单元网格密度及畸变度对面板坝有限元计算精度的影响

Influence of Element Mesh Density and Distortion Degree on Finite Element Calculation Accuracy of Face Rockfill Dams

利用有限元等参变换,推导了广泛适用的六面体单元的畸变度计算公式,并结合单元的边长比、斜交角、锥度等三种畸变参数,进行了误差分析。同时,以单元最大边长为控制标准,设计了不同网格密度的面板堆石坝剖分方案,进行三维非线性有限元计算精度分析。结果表明,单元边长比和锥度对计算精度的影响较小,而斜交角存在明显影响;不同网格密度剖分方案的能量相对误差随单元数量的增加而减小,当控制单元最大边长为5~10 m时,计算误差可减至5%~10%,且误差基本趋于稳定;不同网格密度的面板堆石坝计算得到的大坝变形规律一致,量值差异不大。但对于可能存在挤压破坏的混凝土面板而言,宜用子模型细分网格计算局部应力。

Based on the finite element isoparametric transformation, the widely used formula for calculating the distortion degree of hexahedron element was derived, and the error analysis was carried out in combination with three distortion parameters of element, such as side-length ratio, skew angle and taper ratio. Taking the maximum side length of the element as the control standard, the subdivision schemes of face rockfill dams with different mesh densities were designed, and the three-dimensional nonlinear finite element analysis was carried out. The results show that the element side-length ratio and taper ratio have little impact on the calculation accuracy while the skew angle has obvious impact. The relative energy error of different subdivision schemes decreases with the increase of the number of cells. When the maximum side length of the element is 5~10 m, the calculation error can be reduced to 5%~10%, and the error tends to be stable basically. For the face rockfill dams with different mesh densities, the deformation law of dams is consistent. However, for the concrete face plates that may be damaged by compression, it is advisable to use submodel to subdivide the mesh in order to calculate the local stress.