Dynamic analysis of laminated composite plates using a layer-wise mixed finite element model

This paper deals with an accurate, three-dimensional, higher order, mixed finite element (FE) modeling for the free vibration analysis of multi-layered thick composite plates. An 18-node, three-dimensional mixed FE model has been developed by using Hamilton’s energy principle. Continuity of the transverse stress and the displacement fields has been enforced through the thickness of laminated composite plate. Further, in addition to the displacement components, the transverse stress components (σz, τxz, and τyz, where z is the thickness direction) have been invoked as the nodal degrees-of-freedom by applying elastic equations between stress and displacement fields. Thus, the present FE model has a novel feature of maintaining the fundamental elastic relationship throughout an elastic continuum. Natural frequencies of laminated composite plates obtained through the present formulation have been shown to be in good agreement with the available elasticity and closed form solutions. Stress mode shapes have been plotted for the fundamental natural vibration of plates with various lamination schemes. Strain variations through the thickness of laminated plates have also been presented graphically to show the magnitude of discontinuity in the variation of transverse strains at the layer interfaces.