Abstract
ABSTRACTIn the present work, a new class of finite elements (FEs) for the analysis of composite and sandwich plates embedding piezoelectric skins and patches is proposed. By making use of node-by-node variable plate theory assumptions, the new finite element allows for the simultaneous analysis of different subregions of the problem domain with different kinematics and accuracy, in a global/local sense. As a consequence, the computational costs can be reduced drastically by assuming refined theories only in those zones/nodes of the structural domain where the resulting strain and stress states, and their electro-mechanical coupling present a complex distribution. The primary advantage is that no ad-hoc techniques and mathematical artifices are required to mix the fields coming from two different and kinematically incompatible adjacent elements, because the plate structural theory varies within the finite element itself. In other words, the structural theory of the plate element is a property of the FE node in this present approach, and the continuity between two adjacent elements is ensured by adopting the same kinematics at the interface nodes. The finite element arrays of the generic plate element are formulated in terms of fundamental nuclei, which are invariants of the theory approximation order and the modeling technique (Equivalent-Single-Layer, Layer-Wise). In this work, the attention is focused on the use of Legendre polynomial expansions to describe the through-the-thickness unknowns to develop advanced plate theories. Several numerical investigations, such as composite and sandwich multilayered plates embedding piezoelectric skins and patches with various load, boundary conditions, and piezoelectric material polarizations, are carried out to validate and demonstrate the accuracy and efficiency of the present plate element, including comparison with various closed-form and FE solutions from the literature.
Highlights
Plate structures have a predominant role in a variety of engineering applications, such as piezoelectric composite structures modeling, and in the overall design procedure for smart structures and systems
The piezoelectric effect is made available in polarisable crystalline materials through the application of an intense electric field which imparts a net polarization of the crystal cells
In this paper a new methodology for global/local analysis of composite and sandwich plate structure embedding piezoelectric skins and patches has been introduced. This approach makes use of advanced finite plate elements with node-dependent kinematics, which are formulated in the domain of the Unified Formulation
Summary
Plate structures have a predominant role in a variety of engineering applications, such as piezoelectric composite structures modeling, and in the overall design procedure for smart structures and systems. The enormous improvements and formulations of higher-order plate structural theories, considerable work has been recently directed towards the implementation of innovative solutions for improving the analysis efficiency for complex geometries and assemblies, possibly in a global/local scenario. The unknowns are represented independently in each sub-domain and at the interface, where the matching is provided by suitable Lagrange multipliers This method was recently adopted by Carrera et al [30] to couple beam elements of different orders and, to develop variable kinematic beam theories. A new simultaneous multiple-model method for 2D elements with node-dependent kinematics is developed, for the analysis of electro-mechanical problems This node-variable capability enables one to vary the kinematic assumptions within the same finite plate element. The results are compared with various closed-form and Fem solutions and, whenever possible, with exact solutions available from the literature
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have