A Node-Based Element for Analysis of Planar Piezoelectric Structures

Abstract

A novel node-based smoothing element for triangular and quadrilateral meshes is presented for static analysis of planar piezoelectric structures. In contrast to the smoothed finite element formulation that was based on sub-cells within an original quadrilateral element, this new method transforms a general original finite element mesh into a mesh of new smoothing cells individually associated with a single node which is termed as node-based elements. The displacement fields of the element are approximated by the linear interpolation functions of the original mesh while the approximations of mechanical strains and electric potential fields are normalized using the stabilized conforming nodal integration technique over each node-based element. This technique allows field gradients to be directly computed from interpolating shape functions by using boundary integrations along each edge of the node-based element. Furthermore, the present elements do not require any additional degrees of freedom and are insensitive to bad element shapes in the original mesh. Several numerical examples and comparative studies with other numerical results as well as analytic solutions in the literature are carried out in order to demonstrate the simplicity, efficiency and reliability of the novel elements.