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Research Papers

Recursive Differential Systems in Nonlinear Mechanics

[+] Author and Article Information
Claire David1

 Université Pierre et Marie Curie-Paris 6, Institut Jean Le Rond d’Alembert, UMR CNRS 7190, Boîte Courrier No. 162, 4 Place Jussieu, 75252 Paris Cedex 05, Francedavid@lmm.jussieu.fr

Marine Marcilhac, Alain Rigolot

 Université Pierre et Marie Curie-Paris 6, Institut Jean Le Rond d’Alembert, UMR CNRS 7190, Boîte Courrier No. 162, 4 Place Jussieu, 75252 Paris Cedex 05, France

1

Corresponding author.

J. Appl. Mech 77(3), 031018 (Feb 24, 2010) (7 pages) doi:10.1115/1.4000387 History: Received March 08, 2008; Revised April 10, 2009; Published February 24, 2010; Online February 24, 2010

The classical strength of materials for beams is represented through the first two terms of the asymptotic expansion of the solution of Navier’s equations. The method of asymptotic expansions with respect to the inverse of the slenderness of the beam permits us to obtain an approximate solution of Saint-Venant’s problem. For the elasticity of the second order, the displacement field is obtained as the sum of a series, the general term of which at the nth order is the solution of a differential recursive system. We presently propose a general way of solving this kind of system. The exact solution is given explicitly in the case of a slender field (beam).

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 2

The free-embedded cantilever subject to a constant moment of flexion

Grahic Jump Location
Figure 3

The third component of the field u, for a1=a2=0.5, at the second and third orders, as a function of the normalized thickness variable a3¯ and the small parameter ε

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