Engineering Applications of the Arbitrary Polygon Hybrid Stress Finite Element Method

With the continuous expansion and increasing complexity of major engineering projects in China, the safety analysis of engineering structures has been increasingly dependent on numerical methods. Traditional finite element methods have certain limitations in complex geometries, such as strong mesh dependency and low calculation efficiency. The polygonal hybrid stress finite element method (PHSEM), based on the principle of minimum complementary energy and the introduced higher-order stress fields, is capable of accurately capturing stress distributions with fewer elements while improving calculation efficiency. A multi-material slope model considering gravity was established for the left-bank accumulation slope at the Xiluodu Hydropower Station, to verify the applicability and effectiveness of the PHSEM under complex geological conditions. Four representative slope cross sections were selected for stress and strain calculations, and both stress and strain contours were utilized to visually reveal the differences in force distributions and potentially dangerous zones for different sections. The results demonstrate that, the PHSEM can effectively reflect the distribution patterns of slope stresses and strains, providing a reliable basis for the slope stability evaluation, the retaining structure design, and the engineering treatment schemes. Furthermore, the findings highlight the potential of the PHSEM in analyzing complex slopes and large-scale engineering structures, offering valuable references for future numerical simulations and safety assessments of similar major projects.