Topology optimization in structural mechanics can be understood as a computational framework for determining optimal material distributions within a prescribed design domain, subject to given boundary conditions and performance requirements. Since the original contributions of Bendsøe and Kikuchi in the late 1980s, the field has gained substantial prominence due to its impact across applied engineering disciplines, including civil, mechanical, and aerospace engineering. Recent growth in computational resources has further accelerated the development and practical deployment of topology optimization methods. This study first seeks to organize and synthesize current understanding of structural models with intermediate (relative) densities as employed in the SIMP approach, with the aim of proposing strategies to mitigate the physical and numerical difficulties that arise when elasticity problems with density-dependent properties are solved using Galerkin-based discretizations (e.g., FEM, IGA). Particular attention is devoted to optimization settings in which dynamic response or second-order effects are essential, as these aspects often govern feasibility and performance. The overarching goal is to develop SIMP-based topology-optimization formulations for isotropic structures that incorporate advanced constraints and their interactions so that multiple physical phenomena are represented within a unified design procedure, ultimately enabling minimum-weight solutions. Because weight reduction can increase susceptibility to instability, dynamic sensitivity and stress amplification [3], these effects are addressed during optimization through established analysis tools, including natural frequency evaluation, linear buckling assessment, and block-aggregated stress control.