<p>Developing topology optimization methods capable of bypassing sensitivity analysis whilst generating smooth boundaries has always been an important goal pursued by scholars in the field of structural design. This paper is committed to the following objectives: devising a smooth-edged proportional topology optimization (SEPTO) method that relies on no sensitivity analysis; using the SEPTO method to investigate the structural optimization problem with minimum compliance under volume constraints; and obtaining topology designs with smooth boundaries. Among these, the SEPTO method is proposed through multiple strategies and approaches, including elemental volume fractions, a material interpolation scheme based on elemental volume fractions, the PTO approach, a modified updating equation for elemental volume fractions, multiple filters, a sigmoid-based Heaviside smooth function, and a level set function. Subsequently, the optimization design problems of four benchmark structures are solved, and the design results are analyzed to evaluate the efficacy of the SEPTO method and its differences from the other four comparison methods. Simulation results indicate that, in all examples, the SEPTO method exhibits the strongest capability to find optimal solutions and best topology designs compared to the other comparison methods. Additionally, the SEPTO method not only yields simple topology designs with smooth boundaries but also exhibits relatively fast convergence.</p>