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Galerkin Weighted Residual Method for Axially Functionally Graded Shape Memory Alloy Beams

Published online by Cambridge University Press:  02 December 2019

Z. T. Kang ,
Z. Y. Wang ,
B. Zhou Open the ORCID record for B. Zhou [Opens in a new window]  and
S. F. Xue
Z. T. Kang
Affiliation:
College of Pipeline and Civil Engineering China University of Petroleum (East China) Qingdao, China
Z. Y. Wang
Affiliation:
College of Pipeline and Civil Engineering China University of Petroleum (East China) Qingdao, China
B. Zhou*
Affiliation:
College of Pipeline and Civil Engineering China University of Petroleum (East China) Qingdao, China
S. F. Xue
Affiliation:
College of Pipeline and Civil Engineering China University of Petroleum (East China) Qingdao, China
*
*Corresponding author (zhoubo@upc.edu.cn)
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Abstract

This paper focus on the mechanical and martensitic transformation behaviors of axially functionally graded shape memory alloy (AFG SMA) beams. It is taken into consideration that material properties, such as austenitic elastic modulus, martensitic elastic modulus, critical transformation stresses and maximum transformation strain vary continuously along the longitudinal direction. According to the simplified linear SMA constitutive equations and Bernoulli-Euler beam theory, the formulations of stress, strain, martensitic volume fraction and governing equations of the deflection, height and length of transformed layers are derived. Employing the Galerkin’s weighted residual method, the governing differential equation of the deflection is solved. As an example, the bending behaviors of an AFG SMA cantilever beam subjected to an end concentrated load are numerically analyzed using the developed model. Results show that the mechanical and martensitic transformation behaviors of the AFG SMA beam are complex after the martensitic transformation of SMA occurs. The influences of FG parameter on the mechanical behaviors and geometrical shape of transformed regions are obvious, and should be considered in the design and analysis of AFG SMA beams in the related regions.

Keywords

Axially functionally graded beamshape memory alloyBernoulli-Euler beam theoryGalerkin weighted residual method
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 3 , June 2020 , pp. 331 - 345
Copyright
Copyright © 2019 The Society of Theoretical and Applied Mechanics

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