  The present paper treats the problem of finding the asymptotic bounds for the
globally optimal locations of orthogonal stiffeners minimizing the compliance
of a rectangular plate in elastostatic bending. The essence of the paper is the
utilization of a method of analysis of orthogonally stiffened rectangular
plates first presented by Mazurkiewicz in 1962, and obtained herein in a closed
form for several special cases in the approximation of stiffeners having zero
torsional rigidity. Asymptotic expansions of the expressions for the deflection
field of a stiffened plate are used to derive limit-case globally optimal
stiffening layouts for highly flexible and highly rigid stiffeners. A central
result obtained in this work is an analytical proof of the fact that an array
of flexible enough orthogonal stiffeners of any number, stiffening a
simply-supported rectangular plate subjected to any lateral loading, is best to
be put in the form of exactly two orthogonal stiffeners, one in each direction.
