Justification of the Marguerre–von Kármán equations in curvilinear coordinates

Abstract

We apply the method of asymptotic expansions with the thickness as the small parameter to the three‐dimensional shallow shell problem of Marguerre–von Kármán 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. We also establish the existence and regularity of solutions to this two‐dimensional problem.