Most stars are born in clusters and the resulting gravitational interactions between cluster members may significantly affect the evolution of circumstellar disks and therefore the formation of planets and brown dwarfs (BDs). Recent findings suggest that tidal perturbations of typical circumstellar disks due to close encounters may inhibit rather than trigger disk fragmentation and so would seem to rule out planet formation by external tidal stimuli. However, the disk models in these calculations were restricted to disk radii of 40 AU and disk masses below 0.1 M ☉. Here, we show that even modest encounters can trigger fragmentation around 100 AU in the sorts of massive (~0.5 M ☉), extended (≥100 AU) disks that are observed around young star...