A new radiative driven implosion (RDI) model based on smoothed particle hydrodynamics technique is developed and applied to investigate the morphological evolutions of molecular clouds under the effect of ionizing radiation. This model self-consistently includes the self-gravity of the cloud in the hydrodynamical evolution, the UV radiation component in the radiation transferring equations, the relevant heating and cooling mechanisms in the energy evolution, and a comprehensive chemical network. The simulation results reveal that under the effect of ionizing radiation, a molecular cloud may evolve through different evolutionary sequences. Depending on its initial gravitational state, the evolution of a molecular cloud does not necessarily follow a complete morphological evolution sequence from type A?B?C, as described by previous RDI models. When confronted with observations, the simulation results provide satisfactory physical explanations for a series of puzzles derived from bright-rimmed clouds observations. The consistency of the modeling results with observations shows that the self-gravity of a molecular cloud should not be neglected in any investigation on the dynamical evolution of molecular clouds when they are exposed to ionizing radiation.