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

TL;DR

This paper derives asymptotic bounds for the optimal placement of orthogonal stiffeners on rectangular plates in elastostatic bending, showing that two orthogonal stiffeners are optimal regardless of stiffness.

Contribution

It introduces a closed-form analysis method for stiffened plates and proves that two orthogonal stiffeners are globally optimal for various stiffness levels.

Findings

Two orthogonal stiffeners are optimal for stiffened plates.

Analytical bounds for stiffener placement are derived.

Method applies to plates with any lateral loading.

Abstract

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.