Application of the Fekete spectral element method in stress analysis of plates involving holes and complex geometries

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.

Grantor dc:publisher

University of Tennessee at Chattanooga

Year dc:date.available

2021

Author dc:creator

• Shannon, Kyle

Contributors dc:contributor

• Ghasemi, Arash
• Newman III, James C.; Sutton, William H.
• College of Engineering and Computer Science

• Elasticity
• Mathematical models

Licence

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

Language dc:language

English, eng

Repository record dc:identifier

https://scholar.utc.edu/theses/679

OAI identifier oai:identifier

oai:scholar.utc.edu:theses-1847