Browsing by Author "Zhou, Yang"
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Item A general condition for the existence of unconnected equilibria for symmetric arches(Elsevier, 2018) Zhou, Yang; Stanciulescu, IlincaThis paper presents a semi-analytical study of unconnected equilibrium states for symmetric curved beams. Using the Fourier series approximation, a general condition for the existence of unconnected equilibria for symmetric shallow arches is derived for the first time. With this derived condition, we can directly determine whether or not a shallow arch with specific initial configuration and external load has remote unconnected equilibria. These unconnected equilibria cannot be obtained in experiments or nonlinear finite element simulations without performing a proper perturbation first. The derived general condition is then applied to curved beams with different initial shapes and external loads. It is found that initially symmetric parabolic arches under a uniformly distributed vertical force can have multiple groups of unconnected equilibria, depending on the initial rise of the structure. However, small symmetric geometric deviations are required for parabolic arches under a central point load, and half-sine arches under a central point load or a uniformly distributed load to have unconnected equilibria. The validity of the analytical derivations of the nonlinear equilibrium solutions and the general condition for the existence of unconnected equilibria are verified by nonlinear finite element methods.Item Computational Analysis of Curved Structures Exhibiting Instabilities(2017-02-14) Zhou, Yang; Stanciulescu, IlincaThe United States Air Force and the National Aeronautics and Space Administration have made great efforts and spent untold resources to develop reusable hypersonic vehicles since the early 1950s. In spite of great progress, many scientific and technical challenges still exist. This thesis focuses on developing a robust and efficient computational framework for analyzing snap-through, which is a particular concern for the commonly used slender curved structural components of reusable hypersonic vehicles since it can significantly exacerbate fatigue failure. Snap-through is a type of instability where a curved structure suddenly jumps to a remote configuration. This behavior is highly nonlinear involving sudden and large deformations. Snap-through is a dynamic instability triggered by the loss of stability of an equilibrium state. Examining equilibria and their stability is useful and necessary before costlier transient simulations of snap-through. Curved structures undergoing snap-through can have equilibrium states that cannot be captured by path following algorithms. Two types of ``hidden" equilibria are identified: secondary equilibrium branches bifurcated from the primary path and coexisting equilibria unconnected with the primary path. A numerical procedure that combines branch-switching and arclength methods is proposed to retrieve bifurcated secondary branches, and an analytical approach is introduced to obtain unconnected equilibria. With knowledge of the entire equilibrium manifold, transient simulations of snap-through are then investigated. Time integration of snap-through is very challenging because it is a highly nonlinear behavior involving sudden jumps. Even state-of-the-art schemes fail to provide accurate and efficient long-time predictions. This dissertation extends the preliminary work on an efficient composite scheme with significantly enhanced numerical accuracy and computational efficiency in simulating snap-through. In the design of slender curved components of reusable hypersonic vehicles, it is beneficial to efficiently identify the stability boundaries that separate non-snap from post-snap responses for different designs and loading conditions. Obtaining stability boundaries directly from parametric studies is computationally costly even with the most efficient algorithms. To alleviate the cost, an alternative approach to quickly approximate dynamic stability boundaries is proposed. This approach significantly decreases the number of transient simulations needed and therefore greatly accelerates the exploration of dynamic stability boundaries.Item Fast approximations of dynamic stability boundaries of slender curved structures(Elsevier, 2017) Zhou, Yang; Stanciulescu, Ilinca; Eason, Thomas; Spottswood, MichaelCurved 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.Item Nonlinear Buckling and Postbuckling of Shallow Arches With Vertical Elastic Supports(The American Society of Mechanical Engineers, 2019) Zhou, Yang; Yi, Zhuangpeng; Stanciulescu, IlincaThis paper presents an analytical method to investigate the effects of symmetric and asymmetric elastic supports on the nonlinear equilibria and buckling responses of shallow arches. It is found that arches with symmetric elastic supports can bifurcate into secondary paths with high-orderᅠsymmetricᅠmodes. When a small asymmetry exists in the elastic supports, the equilibria of the arch may abruptly split and lead to the occurrence ofᅠremote unconnected equilibria. Such unconnected equilibria can be obtained experimentally or numerically using typical path following controls only with prior knowledge of location of these paths. A small asymmetry in the elastic supports may also make a secondary branch shrink into points connecting surrounding equilibria, resulting in the appearance of more limit points. The analytical solutions are also derived to directly calculate critical loads. We find that the magnitude of the stiffness of symmetric elastic supports has no influence on limits loads and bifurcation loads at branching into secondary paths with symmetric configurations, but greatly affect the bifurcation loads of secondary paths with asymmetric configurations. All critical loads are very sensitive to the degree of asymmetry in the elastic supports. The asymmetry in the supports reduces the top values of all pairs of critical loads compared to the case of symmetric elastic supports. The results obtained from the analytical derivations are confirmed using finite element analysis (FEA).Item Nonlinear elastic buckling and postbuckling analysis of cylindrical panels(Elsevier, 2015) Zhou, Yang; Stanciulescu, Ilinca; Eason, Thomas; Spottswood, MichaelThis 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.Item A robust composite time integration scheme for snap-through problems(Springer, 2015) Chandra, Yenny; Zhou, Yang; Stanciulescu, Ilinca; Eason, Thomas; Spottswood, StephenA 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.