Static and dynamic analysis of doubly-curved functionally graded porous nanoshells integrated with piezoelectric surface layers and flexoelectric effect

Abstract

This study employs the finite element method based on nonlocal elasticity theory to model and analyze static bending, free oscillation, and transient responses of doubly-curved sandwich nanoshells with a functionally graded porous (FGP) core layer and integrated with piezoelectric surface layers resting on a Pasternak-elastic medium. The doubly-curved sandwich nanoshell comprises three layers, including a FGP core layer and two surface layers of piezoelectric material, taking into account the flexoelectricity effect. The notable novelty of this study is that it considers the nonlocal coefficients varying along the thickness direction as mechanical properties of the material. The Lagrangian and Hermite functions are employed to approximate a quadrilateral element with four-nodes, each of which has eight degrees of freedom based on an improved higher-order shear strain hypothesis. These functions are employed to generate the stiffness matrices, mass matrices, and force vectors of the shell in conjunction with different forms of curved shells and boundary conditions. A comprehensive study to evaluate the influence of coefficients such as flexoelectric effect, radius of curvature, nonlocal coefficient, elastic matrix stiffness parameters, porosity parameters, and geometric shapes on the static bending, free oscillation, and transient responses of the doubly-curved sandwich nanoshell with rectangular and circular planforms.