Browsing by Author "Wiebe, Richard"

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    Characterizing Dynamic Transitions Associated with Snap-Through of Clamped Shallow Arches
    (Elsevier, 2013) Chandra, Yenny; Wiebe, Richard; Stanciulescu, Ilinca; Virgin, Lawrence N.; Spottswood, Stephen M.; Eason, Thomas G.
    Slender curved structures can often be found as components of complex structures in civil, mechanical, and aerospace systems. Under extreme loadings, a curved structure might undergo snap-through buckling, i.e., the structure is forced to its inverted configuration, inducing fatigue. Therefore, it is important to identify the stability boundaries of structures and to obtain an accurate description of their performance if the response moves beyond those boundaries. In this paper, a combined experimentalﾖcomputational framework is used to analyze the transient behavior of clamped-clamped shallow arches. We examine, both experimentally and using Finite Element Analysis (FEA), the response of shallow arches under harmonic distributed loading. Various types of responses are identified and regions in the forcing parameter space that lead to snap-through and chaotic responses are determined.
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    Inconsistent Stability of Newmark's Method in Structural Dynamics Applications
    (ASME, 2015) Wiebe, Richard; Stanciulescu, Ilinca
    The stability of numerical time integrators, and of the physical systems to which they are applied, are normally studied independently. This conceals a very interesting phenomenon, here termed inconsistent stability, wherein a numerical time marching scheme predicts a stable response about an equilibrium configuration that is, in fact, unstable. In this paper, time integrator parameters leading to possible inconsistent stability are first found analytically for conservative systems (symmetric tangent stiffness matrices), then several structural arches with increasing complexity are used as numerical case studies. The intention of this work is to highlight the potential for this unexpected, and mostly unknown, behavior to researchers studying complex dynamical systems, especially through time marching of finite element models. To allow for direct interpretation of our results, the work is focused on the Newmark time integrator, which is commonly used in structural dynamics.
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    Relationship between Euler buckling and unstable equilibria of buckled beams
    (Elsevier, 2017) Nistor, Mihaela; Wiebe, Richard; Stanciulescu, Ilinca
    Classic snap-through of curved beams, plates, and shells has long been an object of attention in structural engineering. Euler buckling under axial loading is perhaps an even more entrenched part of the canon of engineering education and practice. In this paper we introduce a relationship between the two phenomena, that to our knowledge has not been directly addressed before. The relationship shows that Euler buckling configurations are connected by the force–displacement curve under transverse loading. The results are used to develop a very simple metric to estimate the number of unstable static equilibria of a buckled structure based only on its geometry with no need for static or dynamic solvers. The study is focused on beams as this allows for an unambiguous discussion of the idea on the simplest possible structure.