  We derive a mathematical model and the corresponding computational scheme to
study deflection of a two-dimensional elastic cantilever beam immersed in a
channel, where one end of the beam is fixed to the channel wall. The immersed
boundary method has been employed to simulate numerically the fluid-structure
interaction problem. We investigate how variations in physical and numerical
parameters change the effective material properties of the elastic beam and
compare the results qualitatively with linear beam theory. We also pay careful
attention to "corner effects" -- irregularities in beam shape near the free and
fixed ends -- and show how this can be remedied by smoothing out the corners
with a "fillet" or rounded shape. Finally, we extend the immersed boundary
formulation to include porosity in the beam and investigate the effect that the
resultant porous flow has on beam deflection.
