Numerical models are pervasive tools in science and engineering for simulation, design, and assessment of physical systems. In structural engineering, finite element (FE) models are extensively used to predict responses and estimate risk for built structures. While FE models attempt to exactly replicate the physics of their corresponding structures, discrepancies always exist between measured and model output responses. Discrepancies are related to aleatoric uncertainties, such as measurement noise, and epistemic uncertainties, such as modeling errors. Epistemic uncertainties indicate that the FE model may not fully represent the built structure, greatly limiting its utility for simulation and structural assessment. Model updating is used to reduce error between measurement and model-output responses through adjustment of uncertain FE model parameters, typically using data from structural vibration studies. However, the model updating problem is often ill-posed with more unknown parameters than available data, such that parameters cannot be uniquely inferred from the data. This dissertation focuses on two approaches to remedy ill-posedness in FE model updating: parametrization and regularization. Parametrization produces a reduced set of updating parameters to estimate, thereby improving posedness. An ideal parametrization should incorporate model uncertainties, effectively reduce errors, and use as few parameters as possible. This is a challenging task since a large number of candidate parametrizations are available in any model updating problem. To ameliorate this, three new parametrization techniques are proposed: improved parameter clustering with residual-based weighting, singular vector decomposition-based parametrization, and incremental reparametrization. All of these methods utilize local system sensitivity information, providing effective reduced-order parametrizations which incorporate FE model uncertainties. The other focus of this dissertation is regularization, which improves posedness by providing additional constraints on the updating problem, such as a minimum-norm parameter solution constraint. Optimal regularization is proposed for use in model updating to provide an optimal balance between residual reduction and parameter change minimization. This approach links computationally-efficient deterministic model updating with asymptotic Bayesian inference to provide regularization based on maximal model evidence. Estimates are also provided for uncertainties and model evidence, along with an interesting measure of parameter efficiency.

Preterm birth (PTB) is the leading cause of childhood death and effects 10% of babies worldwide. First-time diagnosis is difficult, and as many as 95% of all PTBs are intractable to current therapies. The processes of both preterm labor and normal parturition are poorly understood, in part because pregnancy is a protected environment where experimentation contains the risk of causing harm to the gestation and fetus. This proposes the need for non-invasive investigations to understand both normal and high-risk pregnancies. Furthermore, each pregnancy can vary significantly which adds the complex need for patient-specific investigations. To address this need, we propose the development of parameterized ultrasound-based finite element analyses to study the mechanics of the womb. As a first step, this dissertation work conducts sensitivity analyses on cervical, uterine, and fetal membrane parameters as well as model boundary conditions to determine which factors have the greatest impact on cervical tissue stretch. The effects of the range of patient geometries and material properties are reported. Findings show that a soft and short cervix result in greatest stretch at the internal os, and fetal membrane detachment increases cervical stretch. Additionally, patient-specific finite element analyses are performed on low- and high-risk cohorts and results between the two are compared. Patient geometries are documented at various gestational timepoints, and the effect of a cervical pessary is determined based on changes in cervical geometry and stiffness. Findings showed that a soft cervix correlates with sooner delivery, and that high pessary placement is ideal to decrease stretch at the internal os.

A hybrid data-physics driven reduced-order homogenization (dpROH) approach aimed at improving the accuracy of the physics-based reduced order homogenization (pROH), but retain its unique characteristics, such as interpretability and extrapolation, has been developed. The salient feature of the dpROH is that the data generated by a high-fidelity model based on the direct numerical simulations with periodic boundary conditions improve markedly the accuracy of the physic-based model reduction. The dpROH consist of the offline and online stages. In the offline stage, dpROH utilized surrogate-based Bayesian Inference to extract crucial information at the representative volume element (RVE) level. With the inferred data, online predictions are performed using a data-enhanced reduced order homogenization. The proposed method combines the benefits of physics-based reduced order homogenization and data-driven surrogate modeling, striking a balance between accuracy, computational efficiency, and physical interpretability. The dpROH method, as suggested, has the versatility to be utilized across different RVE geometries (including fibrous and woven structures) and various constitutive models, including elasto-plasticity and continuum damage models. Through numerical examples that involve comparisons between different variants of dpROH, pROH, and the reference solution, the method showcases enhanced accuracy and efficiency, validating its effectiveness for a wide range of applications. A novel pseudo-nonlocal eight-node fully integrated linear hexahedral element, PN3D8, has been developed to accelerate the computational efficiency of multiscale modeling for complex material systems. This element is specifically designed to facilitate finite element analysis of computationally demanding material models, enabling faster and more efficient simulations within the scope of multiscale modeling. The salient feature of the PN3D8 is that it employs reduced integration for stress updates but full integration for element matrices (residual and its consistent tangent stiffness). This is accomplished by defining pseudo-nonlocal and local stress measures. Only the pseudo-nonlocal stress is updated for a given value of mean strain or mean deformation measure for large deformation problems. The local stress is then post-processed at full integration points for evaluation of the internal force and consistent tangent stiffness matrices. The resulting tangent stiffness matrix has a symmetric canonical structure with an identical instantaneous constitutive matrix at all quadrature points of an element. For linear elasticity problems, the formulation of the PN3D8 finite element coincides with the classical eight-node fully integrated linear hexahedral element. The procedure is illustrated for small and large deformation two-scale quasistatic problems.

Dynamic finite element modeling and analysis of a refrigeration compressor was investigated as part of a noise emission study. Natural frequencies and normal mode shapes were calculated for the major structural components of the compressor. The components were later combined to form a model of the compressor assembly which was subsequently solved for its dynamic properties. Model development included coordination with test data for verification and revision to improve model prediction accuracy. Considerable efforts were made to accurately represent the hermetic shell which presents several inherent modeling difficulties due to its geometry and other characteristics which result from a deep drawn manufacturing process. The importance of physical simplifications such as geometry representation, thickness variation, attachments, the welded seam, and residual stresses were established. In addition, theoretical limitations of the finite element method were addressed as a cause for analysis-test discrepancies. Housing models developed were found to agree within 12% of experimental natural frequencies up to 1100 Hz. Compatibility of analytical normal modes with resonant dwell experimental deflection shapes was considered. Analytical forced vibration response showed situations when the deflected shapes can be a superposition of modes rather than the pure mode shape. Analytical simulation of the test setup improved the agreement of analysis and test data. Additional components modeled include the internal compressor mechanism and its supports. Analysis showed that interactions with the internal components, particularly resonances within the suspension springs, are important for a valid representation of the compressor assembly. Resonances within the internal suspension components more than double or nearly triple the number of resonance frequencies in the compressor assembly. / Master of Science