PSI - Issue 24

Alessandro Pirondi et al. / Procedia Structural Integrity 24 (2019) 455–469 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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way to produce a plate with two shapes, each one being a natural equilibrium position where the ACL can settle. The bi-stabilty of ACLs is related to the non-zero coupling terms in the laminate stiffness matrix and to the residual stress field that develops after curing due to the mismatch in coefficient of thermal expansion in the unsymmetric stacking sequence. The application of bending and twisting moments can therefore promote the development of a new internal stress equilibrium at a second stable configuration. The use of ACLs to produce a bi-stable morphing structure at room temperature was first exploited by Hyer (1981a) and Hyer (1981b). Jun and Hong (1990) modified Hyer’s theory by taking into account in-plane shear strain. Schlecht and Schulte (1999) firstly provided the bi-stable behavior of asymmetric laminates using MARC Finite Element Analysis (FEA) software. Tawfik et al. (1999) presented a finite element approach using ABAQUS™ to predict the unsymmetric laminate shapes under t hermal curing stresses. The concept of embedding SMA actuation in a composite structure was introduced by Rogers and Robertshaw (1988). Birman et al. (1996) illustrate that SMA fibres embedded within the layers of a composite plate can significantly enhance its global resistance to low-velocity impact and the effectivness of SMA fibre can be further improved by optimizing their distribution throughout the plate. Turner (2000) examined the thermoelastic response of SMA hybrid structures by finite element analysis. A different finite element method was used by Tawfik et al. (2002) to examine the stability behavior of SMA composite panels. In addition, Von Karman nonlinear strains were considered in the formulations. Dano and Hyer (2003) used a mechanism wherein, after SMA wires were stretched between a system of support above the laminate and upon electrical heating of the SMA wires, it could generate enough force to pull the tips of the supports toward each other, thereby cause the laminate to snap. The major underside was the arrangement that looked like cumbersome and impractical. Jung et al. (2010) fabricated a smart structure using shape memory alloy wires embedded into a hybrid composite. Ryu et al. (2011) verified actuation of asymmetric laminate using SMA spring actuator through the comparison between experiment and numerical simulation. Hassanli and Samali (2016) investigated the buckling of curved laminated composite panels reinforced with SMA fibers. Niknami et al. (2017) investigated the effect of induced heat generations on impact responses and phase transformations of hybrid 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. Gandhi et al. (2018) attempted to demonstrate the possibility to trigger the snap-through from one stable configuration to another by means of SMA wires embedded into the laminate, in the perspective of simplifying the manufacturing and operation of the SMAC. In that work, the laminate was modelled by finite elements (FE) in ABAQUS with shell elements with a stacking sequence [0 2 /90 2 ]. The SMA wires were modelled as truss elements with nodes coincident with the nodes of the composite shell. The SME was modelled in a simplified way using the effective coefficient of thermal expansion (ECTE) concept based upon nonlinear thermo-elasticity proposed by Turner et al. (2007). Though the results were positive, it was evident that a strong trial-and-error effort was necessary if all the possible design parameters, namely laminate size and layup, composite elastic constants, SMA wires number and thermomechanical behaviour, SMAC manufacturing cycle, were taken into account. Moving on from that work Gandhi et. al (2019) developed an optimization technique starting from the theoretical framework for optimization of bistable laminates without SMA wires of Betts (2012). The optimization study considered the design of bi-stable SMAC through variation in ply orientations, ply thickness (same for all plies) and laminate edge length to predict the shape after curing, assuming a square laminate like in Betts (2012). The MATLAB’s sequential quadrat ic programming method (Nocedal (1999)) was used to solve the optimization problem. The accuracy of the optimal design was verified against a corresponding finite element model, where the composite plate and the SMA wires were modelled as in Gandhi et al. (2018) but in this case a full thermomechanical constitutive model was used for SMA, that is available as a user-defined material model (UMAT ) for the ABAQUS™ 6.13 software (Lagoudas et al. (2003)). However, since initial conditions in terms of pre-strain and related stress could not be applied in ABAQUS to the one-dimensional truss elements used to represent SMA wires, a mixed solid-shell FE model is necessary where SMA wires and the surrounding composite region were modeled with tetraedral elements while the remainder of the SMAC is simulated with shell elements. The aim of this work is therefore to summarize and review critically the work done by the authors in the past two years to model and optimize a SMAC subjected to bi-stability and post-manufacturing deflection requirements and to present this last evolution.