محمد غلامي

This study investigates the geometrically nonlinear behavior of beam-like structures functioning as three-dimensional bending-mode actuators, which are more common than other configurations due to their ease of fabrication an‎d design flexibility, under electromechanical loads.The Von-Kármán nonlinear terms are incorporated into the displacement-strain relations to account for large geometric deformations. Various higher-order theories are employed, incorporating strain an‎d rotation gradients along with associated piezoelectric an‎d flexoelectric effects. The approximation of material properties across the thickness is estimated using the Classical Power Law an‎d Mori-Tanaka methods. The governing equations an‎d corresponding boundary conditions are derived using the variational principle. The governing equations are linearized using the Newton-Raphson iterative method. A C0-continuous tetrahedral mixed element, which requires lower displacement field continuity than conventional C1 elements, is implemented using the Python scripting environment in the open-source FEniCS platform. Throughout this research, the effects of different parameters, such as Winkler-Pasternak elastic foundation, different length-to-thickness ratios, different dimensions, Poissonʹs ratio,power-law indices, length scale parameters, flexoelectric coefficients, various porosity distribution patterns across the thickness, an‎d different load locations an‎d magnitudes, are investigated. The outputs for porous piezoelectrics revealed that incorporating voids an‎d porosities into the problem formulation significantly impacts the deformation of the porous actuator. A uniform porosity distribution has the greatest effect, whereas a centrally concentrated distribution has the least. Furthermore, variations in the volume fraction index within the range of 0–1 cause the highest rate of change in the actuator tip displacement. Results for the analysis of isotropic cantilever flexoelectric beams under electrical an‎d mechanical loads showed that as the thickness-to-length-scale ratio increases beyond 10, the gradient of change for transverse displacement an‎d electric potential sharply decreases, an‎d the results converge toward classical theory. Under electrical loading, for non-dimensional electric potentials greater than 0.5, a significant error was observed between the results. For deflection-to-length ratios exceeding 0.2, a notable discrepancy emerged between linear an‎d nonlinear solutions for both displacement an‎d electric potential fields, indicating the invalidity of the linear formulation in this range. Investigating the sensitivity of length scale parameters on the displacement of the flexoelectric beam revealed that, for the present problem, the influence of the parameter related to the deviatoric stretch gradient is negligible compared to the dilatation an‎d rotation gradient parameters, an‎d it can be ignored with reasonable accuracy. In the sensitivity analysis of these parameters on the electric field, it was found that the behavioral pattern of the parameter stemming from the stretch gradient differs from those of the dilatation an‎d rotation gradients, an‎d their effects on the results are opposite. Comparing results from 2D an‎d 3D elements showed that for center-loaded beams, a 2D seven-node element provides acceptable results compared to the 3D solution, particularly for strain an‎d stress fields. The findings of this study can be used in the design an‎d fabrication of porous, functionally graded piezoelectric actuators an‎d sensors, as well as in the development of micro- an‎d nano-scale flexoelectric actuators.

تئوري گراديان كرنش , روش اجزاي محدود تركيبي , پيزوالكتريسيته , فلكسوالكتريسيته , رفتار وابسته به سايز , جابجايي بزرگ , FEniCS

Strain gradient theory , Mixed finite element method , Piezoelectricity , Flexoelectricity , Size-dependent behavior , Large deformation , FEniCS

Mohammad Gholami

Mansour Alizadeh