On the one-dimensional modeling of camber bending deformations in active anisotropic slender structures

The paper presents a one-dimensional model for anisotropic active slender structures that captures arbitrary cross-sectional deformations. The 1-D geometrically-nonlinear static problem is derived by an asymptotic reduction process from the equations of 3-D electroelasticity. In addition to the conventional (bending–extension–shear–twist) beam strain measures, it includes a Ritz approximation to account for arbitrary deformation shapes of the finite-size cross-sections. As a particular case, closed-form analytical expressions are derived for the linear static equilibrium of a composite thin strip with surface-mounted piezoelectric actuators. This solution is based on a boundary-layer approximation to the static equilibrium equations in regions where Saint-Venant’s principle for elastic bodies cannot be applied and includes camber bending deformations to account for the local bimoments induced by the distributed actuation in a finite-width strip.