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土石坝等复杂土工结构物有限元三维建模中多采用精度较高的六面体单元辅以部分过渡用的退化单元,而退化单元由于形态不好,会导致有限元计算精度较差。解决该问题的途径之一是采用过渡性的等参元。总结了几种常遇到的过渡等参单元(楔形体、四面体、金字塔)的插值函数和高斯积分局部坐标和权重,并编入了有限元程序。通过比较六面体单元和金字塔单元剖分理想土石坝的有限元计算结果,说明所引入的金字塔单元是满足精度要求的。将各种过渡单元应用于实际土石坝工程的有限元计算,结果表明,使用过渡等参单元是可以在一定程度上提高计算精度的。最后讨论了二次单元在弹塑性有限元动力计算中的应用。二次单元的使用,可以改善动力计算中的超静孔压分布,提高计算精度。
Finite element three-dimensional modeling of complex geotechnical structures such as earth-rock dams often uses more accurate hexahedron elements together with some degenerate elements for transition. However, due to the bad shape of the degenerate element, the finite element calculation accuracy is poor. One of the ways to solve this problem is to use a transitional isoparametric element. Several interpolation functions and Gaussian integral local coordinates and weights of transitional isochronous units (wedge, tetrahedron and pyramid) are summarized, and the finite element program is compiled. Comparing the results of finite element analysis of ideal earth-rock dams with hexahedron elements and pyramid elements shows that the introduced pyramid elements meet the requirements of accuracy. Various transitional units are applied to the finite element calculation of the actual earth-rock dam project. The results show that the use of transition isoparametric units can improve the calculation accuracy to a certain extent. Finally, the application of the secondary element in the elasto-plastic finite element dynamic calculation is discussed. The use of the secondary unit can improve the excess pore pressure distribution in dynamic calculation and improve the calculation accuracy.