A novel shear deformation theory for magneto-electro-elastic nanoplates

Abstract

This study proposes an innovative and efficient theoretical model for analyzing magneto-electro-elastic (MEE) nanoplates. A novel approach, formulated using third- and fifth-order Chebyshev polynomials based on Eringen’s theory and the shear deformation theory, is developed. This formulation automatically enforces the zero-shear-stress condition at the plate’s top and bottom surfaces, eliminating the need for any supplementary constraints. Applying the principle of extended virtual displacement, the formulation is developed in weak form. By integrating a nonlocal isogeometric analysis, the proposed model effectively captures small-scale effects in MEE nanoplate structures. The natural frequencies of the MEE nanoplate are investigated with respect to geometric and a nonlocal parameter. Comparative numerical results verify the reliability and superior performance of the proposed theory over existing higher-order shear deformation models.