A mathematical model for smart functionally graded beam integrated with shape memory alloy actuators

Abstract

This paper presents a theoretical study of the thermally driven behavior of a shape memory alloy (SMA)/FGM actuator under arbitrary loading and boundary conditions by developing an integrated mathematical model. The model studied is established on the geometric parameters of the three-dimensional laminated composite box beam as an actuator that consists of a functionally graded core integrated with SMA actuator layers with a uniform rectangular cross section. The constitutive equation and linear phase transformation kinetics relations of SMA layers based on Tanaka and Nagaki model are coupled with the governing equation of the actuator to predict the stress history and to model the thermo-mechanical behavior of the smart shape memory alloy/FGM beam. Based on the classical laminated beam theory, the explicit solution to the structural response of the structure, including axial and lateral deflections of the structure, is investigated. As an example, a cantilever box beam subjected to a transverse concentrated load is solved numerically. It is found that the changes in the actuator's responses during the phase transformation due to the strain recovery are significant.

Force-displacement characteristics of simply supported beam laminated with shape memory alloys

“…The above analysis suggests that the area of hysteresis loop can achieve the maximum when the phase transformation parameters meet a certain relationship (9). That is to say that the perfect damping effect can be obtained through choosing SMA material with suitable parameters.…”

“…They have been widely applied in mechanical engineering, civil engineering, aerospace engineering and so on [1][2][3][4][5][6]. At present, in the static and dynamic analysis of engineering structure, research on SMA composite structure mainly involves active and passive control of the deformation, vibration and noise of the beam and shell structure, of which the main composite structures adopted are: (1) SMA films are laminated with a substrate [6][7][8][9][10]; (2) SMA wires and alloying pellets are embedded into a substrate [11,12]; (3) SMA fiber woven layer composite structures [13]. For the first laminated structure, the SMA is usually used as a surface, while the other elastic material is used as a substrate.…”

Modal Performance of Two-Fiber Orthogonal Gradient Composite Laminates Embedded with SMA

“…Birman [21] proposed the advantage of the sinusoidal distribution of SMA fibers that results in a significant increase in the buckling load. Sepiani et al [22] found that changes in the thermally driven behavior of a shape memory alloy (SMA)/FGM actuator's responses during phase transformation due to strain recovery are significant. Asadi et al [23] and Babaee et al [24] both studied the nonlinear thermal buckling of an SMA layer and a functionally graded beam/plate on nonlinear elastic foundation.…”

Modeling the behavior of bilayer shape memory alloy/functionally graded material beams considering asymmetric shape memory alloy response

“…However, the authors did not provide analytical derivations for the moment-curvature relations. Another model based on the Euler-Bernoulli theory was proposed by Sepiani et al (2009) considering a variety of thermal loading cases. However, the authors assumed piece-wise linear moment and strain relations and considered the beam behavior during monotonic loading only.…”