Convergence of equilibria of thin elastic plates under physical growth conditions for the energy density

AbstractThe asymptotic behaviour of the equilibrium configurations of a thin elastic plate is studied, as the thickness h of the plate goes to zero. More precisely, it is shown that critical points of the nonlinear elastic functional Eh, whose energies (per unit thickness) are bounded by Ch4, converge to critical points of the Γ-limit of h−4Eh. This is proved under the physical assumption that the energy density W(F) blows up as detF→0