Theses and Dissertations
Issuing Body
Mississippi State University
Advisor
Bhatia, Manav
Committee Member
Lacy, Thomas E.
Committee Member
Zhang, Xu
Date of Degree
12-14-2018
Original embargo terms
Worldwide
Document Type
Graduate Thesis - Open Access
Major
Aerospace Engineering
Degree Name
Master of Science
College
James Worth Bagley College of Engineering
Department
Department of Aerospace Engineering
Abstract
This thesis focuses on the development and convergence study of finite element methods for eigenvalue analysis of arbitrarily shaped domains with multi-material and material-void interfaces. Such configurations can be found in problems with evolving discontinuities and interfaces as in fluid-structure interaction or topology optimization problems. The differential equations considered in this thesis include the elliptic operator, Timoshenko beam and Mindlin plate. The compatibility conditions at the interface are weakly imposed using either Nitsche's method or Lagrange multipliers. The variational statements are derived for each case. The analysis results are benchmarked using Galerkin finite element discretization with bodyitted grids. Nitsche's method shows a direct dependence on a penalty term and for Lagrange multipliers method, additional degrees of freedom are added to the solution vector. The convergence rate of the discretized forms is computationally determined and is shown to be optimal for both Timoshenko beams and Mindlin plates.
URI
https://hdl.handle.net/11668/18560
Recommended Citation
Arsalane, Walid, "Eigenvalue Analysis of Timoshenko Beams and Mindlin Plates with Unfitted Finite Element Methods" (2018). Theses and Dissertations. 1844.
https://scholarsjunction.msstate.edu/td/1844