The failures that result from the loss of stability of a structure often occur through large displacements or buckling. &nbsp;Because they are unrelated to material strength and may produce no permanent damage so that they are reversible, structural instabilities have been the subject of resent research as means to dissipate energy from a system or to capture energy within a system.&nbsp; The initial configuration and the post-buckling configuration are both in states of stable equilibrium.&nbsp; However, each requires different amounts of energy to maintain this equilibrium.&nbsp; The difference in the amount of energy in the stable configurations of a structure is of interest when using buckling phenomena for energy storage or dissipation.&nbsp; Therefore, the ability to quantify the difference in the energy levels between the two different stable configurations can help in the design of systems that control energy flows by taking advantage of these kinds of buckling instabilities.&nbsp; Computational modeling methods can be used to perform such energy calculations and can be readily applied to systematically examine different configurations and loading conditions in order to design structures that can achieve desired amounts of energy dissipation, transfer, or storage.&nbsp; The development and use of such methods are the focus of this work.The transformation between stable structural configurations occurs as a result of a structural instability, often induced by a small perturbation of the system.&nbsp; Such perturbations are typically associated with minor flaws in the material or slight load disturbances.&nbsp; The inherent variability in physically fabricated structures and physically applied loads makes this phenomenon well suited to be studied experimentally.&nbsp; However, the benefits of the ease of exploration of the effects of changes in system parameters like structural shape, material, and boundary conditions make the use of modeling methods, rather than experiments, desirable.&nbsp;&nbsp; Computationally, perturbations can be induced through modifications of an otherwise regular mesh in the interior of a volume or through a slight uneven offset of surface nodes to simulate the material flaws.&nbsp; Alternatively, a slight offset of the applied loads can induce a disturbance sufficient to induce the structural instability. However, these methods may not always result in predictable or repeatable transformations between stable configurations.&nbsp; When exploring the behavior of different designs, distinguishing between what is numerically induced and what is physically induced by a design change may not always be possible.&nbsp; Methods are developed in this work to aid in this distinction. &nbsp;The focus is on the correlation between system stiffness and the energy changes induced during the snap-through buckling of a curved beam.The work will first examine a simple spring and rigid truss structure. Energy measures that are readily calculated from finite element solutions will be correlated to stability criteria that can be analytically predicted.&nbsp; The correlation will be tested for variations in the system parameters, such as spring stiffness or structure geometry so that a method to predict the instability in the finite element model is devised. &nbsp;&nbsp;An understanding of the effect of parameters associated with the numerical approximation of the solution will also be explored.&nbsp; The methods will then be applied to a more complex structure, a deformable curved beam. The design of the beam and the mesh used to approximate it will be altered, and the ability of the method to predict a structural instability and the resulting amount of energy change will be evaluated.&nbsp; This will not only give an indication of how much energy can be stored or dissipated by the structure, but how readily the structure can transform from one configuration to the next.&nbsp; The methods resulting from this work would be of particular benefit to the design of bi-stable structures that can dissipate or store pre-defined amounts of energy.&nbsp; The developed modeling techniques could also be coupled with design optimization routines where the iterative nature of the optimization limits the ability to explore the effect of the mesh and other numerical influences at each design iteration.

A Finite Element Based Method to Predict and Tailor the Energy Associated With Snap-Through Buckling of a Curved Beam

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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