Theses and Dissertations
This collection includes both ASU Theses and Dissertations, submitted by graduate students, and the Barrett, Honors College theses submitted by undergraduate students.
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Description
This investigation is focused on the consideration of structural uncertainties in nearly-straight pipes conveying fluid and on the effects of these uncertainties on the dynamic response and stability of those pipes. Of interest more specifically are the structural uncertainties which affect directly the fluid flow and its feedback on the structural response, e.g., uncertainties on/variations of the inner cross-section and curvature of the pipe. Owing to the complexity of introducing such uncertainties directly in finite element models, it is desired to proceed directly at the level of modal models by randomizing simultaneously the appropriate mass, stiffness, and damping matrices. The maximum entropy framework is adopted to carry out the stochastic modeling of these matrices with appropriate symmetry constraints guaranteeing that the nature, e.g., divergence or flutter, of the bifurcation is preserved when introducing uncertainty.
To support the formulation of this stochastic ROM, a series of finite element computations are first carried out for pipes with straight centerline but inner radius varying randomly along the pipe. The results of this numerical discovery effort demonstrate that the dominant effects originate from the variations of the exit flow speed, induced by the change in inner cross-section at the pipe end, with the uncertainty on the cross-section at other locations playing a secondary role. Relying on these observations, the stochastic reduced order model is constructed to model separately the uncertainty in inner cross-section at the pipe end and at other locations. Then, the fluid related mass, damping, and stiffness matrices of this stochastic reduced order model (ROM) are all determined from a single random matrix and a random variable. The predictions from this stochastic ROM are found to closely match the corresponding results obtained with the randomized finite element model. It is finally demonstrated that this stochastic ROM can easily be extended to account for the small effects due to uncertainty in pipe curvature.
To support the formulation of this stochastic ROM, a series of finite element computations are first carried out for pipes with straight centerline but inner radius varying randomly along the pipe. The results of this numerical discovery effort demonstrate that the dominant effects originate from the variations of the exit flow speed, induced by the change in inner cross-section at the pipe end, with the uncertainty on the cross-section at other locations playing a secondary role. Relying on these observations, the stochastic reduced order model is constructed to model separately the uncertainty in inner cross-section at the pipe end and at other locations. Then, the fluid related mass, damping, and stiffness matrices of this stochastic reduced order model (ROM) are all determined from a single random matrix and a random variable. The predictions from this stochastic ROM are found to closely match the corresponding results obtained with the randomized finite element model. It is finally demonstrated that this stochastic ROM can easily be extended to account for the small effects due to uncertainty in pipe curvature.
ContributorsShah, Shrinil (Author) / Mignolet, Marc P (Thesis advisor) / Liu, Yongming (Committee member) / Oswald, Jay (Committee member) / Arizona State University (Publisher)
Created2017
Description
A method for modelling the interactions of dislocations with inclusions has been developed to analyse toughening mechanisms in alloys. This method is different from the superposition method in that infinite domain solutions and image stress fields are not superimposed. The method is based on the extended finite element method (XFEM) in which the dislocations are modelled according to the Volterra dislocation model. Interior discontinuities are introduced across dislocation glide planes using enrichment functions and the resulting boundary value problem is solved through the standard finite element variational approach. The level set method is used to describe the geometry of the dislocation glide planes without any explicit treatment of the interface geometry which provides a convenient and an appealing means for describing the dislocation. A method for estimating the Peach-Koehler force by the domain form of J-integral is considered. The convergence and accuracy of the method are studied for an edge dislocation interacting with a free surface where analytical solutions are available. The force converges to the exact solution at an optimal rate for linear finite elements. The applicability of the method to dislocation interactions with inclusions is illustrated with a system of Aluminium matrix containing Aluminium-copper precipitates. The effect of size, shape and orientation of the inclusions on an edge dislocation for a difference in stiffness and coefficient of thermal expansion of the inclusions and matrix is considered. The force on the dislocation due to a hard inclusion increased by 8% in approaching the sharp corners of a square inclusion than a circular inclusion of equal area. The dislocation experienced 24% more force in moving towards the edges of a square shaped inclusion than towards its centre. When the areas of the inclusions were halved, 30% less force was exerted on the dislocation. This method was used to analyse interfaces with mismatch strains. Introducing eigenstrains equal to 0.004 to the elastic mismatch increased the force by 15 times for a circular inclusion. The energy needed to move an edge dislocation through a domain filled with circular inclusions is 4% more than that needed for a domain with square shaped inclusions.
ContributorsVeeresh, Pawan (Author) / Oswald, Jay (Thesis advisor) / Jiang, Hanqing (Committee member) / Liu, Yongming (Committee member) / Arizona State University (Publisher)
Created2016