Coupled Deflection Analysis of SMA Fiber Hybrid Composite Active Blade

Abstract

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 was presented. The variational asymptotic method was 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 were obtained following the rule of mixtures. The analytical expressions of the actuation components for the active beam were derived based on Tanaka’s constitutive equation and Lin’s linear phase transformation kinetics for SMA fiber. The general form of constitutive relation was applied to the case of stretching-twist coupling, corresponding to Circumferentially Uniform Stiffness (CUS). The present analysis extended the previous work done for modeling generic passive thin-walled laminated beams. Numerical results shown that significant stretching 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 were also addressed

An analytical model for shape memory alloy fiber-reinforced composite thin-walled beam undergoing large deflection

“…represents the warping function, where G is the classical torsional-related warping, g i (i = 1, 2, 3) are extension, torsion, and bending warping functions, v (a) 1 (s) is the displacement component directly associated with SMA actuation. 14,15 The following von Ka´rma´n-type nonlinear straindisplacement relations are used…”

“…where superscript DT represents the forces or moments associated with the temperature change. 14,15 The variation of total strain energy for the beam can be represented as…”

“…The two-dimensional analysis of the cross section for an anisotropic thin-walled single beam with embedded SMA fibers is carried out on a variational-asymptotical formulation. 14,15 Assume that SMA fibers are orientated along the arbitrarily direction. From Tanaka and Nagaki's constitutive relation for SMA layers, the axial direction stress s SMA can be determined as follows…”

“…1 (s) is the displacement component directly associated with SMA actuation. 14,15 The following von Ka´rma´n-type nonlinear straindisplacement relations are used…”

“…He et al 13 presented an analytical model of thin tube with SMA wires winded and pasted on the outside surfaces of the thin wall tube. Ren et al 14,15 developed a formulation for the active deformation analysis of closed-section composite thinwalled beams with SMA fibers embedded. The general form of constitutive relation was applied to the case of extension-twist coupling and bending-twist coupling, respectively.…”