Non-existence of minimizers for a nonlinear membrane plate under compression

The classical equations of a nonlinearly elastic membrane plate, made of Saint Venant–Kirchhoff material, have been justified by Fox et al. (Arch. Rational Mech. Anal. 124 (2) (1993) 157–199). We show that, under compression, the associated minimization problem admits no solution. The proof is based on a result of non-existence of minimizers of non-convex functionals due to Dacorogna and Marcellini (Arch. Rational Mech. Anal. 131 (4) (1995) 359–399). We generalize the application of their result from plane elasticity to membrane plates. To cite this article: K. Trabelsi, C. R. Acad. Sci. Paris, Ser. I 337 (2003).