  We present a thorough numerical study on the MRI using the smoothed particle
magnetohydrodynamics method (SPMHD) with the geometric density average force
expression (GDSPH). We perform shearing box simulations with different initial
setups and a wide range of resolution and dissipation parameters. We show, for
the first time, that MRI with sustained turbulence can be simulated
successfully with SPH, with results consistent with prior work with grid-based
codes. In particular, for the stratified boxes, our simulations reproduce the
characteristic butterfly diagram of the MRI dynamo with saturated turbulence
for at least 100 orbits. On the contrary, traditional SPH simulations suffer
from runaway growth and develop unphysically large azimuthal fields, similar to
the results from a recent study with mesh-less methods. We investigated the
dependency of MRI turbulence on the numerical Prandtl number in SPH, focusing
on the unstratified, zero net-flux case. We found that turbulence can only be
sustained with a Prandtl number larger than $\sim$2.5, similar to the critical
values of physical Prandtl number found in grid-code simulations. However,
unlike grid-based codes, the numerical Prandtl number in SPH increases with
resolution, and for a fixed Prandtl number, the resulting magnetic energy and
stresses are independent of resolution. Mean-field analyses were performed on
all simulations, and the resulting transport coefficients indicate no
$\alpha$-effect in the unstratified cases, but an active $\alpha\Omega$ dynamo
and a diamagnetic pumping effect in the stratified medium, which are generally
in agreement with previous studies. There is no clear indication of a
shear-current dynamo in our simulation, which is likely to be responsible for a
weaker mean-field growth in the tall, unstratified, zero net-flux simulation.
