Application of nonlocal strain gradient theory to size dependent bending analysis of a sandwich porous nanoplate integrated with piezomagnetic face-sheets

Bending analysis of a sandwich plate is studied in this paper based on first order shear deformation theory and nonlocal strain gradient theory. The sandwich nanoplate is including a porous core and two piezomagnetic facesheets. It is assumed that nanoplate is resting on Pastemak's foundation. Power law function is used to describe change of porosity along the thickness direction. To account size dependency, nonlocal strain gradient theory is employed to predict this behavior. The principle of virtual work is used to derive governing equations in terms of primary functions. A nonlocal parameter and a strain gradient parameter are employed to describe both stiffness reduction and stiffness enhancement of nanoplates. The analytical solution is presented to solve seven governing equation using Navier's solution. The numerical results are presented to evaluate the effect of various distribution of porosities, porosity volume fraction, nonlocal and strain gradient parameter, electric and magnetic potentials, geometrical characteristics, and parameters of foundation on the results of problem.