Modeling and Design of Cantilevered Multistable Laminates Under Elastic Loading

<p dir="ltr">Multistability enables the design of structures capable of inherent shape change and a high degree of programmability. Multistable structures exhibit multiple stable shapes with different geometrical and mechanical properties, which do not need external actuation to maintain their current configuration, making them highly pertinent across several engineering disciplines. Multistability can be induced in a structure either by geometry or by prestrain fields. In this work, we consider one particular type of multistable structures referred to as multistable composite laminates. These laminates derive their multistability from a residual thermal strain developed during the manufacturing process owing to their unsymmetric layups. Multistable laminates display immense potential as control devices for aircraft morphing because of their minimal weight, high strength, and shape adaptability. Traditional aircraft achieve aerodynamic control during flight via mechanical control surfaces, such as ailerons and flaps. These conventional mechanisms usually serve a single purpose, add mechanical complexity in the form of hinges and joints, and create discontinuities in the surface, resulting in increased drag, which is detrimental to the aircraft's performance. Replacing these control surfaces with multistable laminates can be beneficial in reducing system complexity, maintaining surface continuity, and achieving reversible shape and stiffness change without compromising the structure's load-carrying capacity and aerodynamic efficiency. However, the implementation of these laminates into morphing structures requires sophisticated design and analysis techniques to fully understand their behavior and aerodynamic performance. In this work, we develop various analytical and numerical models to study the behavior of multistable laminates with cantilever-type boundary conditions (BCs) under elastic loading. In terms of analytical modeling, we rely on energy-based methods to develop reduced-order models to capture the static stable shapes, stiffnesses, and deformations of the laminates under different loading conditions. In terms of numerical modeling, we employ the finite element (FE) method to analyze these laminates and optimize their design to achieve targeted characteristics. </p><p><br></p><p dir="ltr">The behavior of multistable laminates is highly affected by the boundary constraints imposed during their assembly into larger compliant systems. To understand this, the effects of geometry, prestress, and boundary conditions on the stability of unsymmetric laminates are investigated using an extensible shell model to understand the reason behind their loss of bistability due to clamping. This model is utilized to develop a criterion capable of determining the geometrical requirements to retain bistability in the presence of clamped BCs. Based on the findings from this study, two-section laminates comprising symmetric and unsymmetric lamination regions are proposed as a solution to maintaining multistability after clamping. This design is further improved by introducing slit cutouts, which enable bistability retention over a wider range of geometries, including those with low aspect ratios (length/width). We then evaluate the aero-structural response of these slitted bistable laminates in different flow conditions using wind tunnel tests and static aeroelastic analyses. This work also considers the rich dynamic characteristics of cantilevered multistable composites for energy harvesting applications. In particular, bistable laminates with embedded macro-fiber composite (MFC) piezoelectric transducers are studied to enable power conversion from mechanical vibrations under incident wind flow. A novel concept for a wind energy harvester employing cantilevered bistable composites with embedded MFCs and a tip cylinder is presented. This harvester leverages the distinct dynamical behavior of each of its stable states to generate power from vortex-induced vibrations at multiple flow speed ranges. A reduced-order model of the harvester is developed to analytically calculate the power output, and potential design modifications are suggested for improved performance through an optimization study. A physical demonstrator based on this bistable harvester concept is manufactured and tested in a wind tunnel to validate results from the model. In addition to acting as sensors and energy harvesters, the MFCs can also be used as actuators by converting an input voltage into output displacements. An analytical model to predict static actuation voltages for switching between the stable states of cantilevered bistable laminates using MFCs is presented. Finally, some industrial applications for the novel designs developed as part of this dissertation are discussed along with possible future directions for this work.</p>