Controlling deformations of electro-active truss structures with nonlinear history-dependent response
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abstract
2017 Elsevier B.V. This study presents simulations of shape changing in active truss structures that undergo non-linear and time dependent response. The truss structure comprises of slender members with electro-active (piezoelectric) components joined by pins, allowing for large deformations due to rotations at the pins. A nonlinear time-dependent electro-mechanical constitutive model is considered for the piezoelectric components in the truss systems. In order to find the actuation inputs to achieve a desired shape, the required shape is defined with respect to reference configuration for a equivalent 3 dimensional continuum. The mapping between reference and current configuration is used to calculate the macroscopic strains in the continuum. The corresponding strains along the longitudinal axes of the truss members whose ends coincide with certain material points in the continuum are then calculated. The strains corresponding to the predefined shapes are achieved by applying electric field through the piezoelectric materials, and as a result the truss system undergoes the desired shape changes. The shape changing behaviors in electro-active truss systems are analyzed using a finite element (FE) method, incorporating nonlinear material and geometry. Numerical implementation of the active truss structures is also presented. Two types of truss configurations are considered which are planar and beam configurations. The planar configuration is formed by arrangement of cubical truss elements while the beam configuration consists of several tetrahedral truss elements. Several shape configurations of the planar and beam truss structures are shown as examples. While considerable amount of work has been done with piezo-actuated truss systems under the assumption of linear piezoelectric response, we study the influence of the nonlinear hysteretic electro-mechanical behavior and highlight the differences in the deformations of the truss structures when the nonlinear and time-dependent electro-mechanical and linear electro-mechanical models are considered for the piezoelectric components.
