The Dissipative Particle Dynamics (DPD) simulation technique was used to elucidate the composition-dependent equilibrium morphological behavior of three different symmetric ABA triblock copolymers, which were; poly(epsilon-caprolactone)-poly(dimethylsiloxane)-poly(epsilon-caprolactone) (PCL-PDMS-PCL), poly(epsilon-caprolactone)-poly(ethylene oxide)-poly(epsilon-caprolactone) (PCL-PEO-PCL) and poly(L-lactide)-poly(dimethylsiloxane)-poly(L-lactide) (PLLA-PDMS-PLLA). These polymers were chosen due to their biomedical and biotechnological importance. Polymeric A and B blocks were modeled as connected chain of beads with varying incompatibility. The impact of the block incompatibilities on the microphase separation as well as on the equilibrium phase behaviors were investigated at the mesoscopic scale. A detailed visual analysis of the DPD images and constructed phase diagram showed that quite different equilibrium morphologies were attainable by controlling the molecular weights of the blocks and the strength of the intermolecular interaction between them. More compatible A and B blocks underwent lamellar to cylindrical and cylindrical to spherical phase transitions at lower B block concentrations. Our results clearly showed that, Flory-Huggins interaction parameter (chi) and degree of polymerization (N) were the only control parameters, which determined the shape and size of the phase domains, as well as the extent of equilibrium nanophase separation. Our DPD simulated morphologies were compared with experimental images obtained by Atomic Force Microscopy (AFM).