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At a sufficiently large Reynolds number, the flow around a stationary cylinder results in the formation of the famous von Karman vortex street - a time-periodic flow in which vortices are shed, alternately on either side of the cylinder. When the cylinder performs forced oscillations transverse to the flow direction, the vortex shedding pattern becomes significantly more complex, leading to the formation of so-called "exotic wakes" whose character is controlled by the Reynolds number as well as the dimensionless period and amplitude of the cylinder's motion. In this thesis, we wish to address the following question: do these different patterns arise via (i) a continuous change in vorticity pattern (with quantifiable discrete changes to its topology) in a "complicated" flow or; (ii) via bifurcations of the Navier-Stokes equations? Analysing changes in the wake pattern requires the computation of the time-periodic solution. Near bifurcations, the computation of time-periodic solutions with the classical time-evolution approach can be extremely slow because transients take a long time to decay. Moreover, if the time-periodic flow becomes unstable, it is impossible to obtain with this approach. To tackle this issue, we adopt a finite-element based space-time approach that allows us to directly compute time-periodic solutions, bypassing the computation of transients and allowing for the computation of unstable time-periodic solutions. This approach requires the repeated solution of an extremely large system of linear equations, containing tens of millions of degrees of freedom. The application of direct solvers for the solution of this system is prohibitively expensive. To make the solution of this linear system tractable, we develop a fast preconditioner for the iterative Krylov subspace based iterative solution of the space-time system. The solution strategy makes the cost of directly computing the time-periodic comparable to time-integration over a single period. We apply the newly developed methodology to compute the time-periodic flow past an oscillating cylinder for a Reynolds number of 100 and demonstrate that the transition from the so-called 2S wake pattern to the P+S wake pattern arises through a combination of both mechanism (i) and (ii); a spatio-temporal symmetry-breaking subcritical pitchfork bifurcation of the time-periodic solution at A=A_{P1} (i.e. scenario (ii)) leads to the creation of a time-periodic solution that, through a continuous evolution of the vorticity field along the bifurcating branch (i.e. scenario (i)), leads to the formation of the P+S wake mode. For values of A > A_{P1}, the 2S solution still exists but is unstable. Further, for A > A_{P1}, we discover a second spatio-temporal symmetry-breaking subcritical pitchfork bifurcation of the 2S solution, past which the 2S solution becomes stable again.

Buckling of thin cylindrical shells under uniform axial compression is a long-standing problem in which the experimental buckling load is much lower than the theoretical prediction. There is a huge scatter in the experimental data of nominally equivalent shells, and failures are often catastrophic. "Imperfection-sensitivity" is the commonly accepted reason for the above. The classical theory of buckling of axially loaded thin cylindrical shells predicts that the buckling stress is directly proportional to the ratio of thickness to diameter (t/R), other things being equal. Whereas an empirical evaluation of the experimental data shows that the buckling stress is proportional to (t/R)1.5.The main aim of this research was to resolve the aforementioned paradoxical issues and develop a better understanding of the phenomenon of shell buckling. A comprehensive literature review was undertaken and an up-to-date database of previous experiments was developed. The database was systematically analysed against the reported parameters using standard regression analysis. Effect of any hidden combination of parameters was evaluated by the artificial neural network (ANN) model using the back-propagation method. A validated model was able to predict the buckling load within 10% of the experimental values. It was also observed that the load factors for metals specimens were higher than non-metals. Manufacturing techniques have a noticeable impact on buckling load, for example, shells produced by electroforming had relatively higher buckling strength. It has been reported in the literature that buckling is often initiated by initiation and growth of dimples. To test the effect of isolated dimples on buckling load, a set of experiments was undertaken. The shells were manufactured using PETE with nominal radius-to-thickness ratio of 175 and length-to-radius value of 3.125. The specimens with an isolated dimple had load factor from 0.4 to 0.5. A consistent post-buckling plateau load was observed for all the tested specimens and the failure mode consisted of two tiers of circumferential dimples. Repeated loading on specimens showed that the difference between the bifurcation load and post-buckling plateau load is high in the first test run due to the formation of sharp creases at the edges of the dimples and considerably lower in subsequent runs. This highlighted the need to use an appropriate imperfection shape in numerical simulations in order to obtain the stable post-buckling loads, which has implications for design. In this study, the effect of generalized imperfections in the form of different modes shapes was studied, and it was observed that the axisymmetric imperfection yields lowest load factor. The effect of imperfection in the form of an isolated dimple at the mid-height of the numerical model was studied using Single Perturbation Load Approach (SPLA) and the results agree well with the experimental values. Different shape and magnitude of imperfections were also introduced using asymmetric meshing technique (AMT). It was observed that asymmetric meshing in the form of band or patch affects both buckling loads and buckling mode shapes for linear eigenvalue analysis and affects buckling mode shapes and load-deflection curve behaviour in the post-buckling region for non-linear analysis. The buckling load decreases as the size of patch or band having asymmetric meshing increases, the reduction in buckling load is strongly related to the area of asymmetric meshing and has a weak relationship with the amplitude of asymmetry. The load-displacement behaviour of cylindrical shells under axial compression by using AMT has similar characteristics to that observed in conventional simulations with an initial geometric imperfection.

This dissertation aimed to devise predictive tools for analyzing various support structuresof a high-speed rail (HSR) system to support their design under operational and seismic loads. The detailed objectives are (i) to implement a vehicle-bridge-interaction (VBI) method for analyzing coupled train-track coupled dynamics, (ii) to develop a finite ele- ment (FE) approach for analyzing the interaction of a local domain with a moving load (as the load enters, traverses, and leaves the local domain) based on the application of Perfectly-Matched-Layers (PMLs) and the Domain Reduction Method (DRM), and (iii) to carry out various application studies that explore the interaction of moving loads with flexible or buried structures using the tools developed to verify them and to demonstrate their utility. The methods described above are implemented in commercial finite element analysis software ABAQUS through a combination of MATLAB codes and ABAQUS’ user-defined element (UEL) subroutine interface. These implementations were carried out to enhance the potential impact of the analysis tools developed as part of this dissertation and broaden their applicability. The computational efficiency afforded by the developed tools obviates the need to carry out simulations with large finite element domains (through the use of PML+DRM and proper injection of boundary conditions emanating from far- field (inbound vehicle and/or seismic) loads at the truncated domain boundaries) and to develop explicit multi-degree-of-freedom dynamic models of the considered vehicles.

Big data plays an important role in the fourth industrial revolution, which requires engineersand computers to fully utilize data to make smart decisions to optimize industrial processes. In the additive manufacturing (AM) industry, laser powder bed fusion (LPBF) and direct metal laser solidification (DMLS) have been receiving increasing interest in research because of their outstanding performance in producing mechanical parts with ultra-high precision and variable geometries. However, due to the thermal and mechanical complexity of these processes, printing failures are often encountered, resulting in defective parts and even destructive damage to the printing platform. For example, heating anomalies can result in thermal and mechanical stress on the building part and eventually lead to physical problems such as keyholing and lack of fusion. Many of the aforementioned process errors occur during the layer-to-layer printing process, which makes in-situ process monitoring and quality control extremely important. Although in-situ sensors are extensively developed to investigate and record information from the real-time printing process, the lack of efficient in-situ defect detection techniques specialized for AM processes makes real-time process monitoring and data analysis extremely difficult. Therefore, to help process engineers analyze sensor information and efficiently filter monitoring data for transport and storage, machine learning and data processing algorithms are often implemented. These algorithms integrate the functionality of automated data processing, transferring, and analytics. In particular, sensor data often takes the form of images, and thus, a prominent approach to conducting image analytics is through the use of convolutional neural networks (CNN). Nevertheless, the industrial utilization of machine learning methods often encounters problems such as limited and biased training datasets. Hence, simulation methods, such as the finite-element method (FEM), are used to augment and improve the training of the deep learning process monitoring algorithm. Motivated by the above considerations, this dissertation presents the use of machine learning techniques in process monitoring, data analytics, and data transfer for additive manufacturing processes. The background, motivation, and organization of this dissertation are first presented in the Introduction chapter. Then, the use of FEM to model and replicate in-situ sensor data is presented, followed by the use of machine learning techniques to conduct real-time process monitoring trained from a mixture of experimental and replicated sensor image data. In particular, a cross-validation algorithm is developed through the exploitation of different sensor advantages and is integrated into the machine learning-assisted process monitoring algorithm. Next, an application of machine learning (ML) to non-image sensor data is presented as a neural network model that is developed to estimate in-situ powder thickness to account for recoater arm interactions. Subsequently, an integrated AM smart manufacturing framework is proposed which connects the different manufacturing hierarchies, particularly at the local machine, factory, and cloud level. Finally, in addition to the AM industry, the use of machine learning, specifically neural networks, in model predictive control (MPC) for dynamic nonlinear processes is reviewed and discussed.

Failure of materials and interfaces is mediated by the propagation of cracks. They nucleate locally and slowly then, as they exceed a critical size, accelerate and reach speeds approaching the speed of sound of the surrounding material. As they propagate, they dissipate energy within a confined region at the crack tip, which approaches a mathematical singularity. As a result, the initiation and propagation of cracks is a spatial and temporal multiscale phenomenon. The framework of linear elastic fracture mechanics captures many aspects related to the dynamic propagation of cracks in homogeneous media. However, the propagation of a crack within a medium with heterogeneous elastic or fracture properties cannot be addressed theoretically. It is in these complex, heterogeneous cases that numerical simulations and experiments shine. The material heterogeneity introduces additional length scales to the problem, which characterize the geometrical properties or spatial correlation of the heterogeneities. The interaction of these geometrical length scales with fracture mechanics related ones is not well understood, but it could provide crucial insights for the design of new materials and interfaces with unprecedented fracture properties. This thesis investigates different aspects of crack nucleation and propagation in heterogeneous materials and interfaces, including nucleation of mode II ruptures on interfaces with random local properties, dynamic mode II rupture propagation within elastically heterogeneous media, and dynamic mode I rupture propagation within a material with periodic heterogeneous fracture energy. In this context, when considering mode II dynamic fracture problems, we are making an analogy to frictional interfaces. In fact, the onset of frictional motion is mediated by crack-like ruptures that nucleate locally and propagate dynamically along the frictional interface. To investigate the complex interaction between fracture mechanics and geometry related length scales we adopt a combined approach using numerical, theoretical, and experimental methods. The numerical simulations consider a continuum governed by the elastodynamic wave equation and allow for a displacement discontinuity (the rupture) along a predefined interface. Depending on the nature of the heterogeneity, the fracture propagation problem is solved using either the finite-element or the spectral-boundary-integral method. Here, we introduce a novel three-dimensional hybrid method, which combines the two former numerical methods to achieve superior computational performance, while allowing modeling of local complexity and heterogeneity. From the experimental side we use state-of-the-art techniques, including ultra-high-speed photography, digital image correlation, and multi-material additive manufactured polymers. We show that random local strength results in three different nucleation regimes depending on the ratio of correlation length to critical nucleation size. We show that elastic heterogeneity parallel to the fracture interface promotes transition to intersonic crack propagation in mode II cracks by means of reflected elastic waves. Finally, our experimental results of a crack propagating within a material with heterogeneous fracture energy show that the crack abruptly adjusts its speed as it enters a tougher region and allow us to derive an equation of motion of a crack at a material discontinuity.

A computationally efficient approach to perform systematically convergent real-space all-electron Kohn-Sham density functional theory calculations using an enriched finite element (FE) basis is presented. The enriched FE basis is constructed by augmenting the classical FE basis with atom-centered numerical basis functions, comprising of atomic solutions to the Kohn-Sham problem. Notably, to improve the conditioning, the enrichment functions are orthogonalized with respect to the classical FE basis, without sacrificing the locality of the resultant basis. In addition to improved conditioning, this orthogonalization procedure also renders the overlap matrix block-diagonal, greatly simplifying its inversion. Furthermore, the treatment of electrostatics adopted in this work ensures that the basis is seamlessly applicable to both periodic and non-periodic calculations. A Chebyshev polynomial based filtering technique is used to efficiently compute the occupied eigenspace in each self-consistent field iteration. The basis offers excellent parallel scalability with 92% efficiency at 22 times speedup for a system with 620 electrons. Additionally, a formulation to compute nuclear forces and the stress tensor needed to perform structural relaxation in this basis is also presented. This is done using the notion of configurational forces which arise from the variational derivative of the Kohn-Sham free energy functional with respect to the position of the material point. This approach, originally proposed in the context of classical FE by Motamarri and Gavini [Phys. Rev. B, 97 , 16 (2018)] , enables computation of variationally consistent nuclear forces and the stress tensor in a unified framework without having to explicitly account for Pulay contributions. In this work, we demonstrate the accuracy of the formulation by comparing the computed forces and stresses for various benchmark systems with those obtained from finite-differencing the ground-state energy. Moreover, our calculations are benchmarked against the Gaussian basis for isolated systems and LAPW+lo basis for periodic systems. Lastly, the applicability of the basis is extended to solve the time-dependent Kohn-Sham equations in real time. The formulation is based on a recent work by Kanungo and Gavini [Phys. Rev. B, 100 , 11 (2019)], wherein classical finite elements were used for spatial discretization. The presence of enrichment functions in the basis accelerates all-electron TDDFT calculations. Moreover, the block-diagonal nature of the overlap matrix afforded by the orthogonalized enriched finite element basis enables fast and convenient inversion of the overlap matrix that features in the evaluation of the discrete time-evolution operator. The formulation utilizes the second-order Magnus operator, which contains an exponential of a large sparse matrix, as the time propagator. The action of this operator on an orbital is efficiently performed by using a Krylov-subspace projection method. Calculations show close to optimal rates of convergence of the dipole moment with respect to spatial and temporal discretization. Overall, the work presents an efficient, scalable and accurate basis to perform all-electron DFT calculations. This would be instrumental in the study of defects in crystalline systems where calculations on large systems are inevitable. Moreover, the systematic improvability afforded by the basis makes it a suitable tool to conduct pseudopotential transferability studies.

Recent progresses by the aircraft industry in the development of a quieter supersonic transport have opened the possibility of overland supersonic flights, which are currently banned by aviation authorities in most countries. For the ban to be lifted, the sonic booms the aircraft generate at supersonic speed must be acceptable from a human-perception point of view, in particular inside buildings. The problem of the transmission of sonic booms inside buildings can be divided in several aspects such as the external pressure loading, structure vibration, and interior acoustic response. Past investigations on this problem have tackled all these aspects but were limited to simple structures and often did not account for the coupled fluid-structure interaction. A more comprehensive work that includes all the effects of sonic booms to ultimately predict the noise exposure inside realistic building structures, e.g. residential houses, has never been reported. Thus far, these effects could only be investigated experimentally, e.g. flight tests. In this research, a numerical model and a computer code are developed within the above context to predict the vibro-acoustic response of simplified building structures exposed to sonic booms, at low frequency. The model is applicable to structures with multiple rectangular cavities, isolated or interconnected with openings. The response of the fluid-structure system, including their fully coupled interaction, is computed in the time domain using a modal-decomposition approach for both the structural and acoustic systems. In the dynamic equations, the structural displacement is expressed in terms of summations over the "in vacuo" normal modes of vibration. The interior pressure is expressed in terms of summations over the acoustic modes of the rooms with perfectly reflecting surfaces (hard walls). This approach is simple to implement and computationally efficient at low frequency, when the modal density is relatively low. The numerical model is designed specifically for this application and includes several novel formulations. Firstly, a new shell finite-element is derived to model the structural components typically used in building construction that have orthotropic characteristics such as plaster-wood walls, floors, and siding panels. The constitutive matrix for these types of components is formulated using simple analytical expressions based on the orthotropic constants of an equivalent orthotropic plate. This approach is computationally efficient since there is no need to model all the individual subcomponents of the assembly (studs, sheathing, etc.) and their interconnections. Secondly, a dedicated finite-element module is developed that implements the new shell element for orthotropic components as well as a conventional shell element for isotropic components, e.g. window panels and doors. The finite element module computes the "in vacuo" structural modes of vibration. The modes and external pressure distribution are then used to compute modal loads. This dedicated finite-element module has the main advantage of overcoming the need, and subsequent complications, for using a large commercial finite-element program. Lastly, a novel formulation is developed for the fully coupled fluid-structure model to handle room openings and compute the acoustic response of interconnected rooms. The formulation is based on the Helmholtz resonator approach and is applicable to the very low frequency-range, when the acoustic wavelength is much larger than the opening dimensions. Experimental validation of the numerical model and computer code is presented for three test cases of increasing complexity. The first test structure consists of a single plaster-wood wall backed by a rigid rectangular enclosure. The structure is excited by sonic booms generated with a speaker. The second test structure is a single room made of plaster-wood walls with two double-panel windows and a door. The third test structure consists of the first room to which a second room with a large window assembly was added. Several door configurations of the structure are tested to validate the formulation for room openings. This latter case is the most realistic one as it involves the interaction of several structural components with several interior cavities. For the last two test cases, sonic booms with realistic durations and amplitudes were generated using an explosive technique. Numerical predictions are compared to the experimental data for the three test cases and show a good overall agreement. Finally, results from a parametric study are presented for the case of the single wall backed by a rigid enclosure. The effects of sonic-boom shape, e.g. rise time and duration, and effects of the structure geometry on the fluid-structure response to sonic booms are investigated.

A numerical simulation for evaluating methods of predicting and controlling the response of an elastic wing in an airstream is discussed. The technique employed interactively and simultaneously solves for the response in the time domain by considering the air, wing, and controller as elements of a single dynamical system. The method is very modular, allowing independent modifications to the aerodynamic, structural, or control subsystems and it is not restricted to periodic motions or simple geometries. To illustrate the technique, we use a High Altitude, Long Endurance aircraft wing. The wing is modeled structurally as a linear Euler-Bernoulli beam that includes dynamic coupling between the bending and torsional oscillations. The governing equations of motion are derived and extended to allow for rigid-body motions of the wing. The exact solution to the unforced linear problem is discussed as well as a Galerkin and finite-element approximations. The finite-element discretization is developed and used for the simulations. A general, nonlinear, unsteady vortex-lattice method, which is capable of simulating arbitrary subsonic maneuvers of the wing and accounts for the history of the motion, is employed to model the flow around the wing and provide the aerodynamic loads. Two methods of incorporating gusts in the aerodynamic model are also discussed. Control of the wing is effected via a distributed torque actuator embedded in the wing and two strategies for actuating the wing are described: a classical linear proportional integral strategy and a novel nonlinear feedback strategy based on the phenomenon of saturation that may exist in nonlinear systems with two-to-one internal resonances. Both control strategies can suppress the flutter oscillations of the wing, but the nonlinear controller must be actively tuned to be effective; gust control proved to be more difficult.

Analysis of rolling