Computational performance of irregular finite-element meshes in site seismic response analysis
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摘要: 随着地震工程领域的场地地震反应分析工作向着大规模、复杂化和集成化不断拓展,算法的精确性和高效率优化问题愈发受到人们关注。本文通过数值试验和理论分析对场地地震反应分析中不规则有限元网格的计算性能进行了较为全面的探讨,主要得到如下研究结果:(1)常用的“十分之一波长”网格尺寸存在一定误差,1/15~1/20波长的网格尺寸能够达到更高精度。(2)三角形单元和四边形单元在同等网格尺寸下具有相同精度。同理,非对称、狭长的单元与对称、饱满的单元相比,当二者长边尺寸相同时,前者的短边方向具有更高精度。(3)显式时间积分格式稳定计算的时间步长与单元最小特征尺寸相关联,如矩形单元的短边、三角形单元最小的高、不规则四边形单元最近两边的垂向距离等。不规则有限元网格的时间步长受整体模型的最小网格尺寸控制。(4)非对称、狭长单元以及不规则模型中局部小尺寸网格会控制满足计算稳定性的最大时间步长,从而严重降低计算效率。因此,采用对称、饱满的单元形状并提高同一波速区域中网格尺寸的均匀性,能够大幅度提升计算效率。建议在实际场地地震反应分析工作中针对场地模型资料通常并不十分精细的特点,充分利用本文给出的原则建立高效率离散化模型。
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关键词:
Abstract: As site response analysis work in the field of earthquake engineering increasingly advances towards large-scale, complex and integrated applications, the accuracy and efficiency optimization problems of the algorithm have regained significant focus. This paper comprehensively investigates the computational performance of finite-element mesh models constructed by irregular elements in site response analysis through numerical experiments and theoretical analyses. The main findings are as follows: (1) The commonly used “one-tenth wavelength” mesh size exhibits certain inaccuracies; a mesh size of one-fifteenth to one-twentieth wavelength can achieve higher precision. (2) Triangular and quadrilateral elements demonstrate equivalent accuracy at identical mesh sizes. Similarly, when comparing asymmetric, elongated elements with symmetric, well-proportioned elements of equal long-edge dimensions, the former exhibits higher accuracy along its short-edge direction. (3) The stable time step for explicit time integration schemes correlates with the minimum characteristic dimension of elements—such as the short side of rectangles, the minimum height of triangular elements, or the perpendicular distance between the nearest two edges of irregular quadrilaterals. The time step for irregular finite element meshes is governed by the smallest mesh size in the whole discrete model. (4) Asymmetric, elongated elements and localized fine-scale meshes in irregular models severely constrain the limit time step of computational stability, significantly reducing computational efficiency. Therefore, adopting symmetric, well-proportioned element shapes and improving mesh size uniformity within each region of identical wave velocity can substantially enhance computational efficiency. Considering that site model data in practical seismic response analyses often lack high precision, we recommend utilizing the principles outlined in this study to establish highly efficient discrete models.-
Key words:
- site seismic response /
- finite element mesh /
- element size /
- time step size /
- computational efficiency
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