Semi-Analytical Solution for Thermo-Piezoelectric Bending of FG Porous Plates Reinforced with Graphene Platelets

• Published in: Mathematics (Basel) 2022-11, Vol.10 (21), p.4104
• Main Authors: Alsebai, Fatemah, Al Mukahal, Fatemah H. H., Sobhy, Mohammed
• Format: Article
• Language: English
• Subjects: Bending; Carbon; Convergence; Deformation; differential quadrature method; Elastic properties; Exact solutions; Functionally gradient materials; Graphene; graphene platelets; Investigations; Levy-type solution; Mathematical analysis; Mechanical properties; Nanocomposites; Partial differential equations; piezoelectric; Piezoelectric materials; Piezoelectricity; Plate theory; Platelets (materials); Porosity; Porous materials; Porous plates; Quadratures; Shear deformation; Shear strain; Temperature effects; Thermal properties; Thickness ratio; Transverse shear; Vibration
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math10214104

This research is devoted to investigating the thermo-piezoelectric bending of functionally graded (FG) porous piezoelectric plates reinforced with graphene platelets (GPLs). A refined four-variable shear deformation plate theory is utilized considering the transverse shear strain to describe the displacement components. The porous nanocomposite plate is composed of polymer piezoelectric material containing internal pores and reinforced with FG GPLs. In accordance with modified distribution laws, the porosity and GPLs volume fraction are presumed to vary continuously through the plate thickness. Four GPLs and porosity distribution types are presented. By applying the Halpin–Tsai model, the elastic properties of the nanocomposite plate are calculated. The governing equations are derived based on the present theory and the principle of virtual work. The deduced partial differential equations are converted to ordinary equations by employing Levy-type solution. These equations are numerically solved based on the differential quadrature method (DQM). In order to determine the minimum grid points sufficient to gain a converging solution, a convergence study is introduced. Moreover, the accuracy of the present formulations are examined by comparing the obtained results with those published in the literature. Additional parametric analyses are introduced to investigate the influences of the GPLs weight fraction, distribution types, side-to-thickness ratio, external electric voltage and temperature on the thermal bending of FG GPLs porous nanocomposite piezoelectric plates.