<p>This study presents an efficient numerical approach, marking the first integration of polytree-based adaptive refinement and bubble-enriched smoothed polygonal finite element methods within the dual-yield structural design framework. The behavior of smoothed polygonal elements in response to volumetric locking, both with and without bubble enhancement, is thoroughly analyzed and numerically validated. Two robust indicators, based on plastic dissipation energy and yield stress fields at the limit state, are developed to guide local mesh refinement, thereby enhancing the performance of the proposed discretization techniques. The essential design parameters of structural yield, including the limit load multiplier and collapse mechanism, are accurately determined with optimal computational efficiency. Numerical investigations demonstrate the effectiveness of the proposed method.</p>