Most stars form in a clustered environment. Therefore, it is important to assess how this environment influences the evolution of protoplanetary discs around young stars. In turn, this affects their ability to produce planets and ultimately life. We present here for the first time 3D smoothed particle hydrodynamics/N-body simulations that include both the hydrodynamical evolution of the discs around their natal stars, as well as the dynamics of the stars themselves. The discs are viscously evolving, accreting mass on to the central star and spreading. We find penetrating encounters to be very destructive for the discs as in previous studies, although the frequency of such encounters is low. We also find, however, that encounter influence the disc radii more strongly than other disc properties such as the disc mass. The disc sizes are set by the competition between viscous spreading and the disruptive effect of encounters. As discs spread, encounters become more and more important. In the regime of rapid spreading, encounters simply truncate the discs, stripping the outer portions. In the opposite regime, we find that the effect of many distant encounters is able to limit the disc size. Finally, we predict from our simulations that disc sizes are limited by encounters at stellar densities exceeding ∼2–3 × 103 pc−2.

Protoplanetary disc evolution affected by star-disc interactions in young stellar clusters