Analysis of controlled beam deflections using SMA wires

In this paper the active control of beam deflection through heating and cooling of Shape Memory Alloy (SMA) wires is examined. A phenomenological constitutive law for SMA wires is coupled with beam theory to provide predictions of beam shape upon temperature change in the SMA actuator. Both the linear and nonlinear beam theory are presented, enabling calculation of large deflections. Examples for a single wire attached at the tip of a uniform beam are given, but the procedure can easily be generalized for other configurations and utilized in control algorithms. Issues of design constraints for shape control with shape memory wires are addressed and the model is qualitatively verified by experiments.