Nonlinear Stress Analysis of SMA Beam Based on the Three-dimensional Boyd-Lagoudas Model Considering Large Deformations

In this study, a nonlinear superelastic bending of shape memory alloy (SMA) beam with consideration of the material and geometric nonlinearity effects which are coupled with each other, has been investigated. By using the Timoshenko beam theory and applying the principle of virtual work, the governi...

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Main Authors: R. Zamani, M. Botshekanan Dehkordi
Format: Article
Language:English
Published: Bu-Ali Sina University 2018-03-01
Series:Journal of Stress Analysis
Subjects:
Online Access:https://jrstan.basu.ac.ir/article_2225_6cbfa3e79539a671793e410756447910.pdf
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author R. Zamani
M. Botshekanan Dehkordi
author_facet R. Zamani
M. Botshekanan Dehkordi
author_sort R. Zamani
collection DOAJ
description In this study, a nonlinear superelastic bending of shape memory alloy (SMA) beam with consideration of the material and geometric nonlinearity effects which are coupled with each other, has been investigated. By using the Timoshenko beam theory and applying the principle of virtual work, the governing equations were extracted. In this regard, Von Karman strains were applied to take the large deflections into account. Via Boyd-Lagoudas 3D constitutive model, SMA was  simulated, which was properly reduced to two dimensions. With the development of an iterative nonlinear finite elementmodel, and for the purpose of obtaining characteristic of finite element beam, the Galerkin weighted-residual method was applied. In this study, by considering the different force and support conditions for the SMA beam, their effects on the distribution of martensitic volume fraction (MVF) and stress distribution were investigated. The obtained results indicate that the magnitude of MVF and consequently the level of hysteresis increases, which leads to the reduction of the modulus of elasticity and the strength of the material and therefore the deflection of SMA beam increases consequently. To validate the proposed formulation, the results were compared with other experimental and numerical results and a good agreement was achieved between outcomes.
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spelling doaj.art-eef371c87d884998bc4d11268d0142162022-12-21T20:29:26ZengBu-Ali Sina UniversityJournal of Stress Analysis2588-25972588-30542018-03-0122193010.22084/jrstan.2018.15454.10382225Nonlinear Stress Analysis of SMA Beam Based on the Three-dimensional Boyd-Lagoudas Model Considering Large DeformationsR. Zamani0M. Botshekanan Dehkordi1Mechanical Engineering Department, Shahrekord University, Shahrekord, Iran.Mechanical Engineering Department, Shahrekord University, Shahrekord, Iran.In this study, a nonlinear superelastic bending of shape memory alloy (SMA) beam with consideration of the material and geometric nonlinearity effects which are coupled with each other, has been investigated. By using the Timoshenko beam theory and applying the principle of virtual work, the governing equations were extracted. In this regard, Von Karman strains were applied to take the large deflections into account. Via Boyd-Lagoudas 3D constitutive model, SMA was  simulated, which was properly reduced to two dimensions. With the development of an iterative nonlinear finite elementmodel, and for the purpose of obtaining characteristic of finite element beam, the Galerkin weighted-residual method was applied. In this study, by considering the different force and support conditions for the SMA beam, their effects on the distribution of martensitic volume fraction (MVF) and stress distribution were investigated. The obtained results indicate that the magnitude of MVF and consequently the level of hysteresis increases, which leads to the reduction of the modulus of elasticity and the strength of the material and therefore the deflection of SMA beam increases consequently. To validate the proposed formulation, the results were compared with other experimental and numerical results and a good agreement was achieved between outcomes.https://jrstan.basu.ac.ir/article_2225_6cbfa3e79539a671793e410756447910.pdfSMA beamSuperelastic bendingBoyd-Lagoudas modelTimoshenko beam theoryNonlinear FEM
spellingShingle R. Zamani
M. Botshekanan Dehkordi
Nonlinear Stress Analysis of SMA Beam Based on the Three-dimensional Boyd-Lagoudas Model Considering Large Deformations
Journal of Stress Analysis
SMA beam
Superelastic bending
Boyd-Lagoudas model
Timoshenko beam theory
Nonlinear FEM
title Nonlinear Stress Analysis of SMA Beam Based on the Three-dimensional Boyd-Lagoudas Model Considering Large Deformations
title_full Nonlinear Stress Analysis of SMA Beam Based on the Three-dimensional Boyd-Lagoudas Model Considering Large Deformations
title_fullStr Nonlinear Stress Analysis of SMA Beam Based on the Three-dimensional Boyd-Lagoudas Model Considering Large Deformations
title_full_unstemmed Nonlinear Stress Analysis of SMA Beam Based on the Three-dimensional Boyd-Lagoudas Model Considering Large Deformations
title_short Nonlinear Stress Analysis of SMA Beam Based on the Three-dimensional Boyd-Lagoudas Model Considering Large Deformations
title_sort nonlinear stress analysis of sma beam based on the three dimensional boyd lagoudas model considering large deformations
topic SMA beam
Superelastic bending
Boyd-Lagoudas model
Timoshenko beam theory
Nonlinear FEM
url https://jrstan.basu.ac.ir/article_2225_6cbfa3e79539a671793e410756447910.pdf
work_keys_str_mv AT rzamani nonlinearstressanalysisofsmabeambasedonthethreedimensionalboydlagoudasmodelconsideringlargedeformations
AT mbotshekanandehkordi nonlinearstressanalysisofsmabeambasedonthethreedimensionalboydlagoudasmodelconsideringlargedeformations