensible elastica solution. International Journal of Solids and Structures 38 (2001) 8441-8457