Galerkin-Vlasov approach for bending analysis of flexoelectric doubly-curved sandwich nanoshells with piezoelectric/FGP/piezoelectric layers using the nonlocal strain theory

Flexoelectricity refers to the link between electrical polarization and strain gradient fields in piezoelectric materials, particularly at the nano-scale. The present investigation aims to comprehensively focus on the static bending analysis of a piezoelectric sandwich functionally graded porous (FGP) double-curved shallow nanoshell based on the flexoelectric effect and nonlocal strain gradient theory. Two coefficients that reduce or increase the stiffness of the nanoshell, including nonlocal and length-scale parameters, are considered to change along the nanoshell thickness direction, and three different porosity rules are novel points in this study. The nanoshell structure is placed on a Pasternak elastic foundation and is made up of three separate layers of material. The outermost layers consist of piezoelectric smart material with flexoelectric effects, while the core layer is composed of FGP material. Hamilton’s principle was used in conjunction with a unique refined higher-order shear deformation theory to derive general equilibrium equations that provide more precise outcomes. The Navier and Galerkin-Vlasov methodology is used to get the static bending characteristics of nanoshells that have various boundary conditions. The program’s correctness is assessed by comparison with published dependable findings in specific instances of the model described in the article. In addition, the influence of parameters such as flexoelectric effect, nonlocal and length scale parameters, elastic foundation stiffness coefficient, porosity coefficient, and boundary conditions on the static bending response of the nanoshell is detected and comprehensively studied. The findings of this study have practical implications for the efficient design and control of comparable systems, such as micro-electromechanical and nano-electromechanical devices.