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| 二维有自由面渗流问题的等几何分析求解 |
| Solution of 2D free surface seepage problems using Isogeometric analysis |
| 投稿时间：2024-10-12 修订日期：2024-11-04 |
| DOI： |
| 中文关键词: 有自由面渗流问题 移动网格法 等几何分析 优化 |
| 英文关键词:free surface seepage problem moving mesh method isogeometric analysis optimization |
| 基金项目:国家自然科学基金资助项目(U22A20600, 52079070, 52079002) |
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| 中文摘要: |
| 采用传统移动网格法求解有自由面渗流问题时，自由面迭代修正引发的计算网格调整由于受有限元单元形状限制往往不便。借鉴等几何结构优化的思路，将自由面确定问题视为饱和区上界曲线的位置优化问题。针对二维问题将饱和区表征为NURBS曲面，使用等几何分析求解渗流场，以自由面控制点水头值和纵坐标差异最小为目标进行优化，获得最终的自由面位置。通过将自由面控制点纵坐标修改为其水头值实现自由面的更新，渗流区域的NURBS曲面将自动重新生成从而完成计算网格调整。采用均质矩形土坝、均质梯形土坝、非均质矩形土坝等数值算例验证本文方法的有效性和实用性。结果表明：本文提出方法可有效求解二维有自由面渗流问题且具备良好的数值精度；同时可实现自由面修改后计算网格的实时快捷更新，克服传统移动网格法网格调整不便的局限性。 |
| 英文摘要: |
| In the solution of free surface seepage problems using conventional moving mesh methods, the computational mesh needs continuous modification to update the free surface. However, this process is hindered by constraints on element shapes in the finite element method. Inspired by structural optimization with isogeometric analysis (IGA), this study views determining the free surface as a shape optimization challenge within the saturated zone. The saturated zone is represented as a NURBS surface for 2D free surface seepage problems, and the seepage field is addressed using IGA. The ultimate free surface is obtained by minimizing the discrepancy between head values and the vertical coordinates of control points on the free surface. Throughout the computation, the free surface is updated by adjusting the vertical coordinates of control points to match the head values, leading to automatic reconstruction of the NURBS surface and computational meshes. The proposed method is validated through solving three numerical examples, a homogeneous rectangle earth dam, a homogeneous trapezoidal earth dam and a heterogeneous rectangle earth dam. Results demonstrate the effectiveness and applicability of the new method in solving 2D free surface seepage problems with good numerical accuracy. Furthermore, the method offers convenient and easy mesh updating capabilities, addressing a key limitation of conventional moving mesh methods. |
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