an:02018307
Zbl 1030.74031
Pantz, Olivier
On the justification of the nonlinear inextensional plate model
EN
Arch. Ration. Mech. Anal. 167, No. 3, 179-209 (2003).
00094437
2003
j
74K20 74G65 35Q72
gamma-convergence; cylindrical three-dimensional body; Saint Venant-Kirchhoff material; minimizers; total energy; nonlinear bending energy; vanishing thickness; nonlinear plate model
Summary: We consider a cylindrical three-dimensional body, made of a Saint Venant-Kirchhoff material, and we let its thickness go to zero. For a specific order of magnitude for the applied loads and under appropriate restrictions on the set of admissible deformations, we show that the almost-minimizers of the total energy converge toward deformations that minimize the nonlinear bending energy obtained by \textit{D. D. Fox, A. Raoult} and \textit{J. C. Simo} [ibid. 124, No. 2, 157-199 (1993; Zbl 0789.73039)] using formal asymptotic expansions. Our result is obtained by \(\Gamma\)-convergence arguments.
Zbl 0789.73039