Asymptotic bounds on the globally optimal positions of orthogonal stiffeners for rectangular plates in elastostatic bending

摘要

The present paper treats the problem of finding the asymptotic bounds for theglobally optimal locations of orthogonal stiffeners minimizing the complianceof a rectangular plate in elastostatic bending. The essence of the paper is theutilization of a method of analysis of orthogonally stiffened rectangularplates first presented by Mazurkiewicz in 1962, and obtained herein in a closedform for several special cases in the approximation of stiffeners having zerotorsional rigidity. Asymptotic expansions of the expressions for the deflectionfield of a stiffened plate are used to derive limit-case globally optimalstiffening layouts for highly flexible and highly rigid stiffeners. A centralresult obtained in this work is an analytical proof of the fact that an arrayof flexible enough orthogonal stiffeners of any number, stiffening asimply-supported rectangular plate subjected to any lateral loading, is best tobe put in the form of exactly two orthogonal stiffeners, one in each direction.