Analytical investigation of structurally stable configurations in shape memory alloy-actuated plates

Abstract

a b s t r a c tStrains produced by active materials embedded in plates have been extensively used to manipulate the shape of surface-like engineering structures. Shape memory alloys (SMAs) are active materials that provide a significant amount of strain under large stresses, a characteristic of great utility in such morphing structures. In this work, an analytical approach to approximate the deformation of plates with SMA constituents is developed via the Rayleigh-Ritz method. An additive set of kinematically admissible displacement fields with unknown coefficients is used to describe the plate displacement field. The total potential energy is then calculated using the displacement field, loading conditions, and constitutive relations for the plate layer(s) composed of SMA wire meshes, dense SMA films, and/or elastic material. The unknown coefficients are then found via minimization of the total potential energy. This approach provides closed-form expressions for the approximate deformation of the plates including multistable configurations. The response of circular SMA-based plates is studied herein. The results show that temperature fields with a linear variation in the radial direction induce multistable configurations in which the plate Gaussian curvature is determined by the direction of the temperature gradient. An alternative inversion of the proposed approach is used to directly compute the temperature field required to morph a plate towards a prescribed goal shape. The obtained closed-form expressions show good agreement with detailed non-linear finite element analysis simulations. The proposed approach provides analysts with a low computational cost and relatively simple implementation to assess the potentially stable configurations of SMA-based plates under given loading conditions. Knowledge of such stable configurations is very valuable in the design of SMA-based morphing structures.

Thermally Driven Morphing and Snap-Through Behavior of Hybrid Laminate Shells

“…(1-7) = 0, which is subsequently solved numerically using a Newton-type scheme. We note that Betts et al 39 and Hernandez et al 40 have reported success in obtaining closed form solutions for specific geometry and constitutive properties. Second variations are used to determine the stability of each of the equilibria as per the procedure described in Hyer's seminal work.…”

Finite Element Method on Shape Memory Alloy Structure and Its Applications

“…(11), and phase-transition modulus equation, Eq. (18). A uniform tensile SMA bar, shown in Figure 2(a), is numerically simulated to verify the MATLAB program.…”

“…Some researchers [15][16][17] implemented finite element analysis on SMA structures based on the secondary development functions of ANSYS. Many researchers [18][19][20][21] implemented finite element simulation on SMA structures using the secondary development functions of ABAQUS. Although some universal finite element software can simulate the thermo-mechanical behaviors of SMA based on their secondary development functions, the problems of convergence often occur when a SMA structure undergoes large and uneven deformations.…”

Modeling and design optimization of shape memory alloy-enabled building skins for adaptive ventilation

“…The two main components of the adaptive skins are a flexible panel and SMA wires. The capability of SMAs in wire form to provide controlled deformation to plates and shell systems has been demonstrated in previous works addressing self-foldable origami sheets (Halbert et al, 2016;Lee et al, 2013;Peraza Hernandez et al, 2014, compliant mechanisms Hwang and Higuchi, 2015), and multistable plates (Dano and Hyer, 2003;Peraza Hernandez et al, 2015); hence, SMAs are expected to be a viable option for panel-based adaptive skins. Figure 1(a) shows the working principle of the presented adaptive skins.…”