On the non-linear high-order theory of unidirectional sandwich panels with a transversely flexible core

The paper presents a general geometrically non-linear high-order theory of sandwich panels that takes into account the high-order geometrical non-linearities in the core as well as in the face sheets and is based on a variational approach. The formulation, which yields a set of rather complicated governing equations, has been simplified in two different approaches and has been compared with FEA results for verification. The first formulation uses the kinematic relations of large displacements with moderate rotations for the face sheets, non-linear kinematic relations for the core and it assumes that the distribution of the vertical normal stresses through the depth of the core are linear. The second approach uses the general formulation to the non-linear high-order theory of sandwich panels (HSAPT) that considers geometrical non-linearities in the face sheets and only linear high-order effects in the core. The numerical results of the two formulations are presented for a three point bending loading scheme, which is associated with a limit point behavior. The results of the two formulations are compared in terms of displacements, bending moments and shear stresses and transverse (vertical) normal stresses at the face-core interfaces on one hand, and load versus these structural quantities on the other hand. The results have compared well with FEA results obtained using the commercial codes ADINA and ANSYS.