### Asymptotical Construction of Geometrically Nonlinear Plate Model for Functionally-Graded Magneto-Electro-Elastic Laminates

Hui Chen, Wenbin Yu
2010 51st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference 18th AIAA/ASME/AHS Adaptive Structures Conference 12th   unpublished
This paper aims at constructing a geometrically nonlinear model using the variational asymptotic method for analyzing magneto-electro-elastic composite laminates. By taking advantage of the inherent small parameter characterized by the ratio of the thickness to the in-plane dimension of the plate, we systematically reduced the original multiphysically coupled three-dimensional model to a series of two-dimensional plate models. A companion one-dimensional through-the-thickness analysis provides
more » ... he necessary constitutive models needed for the plate analysis. For practical uses, we also fit the asymptotically correct second-order electromagnetic enthalpy into a generalized Reissner-Mindlin model. The three-dimensional displacement/strain/stress fields as well as the electric/magnetic potentials and fluxes of the plate are obtained through recovery relations of the one-dimensional through-the-thickness analysis. Without introducing any a priori kinematic, electric, or magnetic assumptions in the derivation, the present plate model is rigorously derived to capture geometrical nonlinearity and is valid for large deformations and global rotations. The efficiency and the accuracy of the proposed method has been validated by comparing results with three-dimensional exact solutions for several problems featuring electromagnetic and elastic coupling. Present z U₃ Max error 0.01% (a) transverse deflectionŪ 3 , x 2 = b/2, b/h = 15 Exact (3D) Present z U₃ Max Error 0.03% (b) transverse deflectionŪ 3 , x 2 = b/2, b/h = 10 Exact (3D) Present z U₂ (c) longitudinal displacementŪ 2 , x 2 = 0, b/h = 15 Exact (3D) Present z U₂ (d) longitudinal displacementŪ 2 , x 2 = 0, b/h = 10 Exact (3D) Present z ϕ Max error 1.31% (e) magnetic potentialψ, x 2 = b/2, b/h = 15