Conventional density-based topology optimization often produces indistinct or non-smooth boundaries, making direct conversion to practical design models difficult. Recent studies have explored simultaneous shape and topology optimization to address this limitation, but these approaches typically require additional procedures, such as adaptive mesh refinement. This study presents a density-based topology optimization framework formulated on a deformable triangular mesh, in which element densities and nodal movements are simultaneously treated as design variables. By introducing nodal movements as additional design variables, the design space is significantly expanded compared to fixed meshes. An enriched finite element method is employed to minimize the stiffening due to element distortion while geometric constraints on element shape preserve element validity and quality. Non-physical artifacts such as single-node connections are suppressed using a patch-based approach. As a result, the proposed framework produces optimized structures with smooth boundaries without requiring additional mesh modification procedures. The effectiveness of the proposed framework is demonstrated through a variety of numerical examples, including representative benchmark examples with complex geometries. The optimized results consistently exhibit smooth and well-defined structural boundaries and can be directly transferred to computer-aided design environments without any post-processing. Overall, the proposed optimization framework is well-suited for problems involving complex design domains or requiring accurate boundary representation. This work was supported by the Development of Core Technologies for Manufacturing Foundation Models Program (RS-2025-15458052) and the Korea Institute for Advancement of Technology (KIAT) grant (RS-2024- 00409092, 2024 HRD Program for Industrial Innovation) funded by the Korea Government (MOTIE); and by the InnoCORE program of the Ministry of Science and ICT (N10250154).