The present research aims to propose a new methodology for the failure analysis of heterogeneous thin plates. The problem is solved under the framework of hierarchial multiscale analysis. It is assumed that plates are composed of periodic microstructure and the repeating unit is selected as representative volume element (RVE) or unit cell for microscopic problems. In-plane plates displacements and transverse deflection of the plate are resolved into macroscopic and periodic microscopic displacement components using two scale asymptotic analysis. Damage is introduced as a single internal variable, following the concepts of continuum damage mechanics (CDM). Transformation field analysis (TFA) is used to separate elastic and in-elastic strain components. Elastic influence function (EIF) and damage influence function (DIF) are obtained by solving corresponding microscale problems, which completes the description of asymptotic macroscopic displacement field. 3-point bending test, uniaxial tensile test and analysis of impact due to high velocity projectile are carried out using commercial finite element code (Abaqus) in order to verify the proposed approach.

Decision makers often confront an inability to understand the consequences of interactions within systems of systems (SoS), which can have physical and human components and exhibit hybrid (continuous and discrete) dynamics. The human and physical interactions with the environment and related uncertainties can make optimization and control difficult and result in unintended consequences. As examples, transportation networks may experience lengthy delays or gridlock, and economic stimuli may be ineffective, as a result of suboptimal network control policies. The objective of this dissertation is to motivate, propose and implement a framework that provides decision support in order to manage and operate human-physical networks with hybrid dynamics. The stochastic human-physical analysis framework facilitates the integration of system simulation, uncertainty analysis and optimization under uncertainty for this class of problems. Specifically, this dissertation: 1) motivates the necessity for a SoS approach to optimizing network control policy; 2) proposes a SoS approach to policy analysis and design under uncertainty; 3) develops an integrated discrete choice and agent-based simulation approach for stochastic human-physical networks with hybrid dynamics; 4) develops and validates computationally inexpensive surrogate models to predict high-fidelity simulation outputs, and uses these models to perform probabilistic reachability analysis and sensitivity analysis; and 5) performs uncertainty propagation and stochastic policy optimization considering both cooperative and non-cooperative decision-makers.

As engineering systems grow in size and complexity, it is becoming increasingly difficult to assess their performance through full scale testing. Modeling and simulation fill the gap left by the lack of full scale testing for an actual use environment. Modeling and simulation-based assessment also requires the quantification of uncertainty in the predicted response of the system model, in order to establish the confidence in representing the actual system behavior. Sources of uncertainty arise from (1) the stochastic nature of components, (2) their coupling with each other, (3) from data, (4) model assumptions and (5) model approximations. Computational models for large systems are built in a hierarchical way from component, subsystem to system level. Individual component data is more readily available then full system data. This research proposes a framework that allows quantification of uncertainty in a hierarchical system model prediction and uses the available data at multiple levels. Sources of both aleatoric and epistemic uncertainty are included in such quantification. Techniques to quantify margins of performance and uncertainties in order to estimate the confidence in the system model prediction are investigated. Finally, the results of the uncertainty analysis are used to develop a decision making methodology that allocates resources for further data collection and model improvement activities.

Fluid-structure impact analysis is a topic of increasing interest to engineers and designers in the shipbuilding and aerospace industries, and recent advances in the availability of computational power have allowed for risk assessments of these types of problems to be conducted. The space shuttle solid rocket booster (SRB) splashdown event is one example of a complex structural system experiencing damage as a result of water impact. NASA witnessed several instances of the damage to the forward skirt of the SRB following shuttle launches in the 1990s. However, initial risk assessments of SRB impact based upon finite element modeling produced predictions that did not agree with the observed frequency of damage. The discrepancy was attributed to model uncertainty, computational approximations in the coupled fluid and structural domains, and uncertainty regarding the structural failure definition. The research presented herein addresses these issues through a systematic model development and validation framework for fluid-structure impact analysis. The details of the finite element approach for modeling of the SRB splashdown sequence are presented, along with a systematic approach for mesh refinement in the fluid and structural analysis domains. A model validation exercise is conducted using laboratory experimental data obtained with a small-scale aluminum cylinder and water drop tank, thus lending increased confidence in the corresponding finite element model prediction. The buckling nature of the SRB forward skirt damage is investigated through nonlinear finite element analysis in order to develop an improved failure definition, and this new limit state results in a failure rate prediction that is in agreement with the observed frequency of damage. Finally, a methodology based upon Bayesian networks is presented for quantifying any increased confidence in the SRB splashdown model prediction based upon the experimental cylinder test data, using concepts of similitude and dimensional analysis.

Over the past decade, catastrophic events such as the World Trade Center attacks, Hurricane Katrina, and the Minneapolis bridge collapse have affected societal perception of the risks affecting our lives. It has also led to the realization that a more systematic and holistic approach to risk management is needed, one that takes into consideration the risks and potential mitigation strategies associated with natural hazards, man-made accidents, and intentional acts in an integrated all-hazards risk management (AHRM) framework. This would enable the risk manager to prioritize among risks and to make more effective resource allocation and policy decisions. This dissertation includes the development of an AHRM methodology, quantification of risks posed by various hazards, development of a functional relationship between risk mitigation investment and risk reduction, defining and solving an all-hazards risk mitigation resource allocation optimization problem, and application of the methodology to a case study region. Directions for further research are also provided.

<p>Reliability analysis is critically important to a wide array of engineering fields that increasingly depend on computational models to predict system performance. However, previously available methods for performing this analysis either 1) require these models to be evaluated a large number of times leading to computational costs that are often unaffordable when the model is computationally expensive, or 2) provide potentially inaccurate reliability estimates due to simplifying approximations that reduce the cost of the analysis. Surrogate models can provide a practical alternative by replacing the computationally expensive model with one that is much less expensive to evaluate.</p> <p>This dissertation develops an efficient method for constructing Gaussian process surrogate models, specifically tailored for their use in reliability analysis, while simultaneously ensuring that the resulting surrogate is an accurate representation of the original computational model that it is intended to replace. This combination of efficiency and accuracy is achieved by using the uncertainty structure of Gaussian process models to guide the selection of training points, focusing them only in the region where accuracy is required, and only converging when the uncertainty in that region is sufficiently reduced. The resulting model is then used in a sampling-based reliability analysis method to provide accurate reliability estimates at a small fraction of the cost previously required to achieve this level of accuracy. This new method, named Efficient Global Reliability Analysis, was applied to a variety of test problems involving highly nonlinear and/or computationally expensive response functions with great success.</p> <p>Efficient Global Reliability Analysis (EGRA) was also applied to several classes of reliability problems that are historically difficult to solve either efficiently or accurately.</p> <p>1. Reliability analysis with uncertainty on the input distributions. Because the limit state is modeled independently of the input distributions, it remains accurate for changes in those distributions, allowing EGRA to only build the surrogate model one time and then simply resampling it as the distributions change.</p> <p>2. System-level reliability analysis. Through a slight modification of the EGRA algorithm, the method is able to focus only on the component responses that lead to system failure and ignore the others. This leads to substantial computational savings without sacrificing accuracy.</p> <p>3. Reliability-based design optimization (RBDO). By combining EGRA with an efficient design optimizer and various formulations for combining surrogate models at the design and random variable levels, accurate RBDO solutions can be realized at a small fraction of their typical cost. These cost savings are especially dramatic when the design variables are distribution parameters. However, some work remains to make these RBDO methods feasible when applied to problems with a large number of design variables, due to the difficulty in finding suitable bounds for each variable to ensure that the Gaussian process model for the probabilistic constraint is smooth and continuous.</p> <p>Through these applications, new methods of accurately solving these classes of problems have been created that are far more efficient than previously available methods.</p>

This study is concerned with the accurate prediction of response of structural components under mechanical loads in the presence of various types of irregularities in homogeneous as well as inhomogeneous systems like laminated composites and bonded patch repaired plates. For accurate modeling of such systems, new two-dimensional models are developed to represent the three-dimensional stress field near an irregularity and two-dimensional ones away from it. The developed scheme is implemented using MATLAB as the computational platform. Apart from such implementation, a number of other advanced computational procedures like VCCT based fracture mechanics computations, ordinary Kriging interpolation scheme for adaptive model refinement, geometrically nonlinear analysis, and a simple but novel approach to delamination analysis are implemented. The software is verified and/or validated with a number of critical examples. Also, it is used to predict the behavior of damaged homogeneous and laminated plates with and without bonded patch repair. Important conclusions are drawn regarding the behavior of patch repaired plates as well as the efficiency of the proposed modeling schemes.

The role of uncertainty management is increasingly being recognized in the design of complex systems that require multi-level multidisciplinary analyses. Most previous studies in this direction have only dealt with aleatory uncertainty (i.e., natural or physical variability). However, various modeling errors, assumptions and approximations, measurement errors, and sparse and imprecise information introduce additional epistemic uncertainty in model prediction. Therefore, an approach to multidisciplinary uncertainty analysis and system design that addresses both aleatory and epistemic uncertainty is needed. The objective of this dissertation is to develop a methodology that provides decision support to engineers for multidisciplinary design and analysis of systems under aleatory uncertainty (i.e., natural or physical variability) and epistemic uncertainty (due to sparse and imprecise data). Specifically, the dissertation accomplishes this objective through: (1) Development of a probabilistic approach for the representation of epistemic uncertainty; (2) Development of a probabilistic framework for the propagation of both aleatory and epistemic uncertainty; (3) Development of formulations and algorithms for design optimization under aleatory and epistemic uncertainty, from the perspective of system robustness and reliability; (4) Development of a framework for uncertainty propagation in multidisciplinary system analysis; and (5) Development of formulations and algorithms for design optimization under aleatory and epistemic uncertainty for multidisciplinary systems, from the perspective of system robustness and reliability. The methodology developed in this dissertation is illustrated through problems related to spacecraft design and analysis, such as the conceptual upper-stage design of a two-stage-to-orbit vehicle, and design and analysis of a fire detection satellite.

A probabilistic framework is developed in this dissertation for numerical simulation of the degradation of cementitious materials under external sulfate attack. The model combines detailed approaches for four essential components of degradation: (i) diffusion of ions, (ii) chemical reactions of the cement hydration products with the diffused species, (iii) damage accumulation due to cracking, and (iv) changes in mechanical properties due to mineralogical evolution. The model is calibrated and validated using experimental results available from the literature. Sensitivity analyses are performed to identify the most influential parameters affecting the mineralogical features and the progression of damage in the structure. Uncertainty in the chemical equilibrium model is addressed through Bayesian calibration of the model parameters. The probabilistic framework accounts for various sources of uncertainty physical variability due to inherent randomness of physical processes and parameters, and data uncertainty due to sparse or imprecise data. Various approaches for statistical representation of the uncertainties are investigated and incorporated in the durability assessment framework. The methodology for assessing the durability of the structure is implemented using nested and single-loop Monte Carlo simulation. Finally, the application of the framework is demonstrated by assessing durability of a concrete vault wall exposed to sulfate solution, incorporating uncertainty in various components of the model.

Fatigue crack growth is a stochastic process and different kinds of uncertainty physical variability, data uncertainty and modeling errors should be included within the analysis to more accurately represent the fatigue life of the component. This dissertation systematically identifies, quantifies, and incorporates different types of uncertainties within an overall probabilistic life prediction modeling approach. The uncertainty quantification (UQ) methodology is implemented with 3-dimensional planar and non-planar fatigue crack modeling, for structural components subjected to multi-axial, variable amplitude loading conditions. Included within the scope of this work are UQ methods for material properties and model parameters, as well as methods which focus on model error quantification including FEA discretization error and surrogate modeling error. Additionally, the uncertainty quantification and propagation methodology is developed to be computationally efficient to enable the component reliability assessment to be performed within a Monte Carlo Scheme. The proposed methodology is illustrated for application to a rotorcraft mast component.