Applying Levy and DQ Methods to Hygrothermal Deformation of Piezoelectric/GPLs Plates with Porosities Lying on Elastic Foundations Using a Quasi-3D Plate Theory

Fatemah H. H. Al Mukahal, Fatemah Alsebai and Mohammed Sobhy ()
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Fatemah H. H. Al Mukahal: Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia
Fatemah Alsebai: Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia
Mohammed Sobhy: Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al-Ahsa 31982, Saudi Arabia

Mathematics, 2025, vol. 13, issue 5, 1-34

Abstract: The hygrothermal deformation of nanocomposite piezoelectric plates containing internal pores lying on elastic foundations is illustrated in this paper by utilizing a novel quasi-3D plate theory (Q3DT). This nanocomposite plate has been strengthened by functionally graded graphene platelets (FG GPLs). For the purpose of identifying the FG porous materials, four alternative patterns of porosity distribution are employed, with the first pattern having a uniform distribution and the others having an uneven one. The material properties of the reinforced plate are estimated based on the Halpin–Tsai model. From the proposed theory and the virtual work principle, the basic differential equations are derived. The Levy method is used to convert the deduced partial differential equations to ordinary ones. The differential quadrature method (DQM) as a fast-converging method is utilized to solve these equations for various boundary conditions. The minimal number of grid points needed to obtain the converging solution is found by introducing a convergence study. After validating the obtained results with the studies of other researchers, this study’s findings are provided tabularly and graphically with numerous comprehensive discussions to examine the impact of the various factors of the proposed responding system.

Keywords: piezoelectric material; porosities; graphene platelets; Levy solution; differential quadrature method; quasi-3D plate theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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