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Thermo-electro-mechanical modeling and structural response of a flexible beam with external SMA actuators

A thermo-electrical and thermo-mechanical model is developed to predict a shape memory alloy (SMA) tendon-actuated compliant beam structure. A geometrically non-linear static analysis is first carried out to investigate the deformed shape of a flexible beam with a SMA tendon actuated electrically. It is found that, when the beam tip deflection is less than 10% of its length, an approximate linear beam model is appropriate, allowing the use of linear beam theory in modeling the dynamic structural response. While the model with nonlinear beam theory is still preferred in model prediction, identification and for full understanding of structure behaviors. The actuation force applied by the SMA actuator to the beam is evaluated by using a thermodynamically based thermomechanical constitutive model for SMA. To calculate the temperature history in the SMA actuator for given electrical current input, the heat conduction equation in the SMA actuator is solved with the electrical resistive heating being modeled as a distributed heat source. Finally, the three steps in the formulation are connected through an iterative scheme that takes into account the static equilibrium of the beam, thus translating an input electrical current history into a beam strain output. The predictions of the proposed model are correlated with experimental results.