Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Aeronautics and Astronautics

First Advisor

Robert A. Canfield, PhD


Fluid-structure interaction problems prove difficult due to the coupling between fluid and solid behavior. Typically, different theoretical formulations and numerical methods are used to solve fluid and structural problems separately. The least-squares finite element method is capable of accurately solving both fluid and structural problems. This capability allows for a simultaneously coupled fluid structure interaction formulation using a single variational approach to solve complex and nonlinear aeroelasticity problems. The least-squares finite element method was compared to commonly used methods for both structures and fluids individually. The fluid analysis was compared to finite differencing methods and the structural analysis type compared to traditional Weak Galerkin finite element methods. The simultaneous solution method was then applied to aeroelasticity problems with a known solution. Achieving these results required unique iterative methods to balance each domain's or differential equation's weighting factor within the simultaneous solution scheme. The scheme required more computational time but it did provide the first hands-off method capable of solving complex fluid-structure interaction problems using a simultaneous least-squares formulation. A sequential scheme was also examined for coupled problems.

AFIT Designator


DTIC Accession Number