A unified formulation to assess multilayered theories for piezoelectric plates

This paper proposes a unified formulation for the electro-mechanical analysis of multilayered plates embedding piezo-layers. Both equivalent single layer (ESL) and layer-wise (LW) models have been considered. Zig-zag effects have been described by employing the Murakami zig-zag function (MZZF). Linear up to fourth-order expansions are used for displacement variables. Electric potential has been restricted to LW descriptions. Governing equations have been derived in terms of a few ‘fundamental nuclei’ with only nine terms each. These equations have been presented in a manner which is ‘formally’ not affected by the assumptions that have been introduced for displacement and electrical variables. Closed-form solutions and related numerical verifications show that the unified formulation could lead to a quasi-three-dimensional description of global and local characteristic of static and dynamic response of pieloelectric plates. The convenience of implementing the MZZF has been underlined. Quite different accuracy has been obtained by different theories with respect to mechanical and electrical loadings respectively. Layer-wise analyses could be required in thick plate geometries. Furthermore, an accurate description of the electro-mechanical coupling demands a layer-wise description of the displacement or at least the separated modeling of the piezoelectric and the structural layers, even though thin plates are considered.