Marguerre-von Karman equations in curvilinear coordinates

We apply the method of asymptotic expansions with the thickness as the small parameter to the three-dimensional shallow shell problem of Malguerre-von Karman written in curvilinear coordinates, with the displacement as the unknown. We prove that the leading term of the asymptotic expansion can be identified with the solution of a two-dimensional problem. (C) Academie des Sciences/Elsevier, Paris