基于多面体有限元的高混凝土坝易损性分析

    Vulnerability analysis of high concrete dam based on polyhedral finite element method

    • 摘要: 针对传统四面体与六面体有限元网格在精度、自适应性和收敛速度上的不足,开发一种基于光滑有限元法(S-FEM)的多面体有限元程序,以提升混凝土重力坝地震易损性分析的效率与精度。通过S-FEM与多面体单元的耦合,结合隐式形函数构造与平滑域划分技术,构建高精度多面体有限元模型;并采用悬臂梁与复杂几何模型验证其收敛性和计算效率;进一步以西畴重力坝为案例,基于增量动力分析(IDA)方法,以坝顶位移和损伤指数为性能指标,评估其在不同地震动强度下的易损性。结果表明:多面体单元在相同网格密度下较四面体单元收敛速度显著提升,且对网格畸变不敏感;案例坝在设计地震动(0.14g)和校核地震动(0.16g)作用下,轻微损伤概率分别为58.64%和75.89%,溃坝概率均趋近于0%。本文创新性地将S-FEM与多面体单元结合,突破了传统网格划分的几何限制,显著提升了复杂结构非线性分析的数值稳定性与计算效率,为高混凝土坝抗震性能评估与设计提供了可靠的理论支撑与工具,具有重要工程应用价值。

       

      Abstract: To address the limitations of traditional tetrahedral and hexahedral finite element meshes in terms of precision, geometric adaptability, and convergence speed, a polyhedral finite element program based on the Smooth Finite Element Method (S-FEM) was developed to enhance the efficiency and accuracy of seismic vulnerability analysis for concrete gravity dams. By integrating S-FEM with polyhedral elements, a high-precision polyhedral finite element model was constructed through implicit shape function construction and smoothing domain partitioning techniques. The convergence and computational efficiency of the program were validated using cantilever beam and complex geometric models. Furthermore, taking the Xichou gravity dam as a case study, the Incremental Dynamic Analysis (IDA) method was employed to evaluate the dam’s vulnerability under varying seismic intensities, with dam crest displacement and damage index as performance indicators. The results demonstrate that polyhedral elements exhibit significantly improved convergence speed compared to tetrahedral elements at identical mesh densities, along with insensitivity to mesh distortion. Under design seismic motion (0.14g PGA) and check seismic motion (0.16g PGA), the probabilities of minor damage for the case dam were 58.64% and 75.89%, respectively, while the probability of dam failure approached 0% in both scenarios. This study innovatively combines S-FEM with polyhedral elements, overcoming the geometric constraints of traditional mesh generation and significantly improving the numerical stability and computational efficiency for nonlinear analysis of complex structures. It provides reliable theoretical support and practical tools for seismic performance evaluation and design of high concrete dams, demonstrating substantial engineering applicability.

       

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