Refined Theory for Bending and Torsion of Perforated Plates

Abstract

An asymptotic solution is given for the effective elastic constants and the stresses in a perforated plate which is loaded in bending and torsion. In this solution terms 0(h /R )2 are neglected with respect to unity; h being the plate thickness and R the hole radius. In addition to the doubly periodic solution of the classical plate problem another bi-potential problem and two auxiliary problems, viz., a plane strain and a torsion problem for a half-infinite strip, have to be solved. The asymptotic solution together with an approximate solution for an infinitely thick plate permits us often to construct a solution which covers the entire range of h /R ; viz., 0≤h /R <∞. In a number of cases accurate interpolation requires additional finite-element calculations. The numerical data presented here apply to a square or an equilateral triangular hole pattern.