zbMATH — the first resource for mathematics

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

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