Investigation of mechanical responses of flexo-magnetic variable thickness nanoplates resting on elastic foundations, taking into account geometrical imperfections

This work utilizes the finite element approach together with an innovative shear strain theory to investigate the static bending behavior, free vibration features, and static buckling phenomena of flexo-magnetic nanoplates. The inquiry specifically examines the fluctuation in both the thickness of the plate and the elasticity of the foundation. The influence of initial geometrical imperfections, including several categories such as local and global faults, is also taken into account. The influences of several factors, including the law governing thickness fluctuation, types of imperfections, boundary conditions, and elastic foundation, on the mechanical response of the plate are considered. Outcomes of the work include new and original discoveries that have not been discussed in previous research, adding to both theoretical comprehension and practical implementation.