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摘要:
等几何分析（IGA）中非均匀有理B样条（NURBS）被同时用作计算机辅助设计（CAD）中的建模工具以及有限元分析（FEA）中的逼近函数。NURBS模型中常见的缝隙和重叠问题使得分析变得困难。基于Mindlin板理论，对含有缝隙与重叠部分的NURBS模型进行等几何分析，采用Nitsche方法处理模型交界面上的非协调问题，并通过标准数值仿真算例的计算结果与解析解对比验证方法的可行性。研究结果表明：基于Nitsche的等几何方法可以用来对含局部缝隙与重叠特征的非协调Mindlin板模型进行分析；NURBS次数越高，等几何分析计算结果越精确，并且收敛速度越快。
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关键词:
- 等几何分析 (IGA) /
- Mindlin板 /
- 非协调 /
- Nitsche方法 /
- 缝隙与重叠
Abstract:In the frame of isogeometric analysis (IGA), non-uniform rational B-spline (NURBS) serves as both the description of geometries in computer aided design (CAD) and the shape function in finite element analysis (FEA). The common problems of gap and overlapping in NURBS models increase the difficulty of analysis. Based on Mindlin plate theory, the NURBS plate models with gap and overlapping were analyzed by IGA method. The Nitsche method was employed to solve non-conforming problem along models' interfaces. The simulation results of benchmark problem obtained by IGA method were compared with analytical solutions to verify the validity of the presented method. It is demonstrated that Nitsche based IGA method can be used to analyze non-conforming Mindlin plate models with local gap and overlapping feature. Higher NURBS polynomial degrees will produce more accurate IGA results and faster convergence.
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Key words:
- isogeometric analysis (IGA) /
- Mindlin plate /
- non-conforming /
- Nitsche method /
- gap and overlapping
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图 8 不同次数下的非协调方板前10阶频率相对误差
Figure 8. Relative errors of first ten mode frequencies of non-conforming square plate with different polynomial degrees
图 9 不同次数下的第1阶和第2阶非协调方板频率参数收敛
Figure 9. Convergence of first two mode frequency parameters of non-conforming square plate with different polynomial degrees
表 1 非协调固支方板频率参数
Table 1. Frequency parameters of non-conforming clamped square plate
模态阶数 h/l=0.1 h/l=0.2 等几何分析 Liew等[16] 等几何分析 Liew等[16] 1 3.297 0 3.295 4 2.688 4 2.687 5 2 6.270 5 6.285 8 4.680 9 4.690 7 3 6.304 7 6.285 8 4.702 1 4.690 7 4 8.810 6 8.809 8 6.298 6 6.298 5 5 10.377 1 10.378 8 7.174 3 7.176 7 6 10.484 3 10.477 8 7.278 3 7.275 9 7 12.539 4 12.552 9 8.507 0 8.515 5 8 12.570 0 12.552 9 8.522 7 8.515 5 9 15.296 0 15.291 8 10.008 9 10.012 6 10 15.305 7 15.291 8 10.017 7 10.012 6 
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