Static response of a layered magneto-electro-elastic half-space structure under circular surface loading

A cylindrical system of vector functions, the stiffness matrix method and the corresponding recursive algorithm are proposed to investigate the static response of transversely isotropic, layered magneto-electro-elastic (MEE) structures over a homogeneous half-space substrate subjected to circular surface loading. In terms of the system of vector functions, we expand the extended displacements and stresses, and deduce two sets of ordinary differential equations, which are related to the expansion coefficients. The solution to one of the two sets of these ordinary differential equations can be evaluated by using the stiffness matrix method and the corresponding recursive algorithm. These expansion coefficients are then integrated by adaptive Gaussian quadrature to obtain the displacements and stresses in the physical domain. Two types of surface loads, mechanical pressure and electric loading, are considered in the numerical examples. The calculated results show that the proposed technique is stable and effective in analyzing the layered half-space MEE structures under surface loading.