A quasi-3D HSDT theory for bending analysis of porous double-curvature FG shells with a piezoelectric layer on Kerr-type foundation

Porosity introduced in functionally graded materials (FGMs) during manufacturing can adversely affect the strength and durability of components used in industrial applications. The main purpose of this study is to investigate the static bending behavior of doubly curved functionally graded (FG) porous shells integrated with a piezoelectric fiber-reinforced composite (PFRC) layer on their external surface. The analysis is performed using a refined quasi-3D theory accounting for both shear and normal strains with the PFRC layer acting as an actuator for the FG shells. The shells are subjected to sinusoidal electromechanical loads and the mechanical properties of the porous shell vary continuously through the thickness, modeled using an exponential function incorporating the effect of porosity. The governing equations are formulated using the variational energy principle and solved using Navier’s method. The study accounts for electric potential effects and examines the influence of Kerr foundation parameters including porosity, inhomogeneity parameter, applied voltage, and geometric ratios. Validation against previously published works confirms the accuracy and effectiveness of the proposed theory. The results indicate that spherical structures provide the best compromise between stiffness, stability, and stress uniformity. Therefore, mechanical neutral zones independent of porosity and applied voltage offer potential for adaptive intelligent structures’ design.