三维过渡等参单元在岩土工程有限元分析中的应用

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。

Application of three-dimensional transitional isoparametric elements to finite element analysis of geotechnical engineering problems

In the 3-D finite element analysis of complex geotechnical structures such as earth-rockfill dams, the hexahedral elements with a high precision are generally adopted with being supplemented by some degradation elements as transition. Because of their poor geometric properties, the degradation elements could degrade the precision of the finite element method. One way to overcome such a problem is to adopt transitional isoparametric elements. Here the interpolation functions, integral coordinates and weighting coefficients are summarized for some common transitional elements such as 3D wedge, tetrahedron and pyramid elements and implemented into a finite element program. By comparing the finite element analysis results of an ideal earth dam using hexahedron elements and pyramid elements, respectively, it is shown that the pyramid elements are sufficient with regard to the precision. The three kinds of transitional elements are then used in analyzing a real earth-rockfill dam, and the numerical results show that use of transitional isoparametric elements can improve the computional accuracy to some extent. Finally, the quadratic isoparametric elements are analyzed and adopted in a dynamic analysis of the elastoplasticity problem. Use of the quadratic isoparametric elements can substantially improve the precision in calculating the excess pore pressure.