Abstract
A layerwise hybrid strain based lower order flat triangular laminated composite shell finite element with piezoelectric effects has been developed and reported in this paper. This layerwise three-node triangular shell element is formed by stacking a lower-order flat triangular shell element with piezoelectric effects. In every node there are seven degrees of freedom (dof). These include three translational dof, three rotational dof, and one electric potential dof. The important drilling dof (ddof) is included in every node. The degenerated three dimensional solid assumption and the first order shear deformation theory (FSDT) were adopted. Consequently, shear and membrane lockings are eliminated. This feature is superior to those elements based on the displacement formulation. Explicit expressions for the consistent element mass and stiffness matrices were obtained by using the symbolic algebraic package, MAPLE V. Thus, it reduces considerably the computational time as opposed to those applying numerical matrix inversion and numerical integration for the derivation of element matrices.
Appendix 1C: Consistent Mass Matrix of Lower Order Triangular Shell Element
