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

作者：Sepiani H^*; Ebrahimi F; Karimipour H

来源：Journal of Mechanical Science and Technology, 2009, 23(12): 3179-3190.

DOI：10.1007/s12206-009-0919-x

• Shape memory alloy (SMA)
• Functionally graded material (FGM)
• Smart actuator beam
• Classical laminated beam theory (CLBT)

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.

• 出版日期2009-12