Abstract

Shape-adaptive or morphing capability in both aerospace structures and wind turbine blade design is regarded as significant to increase aerodynamic performance and simplify mechanisms by reducing the number of moving parts. The underlying bistable behavior of asymmetric cross-ply composites makes them a suitable candidate for morphing applications. To date, various theoretical and experiential studies have been carried out to understand and predict the bistable behavior of asymmetric laminates and especially the curvature obtained in their stable configurations. However, when the bi-stable composite plate is integrated with shape memory alloy wires to control the curvature and to snap from a stable configuration to the other (shape memory alloy composite, SMAC), the identification of the design parameters, namely laminate edge length, ply thickness and ply orientation, is not straightforward. The aim of this article is to present the formulation of an optimization problem for the parameters of an asymmetric composite laminate integrated with pre-stressed shape memory alloys (SMA) wires under bi-stability and a minimum deflection requirement. Wires are modeled as an additional ply placed at the mid-plane of the composite host plate. The optimization problem is solved numerically in MATLAB and optimal design variables are then used to model the SMAC in ABAQUS™. Finite element results are compared against numerical results for validation.

Highlights

  • IntroductionMorphing structures applications are of interest in both aerospace structures [1] and wind turbines [2], which take benefit of significant shape changes to increase performance and efficiency

  • Morphing structures applications are of interest in both aerospace structures [1] and wind turbines [2], which take benefit of significant shape changes to increase performance and efficiency.Asymmetric composite laminates (ACL) may be formulated such that they possess two stable shapes, each of which is a natural equilibrium position

  • The appearance of the Martensite Volume Fraction (MVF), ξ, and the Transformation Strain (TRNS), t, in the stress-strain relation for the epoxy/shape memory alloys (SMA) ply in Equation (26) manifest the presence of the SMA wires on the resultant force developed inside the epoxy/SMA ply

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Summary

Introduction

Morphing structures applications are of interest in both aerospace structures [1] and wind turbines [2], which take benefit of significant shape changes to increase performance and efficiency. Niknami et al [23] investigated the effect of induced heat generations on impact responses and phase transformations of hyrbid SMA composite plate through proposing a refined Helmholtz free energy expression and refined constitutive and contact laws, in addition to employing a return-map Newton-Raphson method for enhancement of the numerical solution algorithm. Moving on from the work done in [25], the aim of the present study is to predict the optimal design variables for an asymmetric, square laminate with embedded SMA wires such that the laminate can attain a desired stable configuration after the cure cycle and a second stable configuration is admissible, that can be attained by snap from the first one actuated with the help of SMA wires. The accuracy of the optimal design is verified against SMAC model implemented in ABAQUS to predict the shape after curing and the response of the model

Constitutive Model of SMA Wires
Mathematical Modelling for Composite Laminate
Integration of SMA Wire in Composite Laminate
Optimization of SMAC
Constrained Optimization Problem
Objective Function
Deflection and Bistability Constraint
Simulation of Uniaxial Behavior of an SMA Wire
Objective
FE Simulation of SMAC
Conclusions
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