Size-dependent nonlinear bending analysis of nonlocal magneto-electro-elastic laminated nanobeams resting on elastic foundation

Employing Reddy's third-order shear deformation theory (RTSDT) and nonlocal elasticity theory, a nonlinear bending model of the nonlocal three-layer magneto-electro-elastic (MEE) laminated nanobeam resting on elastic foundation is established by considering von Karman's geometrically nonlinear equations. Nonlinear higher or-der partial differential governing equations of MEE laminated nanobeams can be obtained employing Hamilton variational principle. The three-layered MEE laminated nanobeam is considered to have simply supported boundary condition in the present paper. Meanwhile, the electric and magnetic potential distributions in the laminated nanobeam are determined through Maxwell's magnetic-electro equations and boundary conditions. The governing equations of laminated nanobeams are re-expressed in the dimensionless form by introducing the non-dimensional terms. Employing Galerkin method, the nonlinear higher order partial differential governing equations are simplified into lower order equations. Several cases are explored to indicate the effects of foundation parameters, nonlocal parameter, stacking sequence, external electric voltage and external magnetic potential on bending behaviors of MEE laminated nanobeams.