三维广义有限元及在拱坝计算中的应用

Application of 3-D generalized finite element to arch dam calculation

基于传统有限元理论,将每个结点位移的Lagrange型插值空间推广为具有任意多个广义位移的函数展开式,在不增加结点个数的前提下,仅通过提高结点插值函数的阶数,达到提高有限元精度的目的,建立了三维广义八结点等参单元的有限元列式,探讨了广义有限元的程序实施细则.通过对悬臂梁、曲梁以及5型拱坝的实例计算,体现了广义有限元法的优越性,为拱坝等结构计算分析提供了一种新途径.

Based on the conventional finite element, the Lagrange interpolation space for displacement at each node is extended to an arbitrary function expansion with any number of generalized displacements. Without the increase of the number of nodes, the precision of numerical calculation is improved only by improvement of the order of the interpolation function at each node. In this paper, a 3D finite element numerical form for generalized 8node isoparametric element is developed, and the numerical calculating program of the generalized finite element form is also discussed. The computational examples of a cantilever beam, a curved cantilever beam and a type 5 arch dam indicate the advantages of the generalized finite element method, which provides a new method for structural analysis and calculation for arch dams.