Committee Chair

Ghasemi, Arash

Committee Member

Newman III, James C.; Sutton, William H.

Department

Dept. of Mechanical Engineering

College

College of Engineering and Computer Science

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

In an effort to prove the effectiveness of a methodology that computes more efficiently than traditional FEM methods, this paper details a method that allows for the accurate and efficient solution of an elasticity problem using an hp-SEM code. The code can interchange basis functions to allow us to compare Lagrange with Fekete basis functions, which have the capability of high accuracy and efficiency. The code is applied to solve a traditional elasticity problem with an analytical solution to judge the accuracy on a course mesh. This gives us a method that provides greater accuracy than traditional FEM when comparing the same mesh, and higher efficiency compared to Lagrange bases comparing matrix condition numbers. This produces a flatter curve when varying p-order, which shows that higher orders than the 9th-order methods tested here are easily achievable with this technique. The flexibility of our code is shown by solving solutions with complex geometry and holes.

Acknowledgments

I would like to thank the many teachers at UTC who have supported me and my education at this institution since 2011. In particular, I would like to thank Dr. Will Sutton and Dr. Arash Ghasemi for their advising, mentorship, and teaching over the last several years, which made this thesis possible. Thanks must also be given to Volkswagen Chattanooga, for financing this endeavor, and my wife Allyson, who supported me during the many hours invested into this work and my education.

Degree

M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science.

Date

12-2020

Subject

Elasticity; Mathematical models

Keyword

Complex geometry; Fekete; High order accuracy; High order finite elements; Spectral elements

Document Type

Masters theses

DCMI Type

Text

Extent

xi, 100 leaves

Language

English

Rights

http://rightsstatements.org/vocab/InC/1.0/

License

http://creativecommons.org/licenses/by/4.0/

Date Available

12-31-2021

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