Structural modeling of SMA fiber hybrid active thin-walled composite beams

The constitutive equations relating cross-sectional loads (forces and moments) to cross-sectional displacements (stretching, bending, twisting) of thin-walled laminated beams with integral shape memory alloy (SMA) active fibers is presented. The variational asymptotic method is used to formulate the force-deformation relationships equations accounting for the presence of active SMA fibers distributed along the cross-section of the beam. The constitutive relationships for evaluation of the properties of a hybrid SMA composite ply are obtained following the rule of mixtures. The analytical expressions of the actuation components for the active beam are derived based on Tanaka’s constitutive equation and Lin’s linear phase transformation kinetics for SMA fiber. The general form of constitutive relation is applied to the cases of extension-twist coupling, corresponding to Circumferentially Uniform (CUS) and bending-twist coupling, corresponding to Circumferentially Anti-Symmetric (CAS). The present analysis extends the previous work done for modeling generic passive thin-walled laminated beams. Numerical results show that significant extension, bending and twisting deflection occur during the phase transformation due to SMA actuation. The effects of temperature on structural response behavior during phase transformation from martensite to austenite are significant. The effects of the volume fraction of the SMA fiber, the martensitic residual strain and ply angle are also addressed.