Analysis of Elastic and Viscoelastic Smart Flexible and Foldable Systems

Abstract

Smart or adaptive structures that use multifunctional materials to control the response of a structure have been of considerable interest in recent years. Some examples are foldable and flexible structures that can be actuated by non-mechanical stimuli (thermal, electrical, magnetic, solvent, light, etc.). This study presents analyses of smart flexible and foldable structures, such as slender beams and thin plates/shells integrated with distributed polarized piezoelectric patches. The studied smart flexible and foldable structures are undergoing large rotations and relatively small strains that are triggered by electro-mechanical actuations. The electric actuation is done by stimulating the bonded patches with electric voltages, while the mechanical actuation is in the form of prescribed external surface- and/or body forces. Both elastic and viscoelastic material responses are considered for the foldable and flexible host structures. For the behavior of piezoelectric material, a nonlinear electro-mechanical constitutive equation is taken into account to incorporate large electric field inputs. Two types of piezoelectric patches are considered, namely piezoelectric wafer and active fiber composites. The governing equation of the Reissner’s beam theory is first adopted in order to describe the large deformations of the flexible and foldable systems, and modified for the electro-active beams to derive analytical solutions. This study is then extended to 3-D deformation of plates and shells with considering bending and membrane stiffness subjected to large rotation and displacements. Co-rotational finite element method is used to numerically solve the governing equation of the smart flexible plates. Simulations of various shape changes in smart flexible and foldable systems are presented and parametric studies are also conducted in order to examine the effects of material and geometrical parameters on the overall performance of smart systems.