  The four decay modes $D^{0}\to\phi\pi^{0}$, $D^{0}\to\phi\eta$,
$D^{+}\to\phi\pi^{+}$, and $D^{+}\to\phi K^{+}$ are studied by using a data
sample taken at the centre-of-mass energy $\sqrt{s} = 3.773$~GeV~with the
BESIII detector, corresponding to an integrated luminosity of 2.93 fb$^{-1}$.
The branching fractions of the first three decay modes are measured to be
${\cal B}(D^{0}\to\phi\pi^{0})=(1.168\pm0.028\pm0.028)\times10^{-3}$, ${\cal
B}(D^{0}\to\phi\eta)=(1.81\pm0.46\pm0.06)\times10^{-4}$, and ${\cal
B}(D^{+}\to\phi\pi^{+})=(5.70\pm0.05\pm0.13)\times10^{-3}$, respectively, where
the first uncertainties are statistical and the second are systematic. No
significant signal is observed of the decay $D^+\to\phi{K^+}$ and the upper
limit of its branching fraction is set for the first time, to be
$2.1\times10^{-5}$ at the $90\%$ confidence level. The ratio of ${\cal
B}(D^0\to\phi\pi^0)$ to $\cal B(D^+\to\phi\pi^+)$ is calculated to be
$(20.49\pm0.50\pm0.45)\%$, which is consistent with the theoretical prediction
based on isospin symmetry between these two decay modes.
