Two-dimensional cylindrical magnetohydrodynamic (MHD) simulations are implemented to investigate the dynamical properties of young type Ia supernova remnants (SNRs) undergoing shock acceleration in a turbulent medium. In our simulations, an MHD code is coupled with a semianalytical kinetic treatment of shock acceleration by means of a time-dependent effective adiabatic index. Large-scale density and magnetic field fluctuations are calculated and mapped into the computational domain before simulations. The above configurations allow us to study the time-dependent dynamical properties and magnetic field structure of a benchmark SNR undergoing shock acceleration in a turbulent medium, along with the relative positions of the contact discontinuity. Our simulation results reveal that there is a rippled forward shock, a thinner shocked ejecta layer and a denser, narrower intershock region. The resulting net effect is a higher density difference between the shocked ejecta and the shocked interstellar medium, leading to a growth of the Rayleigh-Taylor instability. The amplified magnetic field occurs not only at the contact discontinuity but also near the immediate downstream of the shock. The spatial location of the maximum magnetic field is in the vicinity of immediate downstream, which is different with Guo et al. Our derived profiles of the relative contact discontinuity positions are compatible with the results of two typical young type Ia SNRs: SN 1006 and Tycho, with the lowest value reaching similar to 1.02 for both cases. Moreover, we find no obvious ejecta protrusions beyond the main forward shock.