High-performance four-node shell element with piezoelectric coupling for the analysis of smart laminated structures

A new four-node bilinear shell element with full piezoelectric coupling is presented. It can be used for the analysis of light-weight smart structures (adaptive structures), i.e. laminated composite structures with piezoelectric patches attached to its surface or embedded within the laminated layers. The piezoelectric patches can be both passive (sensors) or active (actuators). The element has been successfully integrated into ANSYS 7.1 and thus can take full advantage of all capabilities of this commercial package, e.g. the connection to electric circuit elements, so far within the scope of linear problems. The element is a continuum-based degenerated solid shell element based on the Reissner–Mindlin theory of plates. It uses the modification of the enhanced assumed strain (EAS) theory for the in-plane strains together with the discrete shear gap method for the transverse shear strains, hence it is free of both membrane locking and shear-locking in bending. It has six mechanical degrees of freedom at each node without difficulties in the drilling rotations, and up to six voltage degrees of freedom. A special logic has been implemented so as to allow for a natural description of the electric interconnections between the piezoelectric layers. The element passes the structural patch tests from the standard set of tests proposed by MacNeal and Harder (Finite Element Anal. Design 1985; 1:3–20) including warped geometry problems. The piezoelectric behaviour was verified by comparing it with analytical solutions for plannar and curved geometry. A further validation was made by comparison with experimental measurements of harmonic response of actuated beam having both active and passive piezoelectric patches. A good agreement of the results was achieved. It can be concluded that the combination of the theories used makes this element robust and reliable. Copyright q 2006 John Wiley & Sons, Ltd.