Deformations of active flexible rods with embedded line actuators

The 3-D formulation of flexible rods with embedded line actuators is presented in this paper. Both the rod and the line actuator are assumed to be initially curved and relatively positioned in an arbitrary way. The deformed configurations of the rod and actuator are connected by assuming that the principal planes of the rod remain plane and inextensible in the deformed configuration. The resultant forces and moments in the rod and actuator are found by solving the equilibrium equations for both the rod and actuator and applying continuity of tractions on the rod-actuator interface. The formulation is reduced to 2-D and applied to the case of a Shape Memory Alloy (SMA) fiber embedded in a cylindrical rod. The deformed shapes of the rod under repeated thermal actuation and the resulting shape memory loss due to the development of residual stresses are evaluated. Finally, the inverse problem of finding the required actuation force and initial curvature, to acquire a predetermined deformed shape, is solved in closed form for the 2-D case.

Deformations of active flexible rods with embedded line actuators Conference Paper