Date of Award


Document Type

Masters Thesis

Degree Name


Organizational Unit

Daniel Felix Ritchie School of Engineering and Computer Science, Mechanical and Materials Engineering

First Advisor

Yun-Bo Yi

Second Advisor

Peter Laz

Third Advisor

Mohammad Matin


Eigenvalue method, Finite element analysis, Finite element method, Fourier element, Fourier reduction, Thermoelastic instabilities


The objective of the work presented in this thesis is to develop first-order triangular and tetrahedral elements for solutions to Thermoelastic Instabilities (TEI) regarding sliding friction systems in Hotspotter.

Hotspotter software uses a finite element method and an eigenvalue method and is an important tool because currently no other commercial software exists which solves the TEI problem for critical velocities and wave numbers of a system. Hotspotter currently uses quadrilateral and hexahedral elements for two and three dimensional analysis, respectively. Typically, tri and tet elements are used in industry when doing static and dynamic stress analysis. Therefore, the Hotspotter user is currently required to re-mesh the system using quad or hex based elements before importing the mesh into Hotspotter, a time consuming and dispensable process. Development of triangular and tetrahedral elements for TEI analysis will eliminate the re-meshing burden on the Hotspotter user without sacrificing accuracy of results.

Presented in this investigation is the mathematical development of such tri and tet elements. Then, verification of those elements by comparing trial cases against theoretical and Abaqus results. Finally, validation by incorporating the tri elements into Hotspotter and comparing to the quad elements. Results indicate accuracy within 1 percent of the legacy elements which have been validated against experimental data.

Publication Statement

Copyright is held by the author. User is responsible for all copyright compliance.

Rights Holder

Cortney Samuel LeNeave


Received from ProQuest

File Format




File Size

102 pgs


Mechanical engineering, Aerospace engineering, Engineering