Engineering Applications of the Arbitrary Polygon Hybrid Stress Finite Element Method
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(Recommended by LIU Shaobao, M.AMM Editorial Board)-
摘要: 随着我国重大工程建设的规模与复杂度不断提升，工程结构的安全分析对数值方法依赖日益增强. 传统有限元方法在复杂几何问题中存在网格依赖性强、计算效率较低等局限. 任意多边形杂交应力有限元(PHSEM)基于最小余能原理，引入高阶应力场，能够在较少单元数量的情况下，准确计算应力分布并提高计算效率. 该文结合溪洛渡水电站左岸堆积体边坡算例，建立了考虑重力作用的多材料边坡模型，验证了PHSEM在复杂地质条件下的适用性与有效性. 同时，选取了四个代表性边坡剖面进行应力与应变计算，利用应力云图和应变云图直观揭示了不同剖面下的受力差异与潜在危险区段. 结果表明，PHSEM不仅能有效反映边坡应力应变分布规律，还能为边坡稳定性评价、支护措施设计和工程治理方案提供可靠依据. 研究成果同时展示了PHSEM在复杂边坡与大规模工程结构分析中的应用潜力，为今后类似重大工程的数值模拟与安全评估提供了参考依据.Abstract: 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.
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Key words:
- arbitrary polygon /
- hybrid stress finite element /
- numerical simulation /
- high-order stress field /
- engineering application
edited-byedited-by1) (我刊编委刘少宝推荐) -
图 1 模型材料示意图
注 为了解释图中的颜色，读者可以参考本文的电子网页版本，后同.
Figure 1. Schematic diagram of model materials
图 6 剖面模型应力应变计算云图
Figure 6. Contours of stress and strain calculations for the cross-sectional model
图 7 添加防护的剖面5工况示意图
Figure 7. Schematic of cross-sectional working condition 5 with protection
表 1 材料参数
Table 1. Material parameters
material Young’s modulus/Pa Poisson’s ratio density/(kg·m－3) flood deposit body plQ3 2.5×107 0.35 2 000 glaciers and ice-water accumulation bodies fgl+glQ2 5.5×107 0.3 2 350 ancient landslide debris delQ2 3.5×107 0.3 2 250 sand shale P2X 7.5×108 0.35 2 500 basalt P2β 7.5×109 0.25 2 800 
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[1] 潘城. 岩石动态力学特性及破裂机理的晶粒离散元研究[D]. 南京: 东南大学, 2022.PAN Cheng. Investigations of rock dynamic properties and fracture mechanisms using grain-based discrete element method[D]. Nanjing: Southeast University, 2022. (in Chinese) [2] ZIENKIEWICZ O C, TAYLOR R L, ZHU J Z. The Finite Element Method[M]. 7th ed. Oxford: Butterworth-Heinemann, 2013. [3] COOK R D. Concepts and Applications of Finite Element Analysis[M]. 4th ed. New York: John Wiley & Sons, 2007. [4] HUTTON D V. Fundamentals of Finite Element Analysis[M]. New York: McGraw-Hill, 2003. [5] CHAPRA S C, CANALE R P. Numerical Methods for Engineers[M]. 7th ed. New York: McGraw-Hill, 2014. [6] BREBBIA C A, TELLES J C F, WROBEL L C. Boundary Element Techniques[M]. 2nd ed. Berlin: Springer, 2012. [7] CUNDALL P A, STRACK O D L. A discrete numerical model for granular assemblies[J]. Géotechnique, 1979, 29(1): 47-65. [8] PIAN T H H. Derivation of element stiffness matrices by assumed stress distributions[J]. AIAA Journal, 1964, 2(7): 1333-1336. doi: 10.2514/3.2546 [9] PIAN T H H. A historical note about 'hybrid elements'[J]. International Journal for Numerical Methods in Engineering, 1978, 12(5): 891-892. doi: 10.1002/nme.1620120514 [10] PIAN T H H, TONG P. Relations between incompatible displacement model and hybrid stress model[J]. International Journal for Numerical Methods in Engineering, 1986, 22(1): 173-181. doi: 10.1002/nme.1620220112 [11] SAETHER E. Closed-form derivation of an 8-node hexahedral element stiffness matrix by the hybrid stress method[J]. Communications in Numerical Methods in Engineering, 1995, 11(9): 775-787. doi: 10.1002/cnm.1640110908 [12] PIAN T H H, WU C C. Hybrid and Incompatible Finite Element Methods[M]. 1st ed. Boca Raton: Chapman & Hall/CRC, 2005. [13] 魏高峰, 冯伟, 高洪芬. 基于位移插值的Voronoi单元有限元方法[J]. 应用力学学报, 2008, 25(2): 342-346.WEI Gaofeng, FENG Wei, GAO Hongfen. Voronoi cell finite element method based on displacement interpolation[J]. Chinese Journal of Applied Mechanics, 2008, 25(2): 342-346. (in Chinese) [14] ZHOU P L, CEN S. A novel shape-free plane quadratic polygonal hybrid stress-function element[J]. Mathematical Problems in Engineering, 2015, 2015: 491325. [15] 杨锋, 郭然. 多边形应力杂交单元的接触算法研究[J]. 应用数学和力学, 2019, 40(10): 1059-1070. doi: 10.21656/1000-0887.400046YANG Feng, GUO Ran. Study on contact algorithms for the polygonal hybrid stress element method[J]. Applied Mathematics and Mechanics, 2019, 40(10): 1059-1070. (in Chinese) doi: 10.21656/1000-0887.400046 [16] WU C J, CEN S, SHANG Y. Shape-free polygonal hybrid displacement-function element method for analyses of Mindlin-Reissner plates[J]. Engineering With Computers, 2021, 37(3): 1975-1998. doi: 10.1007/s00366-019-00922-x [17] 黎子君, 田静杰, 胡长浩, 等. 考虑蠕变的任意多边形杂交应力单元[J]. 重庆大学学报, 2025, 48(8): 28-39.LI Zijun, TIAN Jingjie, HU Changhao, et al. Arbitrary polygonal hybrid stress element for creep analysis in roadbed engineering[J]. Journal of Chongqing University, 2025, 48(8): 28-39. (in Chinese) [18] 伍文锋, 税思梅. 溪洛渡水电站左岸谷肩堆积体边坡治理和监测[J]. 水电站设计, 2013, 29(4): 97-10.WU Wenfeng, SHUI Simei. Slope treatment and monitoring of the left bank valley shoulder accumulation body at Xiluodu hydropower station[J]. Design of Hydroelectric Power Station, 2013, 29(4): 97-10. (in Chinese) [19] LIU C, TIAN J, HU C, et al. Slope calculation analysis based on arbitrary polygonal hybrid stress elements considering gravity[J]. Symmetry, 2025, 17(2): 265. doi: 10.3390/sym17020265 [20] 胡筱, 尤林, 赵艳. 溪洛渡水电站坝区左岸进水口上方谷肩堆积体边坡综合治理设计[J]. 水电站设计, 2011, 27(3): 31-35.HU Xiao, YOU Lin, ZHAO Yan. Comprehensive treatment design for the slope of valley shoulder accumulation above the left bank intake dam area of Xiluodu hydropower station[J]. Design of Hydroelectric Power Station, 2011, 27(3): 31-35. (in Chinese) -
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