Search for the rare decays $Dto h(h)e^+e^-$

We search for rare decays of $D$ mesons to hadrons accompany with an electron-positron pair (h(h)$e^+e^-$), using an $e^+e^-$ collision sample corresponding to an integrated luminosity of 2.93 fb$^{-1}$ collected with the BESIII detector at $sqrt{s}$ = 3.773 GeV. No significant signals are observed, and the corresponding upper limits on the branching fractions at the $90%$ confidence level are determined. The sensitivities of the results are at the level of $10^{-5} sim 10^{-6}$, providing a large improvement over previous searches.