Considerations on higher-order finite elements for multilayered plates based on a unified formulation

International audienceIn this work, a numerical assessment of a series of multilayered finite plate elements is proposed. The finite elements are derived within the ‘‘Unified Formulation’’, a technique developed by Carrera for an accurate modeling of laminates. The Unified Formulation affords an implementation-friendly possibility to derive a large number of two-dimensional, axiomatic models for plates and shells. An accurate model for multilayered components naturally involves transverse shear and normal stresses, as well as higher-order displacement assumptions in thickness direction. The aim of this work is to give a first insight of the numerical properties of finite elements relying on these formulations. Some considerations concerning the numerical difficulties associated to thickness locking phenomena are presented. A detailed numerical analysis is performed to study the shear locking phenomenon. For the selected case study, once the latter spurious stiffening effect is suppressed with classical or advanced numerical techniques, the resulting elements are shown to behave robustly and accurately

A unified formulation to assess multilayered theories for piezoelectric plates

International audienceThis 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-threedimensionaldescription 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

Closed-form solutions for the free-vibration problem of multilayered piezoelectric shells

International audienceThis paper addresses the free-vibration problem of multilayered shells with embedded piezoelectric materials. A series of hierarchic, two-dimensional axiomatic shell theories are presented within the “Unified Formulation” introduced by the last author. Shells of constant curvature are considered, and no simplifying assumptions on the curvature terms are made in the geometric relations. Closed-form solutions are given for the free-vibration problem of simply supported, orthotropic piezoelectric laminates. The formulations are applied to study the influence of the electro-mechanical coupling on the resonant frequencies. It is demonstrated that the slenderness of plates with through-thickness polarized piezoelectric layers increases the electro-mechanical coupling. For comparison purposes, the fundamental axisymmetric mode of hollow cylinders has been exemplarily considered: with respect to flat plates, the thickness and the curvature of the shells have a less important effect on the piezoelectric coupling

A unified formulation to assess multilayered theories for piezoelectric plates

International audienceThis 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-threedimensionaldescription 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