Preliminary results on the homogenization of thin piezoelectric perforated shells

TL;DR

This paper introduces a new homogenization approach for thin perforated piezoelectric shells using the periodic unfolding method, deriving explicit limit equations and coefficients as the perforations vanish.

Contribution

It presents a novel homogenization technique for thin piezoelectric shells with perforations, providing explicit formulas for the effective properties.

Findings

Explicit homogenized coefficients derived

Limit constitutive laws established

New approach based on periodic unfolding method

Abstract

We consider a composite piezoelectric material whose reference configuration is a thin shell with fixed thickness. In this work, we give a new approach based on the periodic unfolding method to justify the modelling of a thin piezoelectric perforated shells and we establish the limit constitutive law by letting the size of holes is supposed to go to zero. This allows to use the homogenization technique to derive the limitting equations and the homogenizaed coefficients are explicity described.