Theses and Dissertations

Issuing Body

Mississippi State University


Bhatia, Manav

Committee Member

Lacy, Thomas E.

Committee Member

Zhang, Xu

Date of Degree


Original embargo terms


Document Type

Graduate Thesis - Open Access


Aerospace Engineering

Degree Name

Master of Science


James Worth Bagley College of Engineering


Department of Aerospace Engineering


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.