A corotational formulation for the static nonlinear analysis of piezoactuated shells

Piezoelectric sensors and actuators have been widely used in applications including structural vibration control, shape control, energy harvesting. A large amount of works con-cerns the analysis of piezoactuated structures under small displacements assumption, whereas less attention has been devoted to geometrically nonlinear analyses. In many applications (e.g., energy harvesting, shape control of deployable and inflatable structures, piezoelectric valves) the hypothesis of small displacements may not be accurate enough and geometric nonlineari-Ties should be accounted for. Dealing with fully nonlinear formulations leads to complex and potentially demanding analyses, and calls for special attention in the formulation of piezoelec-Tric constitutive relationships. However, geometrical nonlinearities are often mostly related to finite rotations and consequent large displacements rather than large strains. Accordingly, fi-nite strain models may not be necessary for an accurate analysis of piezoactuated structures, whereas large rotations should be accurately accounted for. The corotational formulation, based on the idea of separating large rigid body motions from small strain producing ones, is ideally suited to treat those situations. In this work a novel polar decomposition based coro-Tational formulation for the static analysis of laminated piezoelectric shells is proposed. The small-strain core element formulation here adopted is based on a laminate theory combining single-layer assumptions for the displacement field with a layerwise representation for the elec-Tric potential. A new facet-shell corotational finite element is developed, and its performance is assessed by comparison with benchmark problems available in the literature. The compar-ison shows excellent agreement, highlighting satisfying accuracy and convergence rate of the proposed element.