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

A micromechanical model for smart composite shells with periodically arranged embedded piezoelectric actuators and rapidly varying thickness is developed. The pertinent mathematical framework is that of asymptotic homogenization. The model enables the determination of both local fields and effective elastic and actuation coefficients of smart composite sandwich shells made of generally orthotropic materials. Orthotropy of the constituent materials leads to a significantly more complex set of local problems and is considered in the present paper for the first time. The effective coefficients are determined by means of a set of four simpler problems called 'unit-cell' problems. The actuation coefficients, for example piezoelectric or magnetostrictive, characterize the intrinsic transducer nature of active smart materials 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 cored and hexagonal-triangular mixed cored smart sandwich shells made of orthotropic materials. The effective elastic and piezoelectric coefficients for these structures are calculated and analyzed. It is shown that the model can be used to tailor the effective properties of any smart shell to meet the requirements of a particular application by changing some geometric or material parameters.