Lewicka, Marta2008-11-262008-11-262008-11-26https://hdl.handle.net/11299/45458We prove that the critical points of the $3$d nonlinear elasticity functional over a thin shell of arbitrary geometry and of thickness $h$, as well as the weak solutions to the static equilibrium equations (formally the Euler Lagrange equations associated to the elasticity functional) converge, in the limit of vanishing thickness $h$, to the critical points of the generalized von Karman functional on the mid-surface, recently derived in [14]. This holds provided the elastic energy of the $3$d deformations scale like $h^4$ and the magnitude of the body forces scale like $h^3$.shell theoriesnonlinear elasticityequilibriacalculus of variationsPreprint