Analytic homogenization for torsion of orthotropic sandwich plates: Application to corrugated cardboard

Abstract

This paper presents an analytic homogenization model for the torsion of orthotropic sandwich plates and its application to the torsion modelling of corrugated cardboards. It is very difficult to determine the torsion rigidity of these kinds of 3D structures even numerically because of the boundary condition effects. Inspired by the gridwork homogenization model of Timoshenko, we decompose the plate torsion into two beam torsions. The plate torsion curvature is separated into two beam torsion rates and the beam torsion rigidities in these two directions are introduced to describe the torsion behaviour of the orthotropic plates. We demonstrate that the plate torsion rigidity is equal to a quarter of the sum of the two beam torsion rigidities, which are easily calculated analytically or numerically. This torsion homogenization model can be used not only for corrugated cardboard packaging structures, but also for naval and aeronautic composite structures.