Micromechanical analysis of effective piezoelastic properties of smart composite sandwichshells made of generally orthotropic materials

Abstract

A micromechanical model for smart composite shells with periodically arrangedembedded piezoelectric actuators and rapidly varying thickness is developed. Thepertinent mathematical framework is that of asymptotic homogenization. The modelenables the determination of both local fields and effective elastic and actuationcoefficients of smart composite sandwich shells made of generally orthotropic materials.Orthotropy of the constituent materials leads to a significantly more complex setof local problems and is considered in the present paper for the first time. Theeffective coefficients are determined by means of a set of four simpler problemscalled ‘unit-cell’ problems. The actuation coefficients, for example piezoelectric ormagnetostrictive, characterize the intrinsic transducer nature of active smartmaterials that can be used to induce strains and stresses in a co-ordinated fashion.The theory is illustrated by means of examples pertaining to hexagonal honeycomb coredand hexagonal–triangular mixed cored smart sandwich shells made of orthotropic materials.The effective elastic and piezoelectric coefficients for these structures are calculated andanalyzed. It is shown that the model can be used to tailor the effective properties of anysmart shell to meet the requirements of a particular application by changing somegeometric or material parameters.