PSI - Issue 24

Riccardo Panciroli et al. / Procedia Structural Integrity 24 (2019) 593–600

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R. Panciroli and F. Nerilli / Structural Integrity Procedia 00 (2019) 000–000

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The bistable panels have been modeled utilizing 8-nodes shell layered elements with [0 90] lamination sequence and five integration points through the thickness of each layer. Displacements and rotations of the central node of the panels have been fixed to avoid rigid motions, and a varying temperature has been applied to the panel uniformly. For a given combination of material, panel sizes, and thickness, there is a minimum cooling temperature necessary to introduce the bi-stability. Below such a threshold value the panel deforms in a stable configuration which recalls an hyperbolic paraboloid. Above the threshold value the plate might assume either one of the two stable configurations characterized by a cylindrical surface. Figure 3 shows the e ff ect of the post-curing cooling temperature on the final stable configuration of a square plate 150mm long and 1.3 mm thick with lamina properties as presented in Table 2. Results show that bi-stability is introduced in the laminate for cooling temperatures above 80K, and the overall curvature increases with the cooling gradient. In the following section we explore the possibility to utilize SMA wires to actuate the snap between the two stable configurations of antisymmetric composite panels. A recent work by Gandhi et al. (2018) proposed to actuate the panels by exploiting the two-way shape memory e ff ect of SMA wires. This implies that no prestrain needs to be introduced in the wires, as the wire is capable to indefinitely vary its length by switching between martensite and austenite phases. Here, we utilize the SMA wires presented before, which experimentally show a one-way shape memory e ff ect. This implies that wires must present an initial pseudoplastic residual deformation obtained by prestraining the wires. Another major di ff erence with the work by Gandhi et al. (2018) is that in our model the wires have been located on the outer surface of the panel, as if they were glued on the outside, while Gandhi et al. placed them on the mid-layer. Please note that the anti-symmetric nature of the bistable plate makes the mid-layer not to coincide with the neutral axis. Our approach is much closer to reality as the wires cannot be introduced in the plate at its production stage, since the temperatures during the curing process are higher than A f . Such temperatures would activate the wires to recover the prestrain, vanishing their actuation capabilities. Wires thus need to be glued to the outer surface of the panel at a second stage, and in a prestrained condition. Further, locating the wires away from the neutral axis eases the snap-back phenomena as the bending moment is enhanced this way. 4. Actuation of the panel through SMA wires

Fig. 4. Discretization of the numerical model through shell and beam elements (left), and its corresponding three dimensional visualization (right).

The numerical model is comprised by layered shell elements for the plate, and beam elements for the wire. The panel has been modeled through an equally spaced N by N grid, whereby beam elements have been superposed to the longitudinal edges of the shell elements. This way, we obtained a set of N − 1 equally spaced wires on the external surface of the panel. The beam elements share their nodes with the shell elements. Therefore, to e ff ectively locate them to the outer surface we applied an o ff set to their cross-sectional area to fix their location. Figure 4 shows the actual mesh composed by shell and beam elements, and its corresponding three-dimensional representation. To infer the initial residual pseudoplastic deformation to the wires, we followed the approach presented in Mizzi et al. (2019), which relies on the Birth & dDeath option. The numerical scheme to simulate of the morphing structure reflects the following steps: