Abstract
In this work, a novel high-order formulation for multilayered piezoelectric plates based on the combination of variable-order interior penalty discontinuous Galerkin methods and general layer-wise plate theories is presented, implemented and tested. The key feature of the formulation is the possibility to tune the order of the basis functions in both the in-plane approximation and the through-the-thickness expansion of the primary variables, namely displacements and electric potential. The results obtained from the application to the considered test cases show accuracy and robustness, thus confirming the developed technique as a supplementary computational tool for the analysis and design of smart laminated devices.
Highlights
Multilayer composite beams, plates and shells are today widely employed in several fields of engineering, for example in the aerospace, naval, automotive and biomedical sectors, among others [1]
Besides fully three-dimensional approaches, which may be employed to capture complex localized field details, thin and relatively thick multilayered composite structures have been investigated using suitable plate theories, which are based on specific assumptions about the behavior of some specific field components throughout the laminate thickness and allow reducing the total number of unknowns and the computational cost associated with the numerical models: familiar examples are provided by the Kirchhoff and Mindlin kinematic assumptions in the case of purely structural plates, while the coupling with the electric fields must be considered in piezoelectric plates
The partial differential equations governing the electro-mechanical behavior of a multilayered piezoelectric plate, modelled according to the LW formulation derived in the previous section, can be obtained from the Principle of Virtual Displacements (PVD) for piezoelectric media
Summary
Multilayer composite beams, plates and shells are today widely employed in several fields of engineering, for example in the aerospace, naval, automotive and biomedical sectors, among others [1]. The width of the available design space for this kind of multi-physics multilayer materials, deriving from the variety of properties of the individual laminae and from the layup flexibility, induces the need of a preliminary careful assessment of the properties of the assembled laminate: their heterogeneous nature, the mismatch of material features between contiguous layers and the variety of external loading condition may result in complex multi-physics states that, if not carefully designed, may lead to unwanted behaviors or unforeseen damage/failure patterns For such a reason, several analytical, numerical and computational methods have been developed for the analysis of multilayer composites. Numerical results on single and multiple layers piezoelectric plates are provided by Section 4, which is followed by the Conclusions
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