Effect of Winkler–Pasternak foundations and porosity on the electromechanical buckling responses of PZT-4/PZT-5H smart graded plate subjected to thermal loading

This paper investigates the buckling behavior of porous PZT-4/PZT-5H smart graded plate resting on the Winkler–Pasternak foundations under the combined thermomechanical and thermoelectric loading conditions. The thermomechanical properties of the material are modeled based on sigmoid variation. The study employs von Kármán nonlinear strain theory coupled with the modified first-order shear deformation theory (FSDT) and variational principles to formulate the equations of motion. A higher-order finite element (HOFE) approach with seven degrees of freedom (DOFs) is utilized alongside modified iterative methods to solve the governing equations. The convergence and accuracy of the proposed methodology have been validated against the existing literature. The simulation results provide a detailed analysis of the effects of temperature changes, thermal gradients, material gradation, applied voltage, porous exponent, porosity distribution, and elastic foundations on the structural behavior of the PZT-4/PZT-5H smart graded plates. The study investigates in detail the effects of porosity distribution, porous exponent applied electrical loading, various temperature profiles (uniform, linear, and nonlinear), material gradient exponent, thickness ratio, elastic foundations, and boundary conditions on the buckling behavior of the PZT-4/PZT-5H smart graded plate. These findings offer critical insights into the design and optimization of thermoelectric and thermomechanical stabilities in smart porous structures, making them more efficient, reliable, and performant for use in engineering systems such as MEMS, biomedical devices, and energy-harvesting technologies.