An efficient facet shell element with layerwise mechanics for coupled electromechanical response of piezolaminated smart shells

In this work, an efficient four-node facet shell element is presented for analysis of doubly curved multilayered piezoelectric shells, based on an electromechanically coupled third order zigzag theory. It is motivated by the excellent performance of the shell element developed earlier by the authors for elastic laminated shells. The laminate theory not only incorporates a layerwise description of the inplane displacements but also accounts for the layerwise normal deformation due to the d(33)-effect of the piezoelectric layers. The number of primary displacement variables is, however, the same as for the smeared third order theory (TOT). A quadratic variation of the electric potential across the piezoelectric layers is assumed, while satisfying the equipotential condition of electroded piezoelectric surfaces using the concept of electric nodes. The performance of the element is assessed for the stress analysis under mechanical and electric potential loads, and for the free vibration response of hybrid piezolaminated deep shells in comparison with the three dimensional piezoelasticity based analytical and finite element solutions. The comparison shows excellent accuracy of the present element for the deflection, stresses, sensory potential, electric displacement and natural frequencies of hybrid shells made of composite as well as the highly inhomogenous soft-core sandwich laminates, for which the smeared TOT is shown to produce highly erroneous results. It is also shown to yield better accuracy than the other available elements of similar computational efficiency for hybrid composite shells.