Numerical solutions for magneto–electro–elastic laminated plates resting on Winkler foundation or elastic half-space

Abstract

This article investigates the bending response performances of the magneto–electro–elastic (MEE) laminated plates resting on the Winkler foundation or the elastic half-space subjected to a transverse mechanical loading .By assuming that the foundation is not electrically and magnetically conductive, the scaled boundary finite element method (SBFEM) based on the three-dimensional (3D) theory of elasticity is applied for both the simulation of the MEE laminated plate and the elastic half-space. The SBFEM model considers the generalized displacement involving the elastic displacement, electric potential and magnetic potential as the nodal degree of freedom for the MEE laminated plates, and only the in-plane of the MEE laminated plate or the boundary of the elastic half-space needs to be discretized leading to reduce the spatial dimension by one. Furthermore, in the SBFEM, the governing equations can be solved by using an analytical approach in the radial direction of the scaled coordinate system, so that it is particularly suitable for the simulation of the elastic half-space. For the Winkler foundation–plate system, the global stiffness coupling governing equation that includes the interaction between the MEE laminated plate and the Winkler foundation is derived directly from the 3D elasticity equations of the MEE laminated plate by assuming that the foundation reactions are proportional to the transverse displacements of the plate structure. While for the MEE laminated plate-half-space system, the whole domain is divided into three sub-domains including the MEE laminated plate structure, the near and semi-infinite far foundation systems based on the sub-structure method, and then the stiffness matrix of each sub-domain can be determined by means of the SBFEM. As a result, the global stiffness equation of the plate-half-space system can be assembled according to the principle of the degree of freedom matching at the same nodes. The numerical results obtained for limiting cases by using the proposed method were compared with the published works and showed excellent agreements with the solutions based on the analytical and numerical approaches, so that the accuracy and applicability of the proposed formulations for the analysis of the interaction problems between the MEE laminated plate and the Winkler foundation or elastic half-space can be verified. Moreover, several numerical examples with various material properties, geometries, stacking sequences, aspect ratios, and supported boundary conditions were presented to show the effects of which on the responses of the plate–foundation system.