Instabilities in Elastic and Magneto-Elastic Beams and Shells: from Shell Buckling to the Design of a Programmable Braille Reader

In this thesis, we conduct a comprehensive investigation into structural instabilities of both elastic and magneto-elastic beams and shells, resulting in a creative proposal to design a programmable braille reader. Methodologically, we combine numerical simulations using the finite element method, precision model experiments, and theoretical modeling. Through our studies, we enhance the understanding of fundamental aspects of the longstanding problem of imperfection-sensitive shell buckling. We also show the potential for groundbreaking applications in functional magneto-active structures.First, we examine the effect of defect geometry on the buckling strength of pressurized spherical shells. A comparative study between dimpled and bumpy Gaussian defects reveals that shells with the latter exhibit higher knockdown factors than their dimpled counterparts. An interpretation based on curvature profiles adds support to the findings.Second, we address the importance of imperfection sensitivity in predicting the buckling of spherical shells, a canonical challenge in structural mechanics. We focus on the mechanical response of pressurized spherical shells containing a single defect to a point probe. We quantify the nonlinear force-indentation response of these shells under indentation, seeking to predict their critical buckling capacity non-destructively. We examine systematically how the location of the indentation affects the probing efficacy. We show that non-destructive prediction of the onset of buckling is only attainable when the probe is close to the defect.Third, we present preliminary results from an ongoing investigation into the probing of spherical shells containing a random distribution of defects. Following a probabilistic approach using a large data set obtained from finite element simulations, we analyze the indentation of shells with stochastically located defects. Our findings reveal that the accuracy of the extrapolated (non-destructive) outcomes, including the prediction of the actual knockdown factor, depends strongly on the chosen extrapolation method. Nevertheless, we find that adopting a conservative extrapolation threshold yields a safe lower bound for the knockdown factor, even if these predictions are overly conservative. Fourth, we turn to bistable, hard-magnetic, elastic beams, combining experiments, finite element modeling, and a reduced-order theory to examine their response under combined mechanical and magnetic loading. The beam, with antiparallel magnetization, exhibits reversible snapping between two stable states. Critical field strengths and high-order deformation modes are characterized using a numerical framework that is first validated against experiments. Additionally, we explore the interplay of magnetic loading and a poking force, providing an understanding of these magneto-elastic structural elements.Finally, we tackle the computational design of programmable braille readers. Leveraging bistable shell buckling, magnetic actuation, and pneumatic loading, a building block, the ``dot", is conceptualized. The design process is guided by finite element simulations, which are first validated through experiments on a scaled-up model. The results show the feasibility of selecting design parameters that fulfill geometric and force requirements imposed by Braille standards. The proposed bistability and rapid switching capabilities promise to advance accessibility to tactile information.