Hygrothermal modeling of the buckling behavior of sandwich plates with nanocomposite face sheets resting on a Pasternak foundation

Abstract

In this work we investigate the buckling response of sandwich plates with a polymeric core and two face sheets reinforced by carbon nanotubes (CNTs). The problem is tackled analytically by means of a higher-order sandwich plate theory, where the face sheets are modeled according to a classical plate theory and modified strain gradient theory with temperature-dependent and moisture-dependent material properties. A Mori–Tanaka method is applied to determine the mechanical properties associated with the face sheets, while considering the agglomeration effect of CNTs. The governing equations of the problem are derived from the Hamilton’s principle, whose solutions are recovered by means of a Navier–Stokes method. A thorough sensitivity study of the structural response to different parameters includes the agglomeration and volume fraction of CNTs, the material length scale parameter, the side and aspect ratios, together with the temperature variation and humidity conditions. The sandwich plates are assumed to be immersed within an orthotropic Pasternak foundation, whose normal and shear moduli can affect the overall buckling response of the structure. Numerical experiments show that sandwich plates with nanocomposite face sheets, resting on orthotropic elastic foundations, feature an increased stiffness, where the proposed formulation yields accurate results, due to the possibility of considering the variation in temperature, humidity and agglomeration of the reinforcing CNTs within the solution.