Deformation of a layered magnetoelectroelastic simply-supported plate with nonlocal effect, an analytical three-dimensional solution

In this paper, we present an exact closed-form solution for the three-dimensional deformation of a layered magnetoelectroelastic simply-supported plate with the nonlocal effect. The solution is achieved by making use of the pseudo-Stroh formalism and propagator matrix method. Our solution shows, for the first time, that for a homogeneous plate with traction boundary condition applied on its top or bottom surface, the induced stresses are independent of the nonlocal length whilst the displacements increase with increasing nonlocal length. Under displacement boundary condition over a homogeneous or layered plate, all the induced displacements and stresses are functions of the nonlocal length. Our solution further shows that regardless of the Kirchoff or Mindlin plate model, the error of the transverse displacements between the thin plate theory and the three-dimensional solution increases with increasing nonlocal length revealing an important feature for careful application of the thin plate theories towards the problem with nonlocal effect. Various other numerical examples are presented for the extended displacements and stresses in homogeneous elastic plate, piezoelectric plate, magnetostrictive plate, and in sandwich plates made of piezoelectric and magnetostrictive materials. These results should be very useful as benchmarks for future development of approximation plate theories and numerical modeling and simulation with nonlocal effect. (paper)