Finite element models for laminated shells with actuation capability

Abstract

The formulation of the adaptive shell finite element, developed by the authors in the recent years for the 4-node element, is here extended by setting up new 9-node and 16-node elements. An active layer––made by a piezoelectric material or a similar active medium––is assumed to be included in a stacking sequence of a laminated shell. The actuation capability of the layer is represented by an in-plane assigned strain field that can be thought of as being produced by the converse piezoelectric effect or other induced strain actuation mechanism, like the classical thermoelastic effect. In this way the actuation mechanism is included in a general formulation of shear deformable shell element based on the “mixed interpolation tensorial component” approach, developed by K.J. Bathe, that is known to result into very effective elements. 4-node, 9-node and 16-node are compared in terms of convergence for several assumed cases. Comparisons with closed form solutions, when available, and numerical results allow to verify the accuracy of the formulation and to check the predicting capability of the elements.