In this work, a discontinuous Galerkin formulation for higher-order plate theories is presented. The starting point of the formulation is the strong form of the governing equations, which are derived in the context of the Generalized Unified Formulation and the Equivalent Single Layer approach from the Principle of Virtual Displacements. To express the problem within the discontinuous Galerkin framework, an auxiliary flux variable is introduced and the governing equations are rewritten as a system of first-order partial differential equations, which are weakly stated over each mesh element. The link among neighboring mesh elements is then retrieved by introducing suitably defined numerical fluxes, whose explicit expressions define the proposed Interior Penalty discontinuous Galerkin formulation. Furthermore, to account for the presence of generally curved boundaries of the considered plate domain, the discretisation mesh is built by combining a background grid and an implicit representation of the domain. hp-convergence analyses and a comparison with the results obtained using the Finite Element Method are provided to show the accuracy of the proposed formulation as well as the computational savings in terms of overall degrees of freedom.

We propose the electromechanical impedance technique to monitor the stability of dental implants. The technique consists of bonding one wafer-type piezoelectric transducers to the implant system. When subjected to an electric field, the transducer induces structural excitations which, in turn, affect the transducer’s electrical admittance. The hypothesis is that the health of the bone surrounding the implant affects the sensor’s admittance. A three-dimensional finite element model of a transducer bonded to the abutment of a dental implant placed in a host bone site was created to simulate the progress of the tissue healing that occurs after surgery. The healing was modeled by changing the Young’s modulus of the bone–implant interface. It was found that as the Young’s modulus of the interface increases, the electromechanical characteristic of the transducer changes. Then, the model was used to interpret the experimental results relative to a sensor bonded to an abutment screwed to implants secured into bovine bone samples. The results show that the electromechanical impedance technique can be used to monitor the stability of dental implants although more research is warranted to examine the repeatability of the methodology and its advantage with respect to existing commercial systems.