No. 10 (2008): GFS
RICERCJIS

A rigorous justification of design formulas for torsion in thin profiles

CESARE DAVINI
Georesources and Territory Department, University of Udine, Udine, Italy.
ROBERTO PARONI
Architecture and Planning Department, University of Sassari, Alghero, Italy.
ERIC PUNTEL
Georesources and Territory Department, University of Udine, Udine, Italy.

Peraulis clâf

  • Torsion,
  • thin-walled beams,
  • asymptotic method,
  • Γ-convergence

Cemût citâ

[1]
DAVINI, C., PARONI, R. and PUNTEL, E. 2008. A rigorous justification of design formulas for torsion in thin profiles. Gjornâl Furlan des Siencis - Friulian Journal of Science. 10, 10 (Jan. 2008), 75–88.

Ristret

A rather straightforward derivation of the Γ-limit of the torsion problem on a thin rectangle as the thickness goes to zero is obtained. The limit stresses are evaluated and the distributional nature of one of the stress components is clarified.

Riferiments

  1. Anzellotti G., Baldo S. and Percivale D. (1994). Dimension reduction in variational problems, asymptotic development in Γ-convergence and thin structures in elasticity. Asymptotic Analysis, 9(1): 61-100.
  2. Cabib E., Freddi L., Morassi A. and Percivale D. (2001). Thin notched beams. Journal of Elasticity, 64(2-3): 157-178.
  3. Dal Maso G. (1993). An introduction to Γ-convergence. Progress in Nonlinear Differential Equations and their Applications, 8. Boston, MA: Birkh¨auser Boston Inc.
  4. de Saint-Venant A.J.C.B. (1855). M´emoire sur la torsion de prismes, avec des consid´erations sur leur flexion. . .M´emoires des Savants Etrangers, 14: 233-560.
  5. Dell’Isola F. and Rosa L. (1996). An extension of Kelvin and Bredt formulas. Mathematics And Mechanics Of Solids, 1(2): 243-250.
  6. Higgins T.J. (1942). A comprehensive review of Saint-Venant’s torsion problem. American Journal of Physics, 10(5): 248-259.
  7. Kelvin W.T. and Tait P.G. (1912). Treatise on natural philosophy. Cambridge: Cambridge University Press.
  8. Le Dret H. and Raoult A. (1996). The membrane shell model in nonlinear elasticity:a variational asymptotic derivation. J.Nonlinear Sci., 6(1): 59-84.
  9. Morassi A. (1995). Torsion Of Thin Tubes - A Justification Of Some Classical Results. Journal Of Elasticity, 39(3): 213-227.
  10. Morassi A. (1999). Torsion of thin tubes with multicell cross-section. Meccanica, 34(2): 115-132.
  11. Paroni R. (2006). Theory of linearly elastic residually stressed plates. Mathematics and mechanics of solids, 11: 137-159.
  12. Prandtl L. (1903). Zur torsion von prismatischen st¨aben. Physikalische Zeitschrift, 4: 758-759.
  13. Rodriguez J.M. and Via˜no J.M. (1993a). Asymptotic analysis of Poisson equation in a thin domain – application to thin-walled elastic beams torsion theory .1. domain without junctions. Comptes Rendus De L’Academie Des Sciences Serie I-Mathematique, 317(4): 423-428.
  14. Rodriguez J.M. and Via˜no J.M. (1993b). Asymptotic analysis of Poisson equation in a thin domain – application to thin-walled elastic beams torsion theory .2. domain with junctions. Comptes Rendus De L’Academie Des Sciences Serie I-Mathematique, 317(6): 637-642.