Density-based topology optimization algorithms, such as solid isotropic material with penalization (SIMP), pursue solid/void solutions to yield distinct topologies, however blurry or zigzag boundaries are unavoidable. By contrast, newly developed elemental volume fraction based algorithms pursue solid/void grid points, and the intermediate elements, consisting of both solid and void grid points, are artificially defined as boundary elements through which smooth boundaries can be formed. Smooth-Edged Material Distribution for Optimizing Topology (SEMDOT) algorithm is a typical elemental volume fraction based method developed based on the SIMP framework. However, the current version of SEMDOT needs to use the material penalization scheme in SIMP to facilitate the distinction of solid, void, and boundary elements. This framework restriction has motivated the development of the non-penalized SEMDOT algorithm to establish the physically meaningful relation between the elemental volume fraction and its material property. This study adopts discrete variable sensitivities for solid, void and assumed boundary elements instead of continuous variable sensitivities to eliminate the material penalization scheme and obtain efficient smooth topological layouts. The efficiency, effectiveness, and general applicability of the proposed non-penalized SEMDOT algorithm are demonstrated in three case studies containing compliance minimization, compliant mechanism design, and heat conduction problems, as well as thorough comparisons with penalized SEMDOT. The numerical results show that the convergency of non-penalized SEMDOT is stronger than penalized SEMDOT, and improved results can be obtained by non-penalized SEMDOT.