This work relates to fluid-structure interactions in the context of flapping wing systems. System models of flapping flight are explored by using a coupling scheme to provide communication between a fluid model and a structural model describing a flexible wing. The constructed computational models serve as a tool for investigating complex fluid-structure interactions and characterizing them. Primary goals of this work are construction of models to understand nonlinear phenomena associated with the flexible flapping wing systems, and explore means and methods to enhance their performance characteristics. Several system analysis tools are employed to characterize the coupled fluid-structure system dynamics, including proper orthogonal decomposition, dimension calculations, time histories, and frequency spectra.

Results obtained from two-dimensional simulations conducted for a combination of a two-link structural system and a fluid system are presented and discussed. Comparisons are made between the use of direct numerical simulation and the unsteady vortex lattice method as the fluid model in this coupled dynamical system. To enable three-dimensional studies, a novel solid model is formulated from continuum mechanics for geometrically exact finite elements. A new partitioned fluid-structure interaction algorithm based on the Generalized-α method is formulated and implemented in a large scale fluids solver inside the FLASH framework. Consistent boundary conditions are also formulated by using Lagrangian particles. Several examples demonstrating the effectiveness of the methods and implementation are shown, in particular, for flapping flight at low Reynolds numbers. Unique experiments have also been undertaken to determine the first few natural frequencies and mode shapes associated with hawkmoth wings. The computational framework developed in this dissertation and the research findings can be used as a basis to understand the role of flexibility in flapping wing systems, further explore the complex dynamics of flapping wing systems, and also develop design schemes that might make use of nonlinear phenomena for performance enhancement.