Finite-Element Analysis of an Antagonistic Bistable Shape Memory Alloy Beam Actuator

A finite-element (FE) analysis of the active bistability of an antagonistic shape memory alloy (SMA) beam actuator of TiNiCu is presented. The actuator comprises two coupled SMA beams that are clamped at both ends and coupled in their center by a spacer having different memory shapes being deflected in opposite out-of-plane directions. The actuator is characterized by two equilibrium positions. To determine bistable behavior as a function of geometrical parameters, a force criterion is defined by the coupling force of the beams in austenitic and martensitic states. Bistable behavior is achieved, if the coupling force does not change sign in the entire displacement range. This implies that the austenitic beam dominates the opposing martensitic beam. Thus, selective heating of the SMA beams results in a snap-through motion of the coupled SMA beams. Depending on which of the two beams is in austenitic state, either of the two equilibrium positions is reached without the need for an external force. It is demonstrated that geometrical parameters like initial predeflection and spacer length have a crucial effect on the bistable performance. Bistable regions as well as critical limits characterized by geometry-dependent stability ratios, beyond which the actuator's performance becomes monostable, are identified.