  Fluid-structure interaction (FSI) problems are pervasive in the computational
engineering community. The need to address challenging FSI problems has led to
the development of a broad range of numerical methods addressing a variety of
application-specific demands. While a range of numerical and experimental
benchmarks are present in the literature, few solutions are available that
enable both verification and spatiotemporal convergence analysis. In this
paper, we introduce a class of analytic solutions to FSI problems involving
shear in channels and pipes. Comprised of 16 separate analytic solutions, our
approach is permuted to enable progressive verification and analysis of FSI
methods and implementations, in two and three dimensions, for static and
transient scenarios as well as for linear and hyperelastic solid materials.
Results are shown for a range of analytic models exhibiting progressively
complex behavior. The utility of these solutions for analysis of convergence
behavior is further demonstrated using a previously published monolithic FSI
technique. The resulting class of analytic solutions addresses a core challenge
in the development of novel FSI algorithms and implementations, providing a
progressive testbed for verification and detailed convergence analysis.
