Modeling of a Flexible Beam Actuated by Shape Memory Alloy Wires

A thermomechanical model is developed to predict the structural response of a flexible beam with shape memory alloy (SMA) wire actuators. A geometrically nonlinear static analysis is first carried out to investigate the deformed shape of a flexible cantilever beam caused by an externally-attached SMA wire actuated electrically. The actuation force applied by the SMA actuator to the beam is evaluated by solving a coupled problem that combines a thermodynamic constitutive model of SMAs with the heat conduction equation in the SMA and the structural model of the beam. To calculate the temperature history of the SMA actuator for given electrical current input, the heat transfer equation is solved with the electrical resistive heating being modeled as a distributed heat source along the SMA wire. The steps in the formulation are connected together through an iterative scheme that takes into account the static equilibrium of the beam and the constitutive relation of SMAs, thus translating an electrical current history input into beam strain output. The proposed model is used to simulate the experimental results, thus demonstrating the feasibility of using SMA actuators for shape control of active flexible structural systems.