Bending theory for laminated composite cantilever beams with multiple embedded shape memory alloy layers

2019 ◽  
Vol 30 (10) ◽  
pp. 1549-1568 ◽  
Author(s):  
Nguyen Van Viet ◽  
Wael Zaki ◽  
Rehan Umer
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Numerical Solutions ◽  
Phase Distribution ◽  
Solid Phase ◽  
Axial Stress ◽  
Laminated Composite ◽  
Beam Theory ◽  
Cantilever Beams ◽  
Element Analysis

In this article, a new analytical model is proposed for laminated composite cantilever beams consisting of multiple alternating superelastic shape memory alloy and elastic layers. The model is based on the Zaki–Moumni model for shape memory alloys combined with Timoshenko’s beam theory. The Zaki–Moumni model accounts for solid phase transformation as well as detwinning and reorientation of martensite under multiaxial thermomechanical loading conditions. Mathematical formulas are first derived to characterize the evolution of the solid phase structure within the beam with a prescribed load at the tip during loading and unloading. Analytical moment–curvature and shear force–shear strain relations are then obtained following the strength of materials approach. The present work is the first to fully develop the nonlinear expressions of the axial stress in terms of the distance from the neutral plane and to allow the description of the phase distribution in both the longitudinal and the transverse directions in the beam as the load evolves. The proposed model is validated against finite element analysis and high-accuracy numerical solutions. The influence of temperature and the number of shape memory alloy layers on the superelastic behavior of the laminate is also investigated.

A model for shape memory alloy beams accounting for tensile compressive asymmetry

2019 ◽  
Vol 30 (18-19) ◽  
pp. 2697-2715 ◽  
Author(s):  
Nguyen Van Viet ◽  
Wael Zaki ◽  
Ziad Moumni
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Solid Phase ◽  
Constitutive Relations ◽  
Beam Theory ◽  
Element Analysis ◽  
Proposed Model ◽  
The Finite Element Analysis ◽  
Tension And Compression ◽  
Asymmetric Shape

A new analytical model is derived for cantilever beams made from superelastic shape memory alloy and subjected to tip load. The deformation of the beam is described based on Timoshenko beam theory using constitutive relations that account for asymmetric shape memory alloy response in tension and compression. Analytical moment and shear force equations are developed and the position of the neutral axis and the different solid phase regions in the beam are tracked throughout a full loading–unloading cycle. Validation of the proposed model is carried out against data from the literature and from the finite element analysis considering tensile–compressive asymmetry in shape memory alloy behavior.

Analytical Model for a Functionally Graded Material/Shape Memory Alloy Laminated Composite Cantilever Beam

2018 ◽  
Author(s):  
Wael Zaki ◽  
N. V. Viet
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Analytical Model ◽  
Cantilever Beam ◽  
Functionally Graded Material ◽  
Laminated Composite ◽  
Functionally Graded ◽  
Concentrated Force ◽  
Element Analysis ◽  
Graded Material

Based on the ZM model for shape memory alloys, an analytical model is derived for a functionally graded material (FGM)/shape memory alloy (SMA) laminated composite cantilever beam subjected to concentrated force at the tip. The beam consists of a SMA core layer bonded to identical FGM layers on both sides. The FGM layer is considered to be elastic with an equivalent Young’s modulus related to those of the constituents by means of a power law. Phase transformation within the SMA layer is accounted for in deriving the analytical relations, which are validated against finite element analysis results.

Analytical model for a superelastic Timoshenko shape memory alloy beam subjected to a loading–unloading cycle

2018 ◽  
Vol 29 (20) ◽  
pp. 3902-3922 ◽  
Author(s):  
Nguyen Van Viet ◽  
Wael Zaki ◽  
Rehan Umer
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Analytical Model ◽  
Solid Phase ◽  
Three Dimensional ◽  
Element Analysis ◽  
Dimensional Finite Element ◽  
Three Dimensional Finite Element

We propose a new analytical model for a superelastic shape memory alloy prismatic cantilever beam subjected to a concentrated force at the tip. The force is gradually increased and then removed and the corresponding distribution of phase transformation fields in the beam is determined, analytically, in both the transverse and longitudinal directions. Analytical moment–curvature and shear force–shear strain relations are also derived during loading and unloading of the beam. The proposed model is validated against an exact numerical beam model as well as a three-dimensional finite element analysis model for the same beam, with very good agreement in each case. Moreover, an experiment is proposed and carried out to characterize the load–deflection response of a shape memory alloy beam under the same boundary conditions as those considered in deriving the model. The obtained response is in good agreement with the analytical model as well as three-dimensional finite element analysis simulations. The analytical method provides a direct mathematical way for describing the material and structural properties of the beam and the distribution of the different solid phase regions as they change under the influence of an applied load and allows the determination of details such as the boundaries of solid phase regions immediately and accurately using equations. The same would require postprocessing at possibly significant computational cost and personal effort if finite element analysis or similar numerical methods are used.

scholarly journals Parametric Random Vibration Analysis of an Axially Moving Laminated Shape Memory Alloy Beam Based on Monte Carlo Simulation

Materials ◽  
2022 ◽  
Vol 15 (2) ◽  
pp. 562
Author(s):  
Ying Hao ◽  
Ming Gao ◽  
Jiajie Gong
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Shape Memory Alloy ◽  
Shape Memory ◽  
Random Vibration ◽  
Random Perturbation ◽  
Laminated Composite ◽  
Beam Theory ◽  
Axial Forces ◽  
Axially Moving

The study of the bifurcation, random vibration, chaotic dynamics, and control of laminated composite beams are research hotspots. In this paper, the parametric random vibration of an axially moving laminated shape memory alloy (SMA) beam was investigated. In light of the Timoshenko beam theory and taking into consideration axial motion effects and axial forces, a random dynamic equation of laminated SMA beams was deduced. The Falk’s polynomial constitutive model of SMA was used to simulate the nonlinear random dynamic behavior of the laminated beam. Additionally, the numerical of the probability density function and power spectral density curves was obtained through the Monte Carlo simulation. The results indicated that the large amplitude vibration character of the beam can be caused by random perturbation on axial velocity.

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