Hygrothermal Static Bending and Deflection Responses of Porous Multidirectional Nanofunctionally Graded Piezoelectric (NFGP) Plates With Variable Thickness on Elastic Foundations

ABSTRACT This research article introduces a high‐order finite element model based on the first‐order shear deformation theory to analyze the hygrothermal static responses of nanoscale, multidirectional nanofunctionally graded piezoelectric (NFGP) plates resting on variable elastic foundations. The study considers the material properties of these plates, which are governed by three distinct material laws—Power, Exponential, and Sigmoid as well as various patterns of porosity distribution. The derived governing equations are formulated using Hamilton's principle and incorporate nonlocal piezoelasticity theory, employing a nine‐node isoperimetric quadrilateral Lagrangian element capable of handling six degrees of freedom. A comprehensive parametric study is conducted, examining the influence of the small‐scale parameter, material exponent for multidirectional grading, variable foundation stiffness, porosity‐related exponent, thickness ratio, and the effects of hygrothermal and electrical loading on the NFGP plates, all while considering different boundary conditions. The findings provide valuable insights into the interaction between multidirectional graded smart structures and their foundations under varying hygrothermal and electromechanical conditions, which can significantly enhance the efficiency of designing and developing intelligent structures and systems.