Browsing by Author "Eason, Thomas"

Now showing 1 - 6 of 6
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    A lower bound on snap-through instability of curved beams under thermomechanical loads
    (Elsevier, 2012) Stanciulescu, Ilinca; Mitchell, Toby; Chandra, Yenny; Eason, Thomas; Spottswood, Michael
    A non-linear finite element formulation (three dimensional continuum elements) is implemented and used for modeling dynamic snap-through in beams with initial curvature. We identify a non-trivial (non-flat) configuration of the beam at a critical temperature value below which the beam will no longer experience snap-through under any magnitude of applied quasi-static load for beams with various curvatures. The critical temperature is shown to successfully eliminate snap-through in dynamic simulations at quasistatic loading rates. Thermomechanical coupling is included in order to model a physically minimal amount of damping in the system, and the resulting post-snap vibrations are shown to be thermoelastically damped. We propose a test to determine the critical snap-free temperature for members of general geometry and loading pattern; the analogy between mechanical prestress and thermal strain that holds between the static and dynamic simulations is used to suggest a simple method for reducing the vulnerability of thin-walled structural members to dynamic snap-through in members of large initial curvature via the introduction of initial pretension.
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    Fast approximations of dynamic stability boundaries of slender curved structures
    (Elsevier, 2017) Zhou, Yang; Stanciulescu, Ilinca; Eason, Thomas; Spottswood, Michael
    Curved beams and panels can often be found as structural components in aerospace, mechanical and civil engineering systems. When curved structures are subjected to dynamic loads, they are susceptible to dynamic instabilities especially dynamic snap-through buckling. The identification of the dynamic stability boundary that separate the non-snap and post-snap responses is hence necessary for the safe design of such structures, but typically requires extensive transient simulations that may lead to high computation cost. This paper proposes a scaling approach that reveals the similarities between dynamic snap-through boundaries of different structures. Such identified features can be directly used for fast approximations of dynamic stability boundaries of slender curved structures when their geometric parameters or boundary conditions are varied. The scaled dynamic stability boundaries of half-sine arches, parabolic arches and cylindrical panels are studied.
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    Nonlinear elastic buckling and postbuckling analysis of cylindrical panels
    (Elsevier, 2015) Zhou, Yang; Stanciulescu, Ilinca; Eason, Thomas; Spottswood, Michael
    This paper revisits the buckling analysis of a benchmark cylindrical panel undergoing snap-through when subjected to transverse loads. We show that previous studies either overestimated the buckling load and identified a false buckling mode, or failed to identify all secondary solution branches. Here, a numerical procedure composed of the arclength and branch switching methods is used to identify the full postbuckling response of the panel. Additional bifurcation points and corresponding secondary paths are discovered. Parametric studies of the effect of the rise, thickness, and boundary conditions of the panel on the buckling and postbuckling responses are also performed.
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    Numerical pathologies in snap-through simulations
    (Elsevier, 2012) Chandra, Yenny; Stanciulescu, Ilinca; Eason, Thomas; Spottswood, Michael
    Aircraft structures operating in severe environments may experience snap-through, causing the curvature on part or all of the structure to invert inducing fatigue damage. This paper examines the performance of beam and continuum nonlinear finite element formulations in conjunction with several popular implicit time stepping algorithms to assess the accuracy and stability of numerical simulations of snap-through events. Limitations of the structural elements are identified and we provide examples of interaction between spatial and temporal discretizations that affect the robustness of the overall scheme and impose strict limits on the size of the time step. These limitations need to be addressed in future works in order to develop accurate, robust and efficient simulation methods for response prediction of structures encountering extreme environments.
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    A robust composite time integration scheme for snap-through problems
    (Springer, 2015) Chandra, Yenny; Zhou, Yang; Stanciulescu, Ilinca; Eason, Thomas; Spottswood, Stephen
    A robust time integration scheme for snap-through buckling of shallow arches is proposed. The algorithm is a composite method that consists of three sub-steps. Numerical damping is introduced to the system by employing an algorithm similar to the backward differentiation formulas method in the last sub-step. Optimal algorithmic parameters are established based on stability criteria and minimization of numerical damping. The proposed method is accurate, numerically stable, and efficient as demonstrated through several examples involving loss of stability, large deformation, large displacements and large rotations.
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    Transient behavior of curved structures
    (2013-04-19) Chandra, Yenny; Stanciulescu, Ilinca; Padgett, Jamie E.; Riviere, Beatrice M.; Dick, Andrew J.; Eason, Thomas
    Slender curved structures can often be found as components of complex structures in civil, mechanical, and aerospace systems. Under extreme loadings, the structure might undergo snap-through buckling, i.e., the structure is forced to its inverted configuration, inducing fatigue. The focus of this research is the development of a reliable and accurate model for simulating the nonlinear response of shallow arches under transient loading and characterizing these responses to assess the structure's ability to survive if the structure undergoes instabilities. Since no analytical solutions for general systems with snap-through exist, numerical models are needed in order to predict the response of the structure. The finite element method provides the most generality and can be applied to systems with arbitrarily complex geometries. Unfortunately there are barriers to the numerical prediction. First, the structures exhibit a very complex dynamic response. Coexisting responses are identified under different initial conditions. Chaotic responses are also observed. A framework for analyzing the dynamic responses of slender curved structures is proposed by identifying the relevant features useful in characterizing the transient behavior of shallow arches. State of the art time integrators are often unable to retrieve long time records of the response after a physical instability event. The performance of several time-stepping schemes is analyzed by identifying the important features that affect the numerical accuracy and robustness. We also identify the region where the schemes are stable for such simulations. The interactions between the time-stepping schemes and the spatial discretizations are examined. This investigation results in recommendations for finite elements and time integrators that give the best performance. A new time integrator that is robust and accurate for long-term simulations is proposed. The established numerical framework is validated against experimental data. Fabrication imperfections in the experimental arch and prestressing due to the applied boundary conditions are accounted for. A methodology to determine the boundaries of the stability regions in the parameter space under consideration is proposed. Finally, the effect of initial temperature variation on the transient behavior of shallow arches is also studied. The changes in the snap-through boundaries as the temperature increases are examined.