Date of Award


Document Type


Degree Name

Master of Science (MS)

Legacy Department

Mechanical Engineering

Committee Member

Dr. Paul Joseph, Committee Chair

Committee Member

Dr. Tim Rhyne

Committee Member

Dr. Lonny Thompson


This thesis is a continuation of the model development work by Amir Gasmi in 2011 and Tim Lewis in 2012. The model was originally developed by Gasmi in 2011 to represent non-pneumatic tires. It centers on a thin, circular beam in contact with a rigid surface, which represents the belt package of the non-pneumatic tire. The beam is connected to a wheel with spokes. Gasmi developed a method to approximate these discrete spokes with a continuous load on the belt package. The results of this non-pneumatic tire model agreed very well with non-linear finite element analysis of a non-pneumatic tire. This model was adapted for pneumatic tires by Lewis in 2012. Lewis introduced a superposition scheme to reduce errors introduced by tension in the belts at the edge of contact. The sidewalls were approximated as circular in order to calculate sidewall stiffness. The results presented by Lewis for force versus deflection and counterdeflection agreed reasonably well with experimental measurements, but used stiffness values that were more from curve fitting than from a mechanics analysis of the tire geometry and material properties. The model presented in this thesis was developed directly from Lewis' model. This model includes more representative sidewall modeling based on membrane theory, and more representative belt properties based on composites theory. Unlike in the results presented by Lewis, the sidewall stiffness values (denoted as Kr and Kθ) are not considered to be inputs to the model; rather, the tire's geometrical design parameters (such as outer radius and sidewall width) are the inputs, and the stiffness values are calculated as part of the model. This allows for a more direct connection to tire design. The model has been improved to take into account a stiffness property called pre-tensioning, which allows the sidewalls (or in the case of a non-pneumatic tire, spokes) to maintain their stiffness in tension at small levels of negative deflection. This thesis will present a thorough investigation of the solutions with and without superposition, at a range of conditions. Also presented is an investigation of adjustments to input parameters to account for assumptions made in the model, as well as a sensitivity analysis.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.