On the justification of the nonlinear inextensional plate model. (English) Zbl 1030.74031

Pantz, Olivier

Arch. Ration. Mech. Anal. 167, No. 3, 179-209 (2003).

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 D. D. Fox, A. Raoult and 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.

MSC:

74K20	Plates
74G65	Energy minimization in equilibrium problems in solid mechanics
35Q72	Other PDE from mechanics (MSC2000)

Keywords:

gamma-convergence; cylindrical three-dimensional body; Saint Venant-Kirchhoff material; minimizers; total energy; nonlinear bending energy; vanishing thickness; nonlinear plate model