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The objective of this research was to develop and verify a mathematical model and the necessary material database that allow predicting the physical and material property changes that occur in aluminum casting alloys in response to precipitation-hardening heat treatment. The model accounts for all three steps of the typical precipitation hardening heat treatment; i.e., the solutionizing, quenching, and aging steps; and it allows predicting the local hardness and tensile strength, and the local residual stresses, distortion and dimensional changes that develop in the cast component during each step of the heat treatment process. The model uses commercially available finite element software and an extensive database that was developed specifically for the aluminum alloy under consideration - namely A356.2 casting alloy. The database includes the mechanical, physical, and thermal properties of the alloy all as functions of temperature. The model predictions were compared to measurements made on commercial cast components that were heat treated according to standard heat treatment protocols and the model predictions were found to be in good agreement with the measurements.

Roadside safety hardware has traditionally been approved on the basis of full-scale crash tests. In recent years, nonlinear dynamic Finite Element (FE) programs like LS-DYNA, PAM-Crash or ABAQUS Explicit have been widely used in evaluating new or improved design of roadside hardware. Although a powerful tool, numerical models must be properly verified and validated in order to provide reliable results. Typically, the verification and validation (V&V) process involves a visual comparison of two curves and is based on a purely subjective judgment. This research investigated the use of comparison metrics, which are mathematical measures that quantify the level of agreement between two curves, for comparing simulation and experimental outcomes in an objective manner. A computer program was developed in Matlab® to automatically evaluate most of the comparison metrics available in literature. The software can be used to preprocess and compare either single or multiple channels, guiding the user through friendly graphical interfaces. Acceptance criteria suitable to represent the typical scatter of experimental tests in roadside safety were determined by comparing ten essentially identical full-scale vehicle crash tests. The robustness and reliability of the implemented method were tested by comparing the qualitative score of the computed metrics for a set of velocity waveforms with the corresponding subjective judgment of experts. Moreover, the implemented method was applied to two real validation cases involving a numerical model in roadside safety and a model in biomechanics respectively. Eventually, the program showed to be an effective tool to be used for assessing the similarities and differences between two curves and, hence, for assisting engineers and analysts in performing verification and validation activities objectively.

Every year, millions of people are killed or injured in motor vehicle accidents in the United States. Although recent improvements to occupant restraint systems, such as seatbelts and airbags, have significantly decreased life threatening injuries, which usually occur to the chest or head, they have done little to decrease the occurrence of lower extremity injuries. Although lower extremity injuries are not usually life threatening, they can result in chronic disability and high psychosocial cost. Of all lower extremity injuries, injuries to the knee-thigh-hip (KTH) region have been shown to be among the most debilitating. This project used a finite element (FE) model of the KTH region to study injury. A parametric investigation was conducted where the FE KTH was simulated as a vehicle occupant positioned to a range of pre-crash driving postures. The results indicate that foot contact force and knee kinematics during impact affects the axial force absorbed by the KTH region and the likelihood of injury. The results of the study could be used to reevaluate the lower extremity injury thresholds currently used to regulate vehicle safety standards. Also, the results could be used to provide guidelines to vehicle manufacturers for developing safer occupant compartments.

"Recent full-scale crash tests of the weak-post W-beam guardrail system have resulted in unsatisfactory collision performance as evaluated by the National Cooperative Highway Research Program (NCHRP) Report 350. Since acceptable crash test performance is required in order to use a guardrail on a Federal-Aid Highway in the United States, the poor performance of the weak-post W-beam guardrail is a significant problem to those states that use it. The goal of this project was to improve the impact performance of the weak-post W-beam guardrail system so that it satisfies the requirements of NCHRP Report 350 at test level three."

O trabalho realizado consiste no desenvolvimento das equações pertinentes à teoria de cascas, implementação de programas de elementos finitos em Matlab e resolução de problemas de casca numéricos e analíticos. No desenvolvimento da teoria de cascas é evidenciada a aplicação da curvatura da estrutura no cálculo das forças e momentos resultantes para uma superfície de casca simplificada a uma estrutura localmente bidimensional. O problema de casca é resolvido analiticamente para um caso de curvatura simples e comparado com a resolução por elementos finitos em um programa desenvolvido pelo autor, em que a utilização da curvatura para o cálculo das forças e momentos resultantes é inserida na programação. A análise de elementos finitos é realizada para casos de casca com curvatura simples e dupla curvatura e de duas formas, sendo que a primeira utiliza elementos cujas normais médias são empregadas na montagem da matriz de rigidez, constituindo um elemento de casca e a segunda aplica normais a cada nó de cada elemento, tendo-se assim uma superfície facetada, com comportamento de placa em cada elemento. Os resultados obtidos mostram que o impacto da aplicação da curvatura em geral é pequeno nas regiões mais críticas para as forças e momentos resultantes, como na região de engaste. Porém, algumas regiões da casca apresentam grandes variações, e caso sejam de importância para o usuário, cabe uma análise mais detalhada em que o emprego da curvatura possa ser considerado. / This work presents the development of the shell theory equations, implementation of finite element programs in Matlab and the resolution of numerical and analytical shell problems. Along with the development of the shell theory, the application of the curvature of the structure in the calculation of stress and couple resultants for a shell structure simplified to a bidimensional problem become clear. The shell problem is solved analytically, by means of the application of the shell equations in a shell with simple curvature, and this solution is compared with the numerical solution using the finite element program implemented, considering the curvature of the structure for the stress and couple resultants. Finite element analysis is performed for the simple and double curvature cases of shells, and in two distinct ways, the first one considering averaged normals for neighbor elements, which produces shell elements, the second one using normals to each node of each element, which results in locally flat elements, behaving as plates. Results obtained show that the impact of the application of the curvature in the resultants is usually small in the most critical points, such as the crimp. However, some regions of the shell present huge variation, and further analysis is recommended, since the application of the curvature can be important.

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Vita. / Includes bibliographical references. / Ph.D.

Ductile and brittle failure of solids are closely related to their plastic and fracture behavior, respectively. The two most common energy dissipation mechanisms in solids possess distinct kinematic characteristics, i.e. large strain and discontinuous displacement, both of which pose challenges to reliable, efficient numerical simulation of material failure in engineering structures. This dissertation addresses the reliability and efficiency issues associated with the kinematic characteristics of plasticity and fracture. At first, studies are conducted to understand the relation between two well recognized large strain plasticity models that enjoy widespread popularity in numerical simulation of plastic behavior of solids. These two models, termed the additive hypo-elasto-plasticity and multiplicative hyper-elasto-plasticity models, respectively, are regarded as two distinct strategies for extending the classical infinitesimal deformation plasticity theory into the large strain regime. One of the most recent variants of the additive models, which features the logarithmic stress rate, is shown to give rise to nonphysical energy dissipation during elastic unloading. A simple modification to the logarithmic stress rate is accordingly made to resolve such a physical inconsistency. This results in the additive hypo-elasto-plasticity models based on the kinetic logarithmic stress rate in which energy dissipation-free elastic response is produced whenever plastic flow is absent. It is then proved that for isotropic materials the multiplicative hyper-elasto-plasticity models coincide with the additive ones if a newly discovered objective stress rate is adopted. Such an objective stress rate, termed the modified kinetic logarithmic rate, reduces to the kinetic logarithmic rate in the absence of strain-induced anisotropy which is characterized as kinematic hardening in the present dissertation. In the second part of the dissertation, the computational complexity of finite element analysis of the onset and propagation of interface cracks in layered materials is addressed. The study is conducted in the context of laminated composites in which interface fracture (delamination) is a dominant failure mode. In order to eliminate the complexities of remeshing for constant initiation and propagation of delamination, two hierarchical approaches, the extended finite element method (XFEM) and the s-version of the finite element method (s-method) are studied in terms of their effectiveness in representing displacement discontinuity across delaminated interfaces. With one single layer of 20-node serendipity solid elements resolving delamination-free response of the layered materials, it is proved that the delamination representations based on the s-method and the XFEM result in the same discretization space as the conventional non-hierarchical ply-by-ply approach which employs one layer of solid elements for each ply as well as double nodes on delaminated interfaces. Delamination indicators based on the s-method representation of delamination are then proposed to detect the onset and propagation of delamination. An adaptive methodology is accordingly developed in which the s-method displacement field enrichment for delamination is adaptively added to interface areas with high likelihood of delamination. Numerical examples show that the computational cost of the adaptive s-method is significantly lower than that incurred by the conventional ply-by-ply approach despite the fact that the two approaches produce practically identical results.

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.

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