<p>The design of functionally graded porous structure(PS) faces persistent challenges: (1) a large number of design variables; (2) the lack of explicit, manufacture-ready geometric boundaries; (3) insufficient research on balancing structural performance with computational cost; (4) limited capability for optimizing structures with hybrid pore types; (5) comprehensive studies integrating numerical and experimental validation, safety assessment, and multi-physics extensibility; To address these, this paper proposes a novel explicit design method that governs pore shape through an adaptive parametric equation. This equation directly controls pore shape, size, and orientation, enabling the generation of diverse and complex polygonal arrays. The proposed method directly tackles the stated challenges: It reduces the design variables by up to two orders of magnitude (e.g., from 39,000 to 294 in a benchmark case) compared to density-based methods, while providing explicit boundaries suitable for direct finite element (FE) analysis and additive manufacturing (AM). Systematic parametric studies establish an optimal economic configuration (e.g., a 2 × 1 domain with 30 × 15 pores on a 300 × 150 mesh). The final results show a mere 0.66% discrepancy compared to Abaqus results, and align well with mechanical testing results. It successfully generates and optimizes structures with hybrid polygonal pores and handles complex scenarios including mixed boundary conditions and thermoelastic coupling. Notably, the optimized structures exhibit superior damage tolerance, with only an 11.65% compliance increase under local damage versus a 592.01% increase for a traditional density-based method. This work provides a unified, efficient, and geometrical method for designing reliable, high-performance porous structures.</p>