Coupled higher order and mixed layerwise finite element based static and free vibration analyses of laminated plates

Abstract

A unique finite element model for static and free vibration analyses of thick and thin composite laminates is presented. The model is a combination of 3D mixed layerwise and equivalent single layer (ESL) theories. The ESL is employed in the global part of domain. On the other hand, a stack of 3D elements are used for estimation of the local parameters. The transverse inter laminar stresses are determined by using 18 noded 3D mixed layerwise element with 6 DOF per node in the local region. This mixed element incorporates the interlaminar stresses as the nodal DOF in addition to displacements for ensuring continuity of the transverse stresses in the thickness direction. Nine noded 2D elements with 12 DOF per node are used in the global domain. A transition has been developed for connection and compatibility of differently modelled sub-domains. Hamilton’s variational principle has been used for the free vibration analysis. Present static and vibration analyses of laminates are in good agreement with the available elasticity and closed form solutions. The presented combined mesh modelling reduces number of elements to map the entire domain as compared to full 3D model. This results in substantial reduction of DOF and improves the computational efficiency.