The vestibular system consists of several organs that contribute to ones sense of balance. One set of organs, otoconial organs, have been shown to respond to linear acceleration (1949). Hair bundles (and hair cells), which are the mechano-electric transducers found within otoconial organs, respond to displacement of the overlying otoconial membrane (OM). Structure, position and orientation of the OM within the head may influence the stimulus of hair bundles by changing the deformation characteristics of the OM. Therefore, studying the deformation characteristics of the OM with finite element models presents a unique advantage: the ability to study how different variables may influence the deformation of the OM. Previous OM models have ignored complicated OM geometry in favor of single degree of freedom (De Vries 1951)or distributed parameter models (Grant et al. 1984; Grant and Cotton 1990; Grant et al. 1994). Additionally, OMs have been modeled considering three dimensional geometry (Benser et al. 1993; Kondrachuk 2000; 2001a), however OM layer thicknesses were assumed to be constant. Further, little research has investigated the effect of position and orientation of otoconial organs on the deformation of the OM (Curthoys et al. 1999), due to natural movement of the head. The effect of structure, position and orientation of the utricle of a red ear slider turtle on the stimulation of hair bundles in the OM is investigated here. Using confocal images, a finite element model of the utricle OM is constructed considering its full 3D geometry and varying OM layer thickness. How specific geometric variables, which are missing from other OM models, effect the deformation of the utricle OM is studied. Next, since hair bundles are part of the structure of the OM, their contribution to the deformation of the utricular OM is quantified. Then, using computed tomography of a turtle head and high speed video of turtle feeding strikes, acceleration at the utricle during natural motion is estimated. Finally, the effects of orientation of the utricle in the head on the stimulus of hair bundles within the organ is investigated. In summary, a model and methods are developed through which deformation of the turtle utricle OM through natural movements of the head may be studied. Variables that may contribute to utricle OM deformation are investigated. Utricle OM geometry, hair bundles, position and orientation all play a role in utricle OM deflection and therefore hair bundle stimulus. Their effects are quantified and their roles are discussed in this dissertation. / Ph. D.

Polymeric foam cores are widely used as core materials in sandwich panels subject to blast loads, where high strain rates of the order of 4000 /s are observed. Unlike metallic foams polymeric foams exhibit transversely isotropic response when tested in a laboratory setting. More specifically, they exhibit different hardening along the foam thickness than that in a direction transverse to the thickness. Furthermore, polymeric foams harden differently in tension and compression. In this thesis we adopt ideas from the constitutive model developed by Hoo Fatt et al. cite{hoofatt2}, which captures strain hardening, transverse isotropy and distinguishes the response in tension and in compression, to include isotropic strain rate hardening in our constitutive model. A one dimensional prototype of the model is used to aid in the physical explanation of various variables, and the model is generalized to three dimensions. The material model is implemented as a VUMAT (user defined) subroutine in the commercial finite element software ABAQUS Explicit. We show that the model works robustly in uniaxial deformations as well as in sandwich problems using the test data available in the literature. We provide values of the 39 material parameters for H45, H60, H80, H100, H130 and H200 foams. The constitutive relation is utilized in an optimization problem in which the surrogate optimizer is utilized to minimize the backface deflection of a blast loaded clamped sandwich plate of a fixed mass. The core in the optimized sandwich structure has a stratified configuration (not functionally graded) and has 24% less maximum back face deflection as compared to that in which the six core layers vary from highest density to lowest density or vice a versa. For a sandwich panel subject to a blast load, when the strain rate hardening effect are neglected, we observed a 12% reduction in the predicted peak deflection from that when strain rate effects are considered. It is counter intuitive and needs further investigation. / Master of Science / Sandwich panels are widely used in high performance structures requiring high stiffness, low weight and the ability to withstand blasts. Sandwich panels consist of several layers, and it is possible to vary the material and thickness of each layer to arrive at a sandwich panel design which performs optimally. In this thesis, we numerically find an optimum sandwich panel design so that it deflects the least when exposed to a given blast. The problem is studied using ABAQUS Explicit and the Surrogate Optimization solver built into MATLAB. The outer layers of the sandwich panel are made of a highly stiff material and their thicknesses are fixed. The remaining six inner layers are allowed to be any of six different H45, H60, H80, H100, H130, H200 Divinycell polymeric foams and are allowed to vary in thickness. In order to draw a fair comparison between the designs, we constrain the total mass of the sandwich panel to be 1 kg. In our quest to find the best sandwich panel design, we develop and implement, in ABAQUS Explicit, a custom mathematical model which captures the complex behavior of the polymeric foams. Experimental data in the literature and other techniques were utilized to check that this mathematical model accurately predicts the physical response of polymeric foams in different scenarios. The reader is given all of the theory and physical constants needed to use this mathematical model for the six foams. The optimal sandwich panel deflects 24% less than a baseline design, and it is found that the material properties of the six foams do not vary gradually as they did in the baseline designs.

Simulations of the welding process for butt and tee joints using finite element analyses are presented. The base metal is aluminum alloy 2519-T87 and the filler material is alloy 2319. The simulations are performed with the commercial software SYSWELD+®, which includes moving heat sources, material deposit, metallurgy of binary aluminum, temperature dependent material properties, metal plasticity and elasticity, transient heat transfer and mechanical analyses. One-way thermo-mechanical coupling is assumed, which means that the thermal analysis is completed first, followed by a separate mechanical analysis based on the thermal history. The residual stress state from a three-dimensional analysis of the butt joint is compared to previously published results. For the quasi-steady state analysis the maximum residual longitudinal normal stress was within 3.6% of published data, and for a fully transient analysis this maximum stress was within 13% of the published result. The tee section requires two weld passes, and both a fully three-dimensional (3-D) and a 3-D to 2-D solid-shell finite elements model were employed. Using the quasi-steady state procedure for the tee, the maximum residual stresses were found to be 90-100% of the room-temperature yield strength. However, the longitudinal normal stress in the first weld bead was compressive, while the stress component was tensile in the second weld bead. To investigate this effect a fully transient analysis of the tee joint was attempted, but the excessive computer times prevented a resolution of the longitudinal residual stress discrepancy found in the quasi-steady state analysis. To reduce computer times for the tee, a model containing both solid and shell elements was attempted. Unfortunately, the mechanical analysis did not converge, which appears to be due to the transition elements used in this coupled solid-shell model. Welding simulations to predict residual stress states require three-dimensional analysis in the vicinity of the joint and these analyses are computationally intensive and difficult. Although the state of the art in welding simulations using finite elements has advanced, it does not appear at this time that such simulations are effective for parametric studies, much less to include in an optimization algorithm. / Master of Science

The research focuses on developing a methodology for modeling a pneumatic bias-ply tire with the finite element method for vehicle dynamics simulation. The tire as a load-carrying member in a vehicle system deserves emphasized formulation especially for the contact patch because its representation of mechanics in the contact patch directly impacts the handling and ride performance of a vehicle. On the other hand, the load transfer from the contact patch to the wheel hub is necessary for determining the inputs to a chassis. A finite element (FE) tire model has strong capability to handle these two issues. However, the high cost of computing resources restrains its application mainly in the tire design domain. This research aims to investigate how to balance the complexity of a simplified FE tire model without diminishing its capability towards representing the load transmission for vehicle dynamics simulation. The traditional FE tire model developed by tire suppliers usually consists of an extremely large number of elements, which makes it impossible to be included in a full-vehicle dynamics simulation. The material properties required by tire companies' FE tire models are protected. The car companies have an increasing need for a physical-based tire model to understand more about the interaction between the tire and chassis. A gap between the two sides occurs because the model used for tire design cannot directly help car companies for their purpose. All of these reasons motivate the current research to provide a solution to narrow this gap. Other modern tire models for vehicle dynamics, e.g. FTire or TAME, require a series of full-tire tests to calibrate their model parameters, which is expensive and time-consuming. One great merit of the proposed simplified FE tire model is that determining model inputs only requires small-scale specimen tests instead of full-tire tests. Because much of the usability of a model hinges on whether its input parameters are easily determined, this feature makes the current model low cost and easily accessible in the absence of proprietary information from the tire supplier. A Hoosier LC0 racing tire was selected as a proof of modeling concept. All modeling work was carried out using the general purpose commercial software Abaqus. The developed model was validated through static load-deflection test data together with Digital Image Correlation (DIC) data. The finite element models were further evaluated by predicting the traction/braking and cornering tire forces against Tire Test Consortium (TTC) data from the Calspan flat-track test facility. The emphasis was put on modeling techniques for the transient response due to the lack of available test data. The in-plane and out-of-plane performance of the Hoosier tire on the full-tire test data is used for model validation, not for "calibrating" the model. The agreement between model prediction and physical tests demonstrate the effectiveness of the proposed methodology. / PHD / This research aims to develop a method to build a physically-based tire model less relying on the information of products from tire providers for the purpose of vehicle dynamics simulation. The tire model is a mathematical description of the behavior of tires under various operational conditions. The model is said to be ‘physically-based’ if it is derived from physical laws. In contrast, if the model is termed ‘semi-empirical,’ it means that the model is mainly based on tire measurement data. A physically-based model usually gives more insights to and a better understanding of tire mechanics than a semi-empirical tire model. The tire as a load-carrying member in a vehicle system deserves emphasized formulation especially for the tire-road contact patch because its representation of mechanics in the contact patch directly impacts the handling and ride performance of a vehicle. Therefore, a physically-based tire model is preferred. One kind of physically-based models are developed through the multi-body dynamics (MBD) approach. Various full tire tests are required to identify the parameters associated with the model. Since full tire tests should be conducted on professional tire test machines, the high-cost prevents many users to have a tire model of such kind. The other kind of physically-based models are developed through the finite-element method (FEM). The FEM has strong capability to describe the mechanism of tire-road contact and deformation of the tire body. Also, parameters needed by a finite element tire model are basic material properties of different components of the tire structure, which implies the possibility to acquire parameters through small-scale sample tests instead of full tire tests. However, most of FE tire models are developed for tire design with high complexity, not good for vehicle simulation. This research made efforts to degrade the complexity of the FE tire model and tailor the FE modeling technique suitable for the purpose of vehicle simulation. In addition, the process was designed and implemented for obtaining the necessary parameters associated with the model. A Hoosier LC0 racing tire was selected as a proof of modeling concept without any tire property data provided by tire producers. This research has a practical meaning on building tire models independent of tire companies and at low cost.

An important part of an aerodynamic design process is optimizing designs to maximize quantities such as lift and the lift-to-drag ratio, in a process known as shape optimization. It is the goal of this thesis to develop and apply understanding of mixed finite element method and sensitivity analysis in a way that sets the foundation for shape optimization. The open-source Incompressible Flow Iterative Solution Software (IFISS) mixed finite element method toolbox for MATLAB developed by Silvester, Elman, and Ramage is used. Meshes are produced for a backward-facing step problem, using built-in tools from IFISS as well as the mesh generation software Gmsh, and grid convergence studies are performed for both sets of meshes along a sampled data line to ensure that the simulations converge asymptotically with increasing mesh resolution. As a preliminary study of sensitivity analysis, analytic sensitivities of velocity components along the backward-facing step data line to inflow velocity parameters are determined and verified using finite difference and complex step sensitivity values. The method is then applied to pressure drag calculated by integrating the pressure over the surface of a circular cylinder in a freestream flow, and verified and validated using published simulation data and experimental data. The sensitivity analysis study is extended to shape optimization, wherein the shape of a circular cylinder is altered and the sensitivities of the pressure drag coefficient to the changes in the cylinder shape are determined and verified. / Master of Science / When looking at designing an aircraft, it is important to consider the forces air flow exerts on the wings. The primary forces of interest for aerodynamic analysis are lift, which generally acts upward perpendicular to the flow of air, and drag, which opposes the motion of the wing through the air. Optimization is the process of developing a design in such a way that a specific quantity, such as lift or drag, is either maximized or minimized. Many methods exist of predicting the behavior of air flow, and various methods of optimization exist which take already existing predictive software and progressively alter the design to try to meet the minimized or maximized objective. This thesis outlines a multi-step effort to modify an open source software such that it could be used for design optimization.

This thesis presents the results of a research effort aimed at investigating the crash performance of w-beam guardrail barriers in vehicle-roadside crashes using the finite element method. The developed roadside barrier models can be used to assess the occupant injury risk, vehicle performance, and damage to guardrail barriers during a roadside accident. The finite element models of w-beam guardrail barriers may also help evaluate the crash performance of the w-beam barriers with minor damage in vehicle-barrier crashes. Thus, the results can be used to develop repair guidelines to assist highway personnel in identifying levels of minor barrier damage and deterioration. Finite element models of the weak post w-beam guardrail barriers were developed and simulated using LS-DYNA. The simulation results were validated against full scale crash tests of pickup trucks and passenger cars impacting w-beam guardrail barriers. The maximum dynamic deflection of the guardrail, exit velocity and angle of the vehicle, and occupant injury risk were calculated and compared to the tests. Kinematics of the vehicle and guardrail were assessed qualitatively as well as quantitatively. The analysis showed that simulation results were in good agreement with test data. Additionally, the models were validated against pendulum tests conducted the Federal Outdoor Impact Laboratory (FOIL). Simulation results of pendulum tests showed that the test section taken from the current full scale models performed very similarly to that in the real pendulum tests. The developed finite element models were subsequently used to examine the crash performance of weak post w-beam guardrail barriers with minor damage under vehicle impacts. Only rail/post deflection based minor damage to weak post w-beam guardrail barriers was considered in this study. Simulations were completed to obtain the damaged profiles of the guardrail systems; the damaged weak post guardrail barriers were impacted by the pickup model at mid-span for the second time. The impacting vehicle remained stable in all of these simulations. No conclusions could be drawn however whether these second impacts could have resulted in rail tearing or rupture. / Master of Science

This thesis suggests a formulation for updating physically meaningful parameters in analytical finite element(FE) models using scanning laser Doppler vibrometer(SLDV) dynamic response data. The update formulation is demonstrated in several computer simulations. The formulation is the result of incorporating an analytical FE model into an experimental model. The experimental model efficiently utilizes SLDV data to fully exploit the instrument's capability to automatically make measurements at many locations. The data in the experimental model is posed in a manner consistent with an analytical FE model's representation for harmonic response, simplifying comparison between the two. The experimental model, which uses finite element shape functions as a basis for a least squares fit to the data, can be solved to give a velocity field based only on that data. The function resulting from inserting the analytical model into the experimental model is an expression of the prediction error of the FE model as compared to the test data. This function is minimized using a quasi-Newton optimization routine, reducing the error and resulting in an updated model. Computer simulations of the update algorithm indicate that: 1. Analytically supplied derivatives and variable scaling are required by the optimization routine to consistently converge, 2. The percentage error of updated parameters falls within two standard deviations of the data's percentage error, 3. Error in the position of the laser results in the update algorithm's failure, and, 4. Error in the parameters not included in the update will appear as error in the updated parameters' solution. / Master of Science

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Spacecraft structures rely on honeycomb panels to provide a light weight means to support the vehicle. Honeycomb panels can carry significant load but are most vulnerable to structural failure at their joints where panels connect. This research shows that predicting sandwich panel joint capability using finite element analysis (FEA) is possible. This allows for the potential elimination of coupon testing early in a spacecraft design program to determine joint capability. Linear finite element analysis (FEA) in NX Nastran was used to show that adhesive failure can be predicted with reasonable accuracy by including a fillet model on the edge of the fitting. Predicting the ultimate failure of a joint using linear FEA requires that engineering judgment be used to determine whether failure of certain bonds in a fitting will lead to ultimate joint failure or if other bonds will continue to carry the joint's load. The linear FEA model is also able to predict when the initiation of core failure will begin. This has the limitation that the joint will still be able to continue to carry significantly more load prior to joint ultimate failure even after the core has begun to buckle. A nonlinear analysis is performed using modified Riks' method in Abaqus FEA to show that this failure mode is predictable. The modified Riks' analysis showed that nonlinear post-buckling analysis of a honeycomb coupon can predict ultimate core failure with good accuracy. This solution requires a very high quality mesh in order to continue to run after buckling has begun and requires imperfections based on linear buckling mode shapes and thickness tolerance on the honeycomb core to be applied. / Master of Science / Spacecraft structures rely on honeycomb panels to provide a light weight means to support the vehicle. Honeycomb panels consist of two thin metal sheets separated by a light weight honeycomb grid. The panels operate in a similar way to how an I-Beam works on a bridge. These panels can carry significant load but are susceptible to failure because the panels must be glued together when they are built. This research shows that predicting honeycomb panel joint capability using finite element analysis (FEA) is possible. FEA allows the engineer to model and predict failure in complex structures by mathematically combining many small shapes called elements which have known behaviors and properties into the shape of the actual tested article. The elements deflect in a known manner based on the load applied to the model. The honeycomb panel joint is predicted to break when the deflection in a particular element is higher than the element’s material capability. Obtaining the load where the panel breaks is critical information to have during the design of a spacecraft structure. Using the techniques presented in this thesis allows for the potential elimination of coupon testing early in a spacecraft design program to determine joint capability. Coupon testing is where honeycomb panels are built and tested to failure. This testing is very expensive in terms of both cost and program schedule and therefore using analysis to eliminate its need or to reduce its scope provides significant benefit to the spacecraft program.