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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