A triangular finite element with drilling degrees of freedom for static and dynamic analysis of smart laminated structures

Abstract

In this work a new three-node finite element with piezoelectric coupling is presented. It can be used for the static and dynamic analysis of light-weight smart structures, i.e. laminated composite structures with piezoelectric patches attached to its surface or embedded within the laminated layers. The element is a continuum-based degenareted plate element based on the Reissner–Mindlin theory. It uses the Allman formulation for the in-plane strains together with the generalization of the discrete Kirchhoff technique to include the transverse shear strains. It has six mechanical degrees of freedom per node with no difficulties in the drilling rotations and one electrical degree of freedom per finite element. The electric field is assumed constant across the thickness of each piezoelectric layer. The bending and membrane consistent mass matrices are derived for applications on structural dynamics. Since this finite element was firstly developed to allow the active vibration control of the flexible multibody components, which formulation may be based on the diagonalization of the mass matrix, a comparison of a set of numerical results is obtained using a mass matrix diagonalization. The numerical results obtained by this finite element correlated well with other published results.