A 3-D elasticity solution for a sandwich composite with functionally graded core subjected to transverse loading by a rigid sphere

This study presents an analytical three-dimensional elasticity solution method for a sandwich composite with a functionally graded core subjected to transverse loading by a rigid spherical indentor. The governing equations are derived from Reissner’s functional and are solved by enforcing continuity of traction and displacement components between the adjacent layers. The sandwich panel consists of orthotropic face sheets bonded to an isotropic core with a Young’s modulus that varies exponentially with respect to the transverse direction. Without the usual assumption of a Hertzian-type contact pressure distribution, the sphere’s unknown contact area and pressure distribution due to indentation are obtained by utilizing an iterative solution method. As a result, the complete stress and displacement fields are determined within the functionally graded sandwich panel. To examine the results produced by this solution method, displacements and stresses are presented with respect to varying degrees of core stiffness at the face sheet interface. Results of this analysis demonstrate that the interfacial normal and transverse shear stresses are not necessarily reduced by the incorporation of a FG core.