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<p>Carbon-fiber reinforced polymers (CFRPs) are often used in the aerospace and automotive  industries for their high strength-to-weight ratios and corrosion resistance. A new class of  composites – known as Prepreg Platelet Molded Composites (PPMCs) – offers further  advantageous such as high forming capabilities with modest compromises in strength and stiffness.  One such property of PPMCs that have garnered interest over the years is their apparent  insensitivity to notches. Previous studies have researched the effect of specimen size and platelet  length on its effect on the open-hole performance of PPMCs. Research however has focused on  thinner samples with smaller hole sizes and neglected thicker samples with larger holes.  Additionally, while platelet sizes have been investigated for unnotched samples, platelet width on  notched samples is less clear from the literature. The present thesis offers some investigations to  aid in filling this knowledge gap. </p> <p><br></p> <p>The objective of this work is to study two parameters that could influence the performance of PPMCs under open-hole tension. First, thick (7.6 mm) specimens are subjected to large hole  sizes (up to 19.08 mm) to investigate their behavior in comparison to the smaller sample sizes  previously investigated in the literature. Through-thickness DIC measurements are taken to  investigate strain gradients in these thicker specimens. Second, various platelet widths are tested  to research their influence on notch insensitivity of open-hole tensile PPMC specimens. Lastly, a  finite element based continuum damage mechanics model is implemented to predict macro-level  structural properties using only material properties of the parent prepreg. It is found that large holes  in thick samples increase notch sensitivity compared to other samples of similar diameter-to-width  ratios. Narrower platelets were found to produce higher unnotched strengths, while wider platelets  offered more notch insensitivity. Lastly, the finite element model developed was found to  qualitatively replicate features and failure modes that are exhibited by PPMCs, though strength  predictions became inaccurate at larger specimen sizes. Recommendations are made for future  work on the basis of these findings.   </p>

The project considers the class of deterministic continuous-time optimal control problems (OCPs) with piecewise-affine (PWA) vector fields and polynomial data. The OCP is relaxed as an infinite-dimensional linear program (LP) over space of occupation measures. The LP is then written as a particular instance of the generalized moment problem which is then approached by an asymptotically converging hierarchy of linear matrix inequality (LMI) relaxations. The relaxed dual of the original LP gives a polynomial approximation of the value function along optimal trajectories. Based on this polynomial approximation, a novel suboptimal policy is developed to construct a state feedback in a sample-and-hold manner. The results show that the suboptimal policy succeeds in providing a stabilizing suboptimal state feedback law that drives the system relatively close to the optimal trajectories and respects the given constraints.

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In this thesis, we mainly investigate the application of a nodal discontinuous Galerkin spectral element method (DGSEM) for simulating processes in column liquid chromatography. Additionally, we investigate the effectiveness of a total variation diminishing in the mean (TVDM) limiter in controlling spurious oscillations related to the Gibbs phenomenon. With an order-of-accuracy test, we demonstrated that our nodal DGSEM achieved and, in multiple instances, even exceeded theoretical convergence rates, especially with an increased number of elements, validating the use of high-order basis functions for achieving high-order accuracy. We also demonstrated how setup parameters could affect process outcomes, which suggests that numerical simulations can help guide the development of experimental methods since they can explore the solution space of an optimization problem much faster than experimental procedures by leveraging computational speed. Finally, we showed that the TVDM limiter successfully eliminated severe oscillations and negative concentrations near shock regions but introduced significant smearing of the shocks. These findings validate the nodal DGSEM as a highly accurate and reliable tool for detailed modeling of column liquid chromatography, which is essential for improving efficiency, yield, and product quality in biopharmaceutical manufacturing.

In this dissertation we present an analysis for the discontinuous Galerkin discretization error of multi-dimensional first-order linear symmetric and symmetrizable hyperbolic systems of conservation laws. We explicitly write the leading term of the local DG error, which is spanned by Legendre polynomials of degree p and p+1 when p-th degree polynomial spaces are used for the solution. For special hyperbolic systems, where the coefficient matrices are nonsingular, we show that the leading term of the error is spanned by (p+1)-th degree Radau polynomials. We apply these asymptotic results to observe that projections of the error are pointwise O(h^p+2)-superconvergent in some cases and establish superconvergence results for some integrals of the error. We develop an efficient implicit residual-based a posteriori error estimation scheme by solving local finite element problems to compute estimates of the leading term of the discretization error. For smooth solutions we obtain error estimates that converge to the true error under mesh refinement. We first show these results for linear symmetric systems that satisfy certain assumptions, then for general linear symmetric systems. We further generalize these results to linear symmetrizable systems by considering an equivalent symmetric formulation, which requires us to make small modifications in the error estimation procedure. We also investigate the behavior of the discretization error when the Lax-Friedrichs numerical flux is used, and we construct asymptotically exact a posteriori error estimates. While no superconvergence results can be obtained for this flux, the error estimation results can be recovered in most cases. These error estimates are used to drive h- and p-adaptive algorithms and assess the numerical accuracy of the solution. We present computational results for different fluxes and several linear and nonlinear hyperbolic systems in one, two and three dimensions to validate our theory. Examples include the wave equation, Maxwell's equations, and the acoustic equation. / Ph. D.