GENERALIZED FINITE ELEMENT OF EXCAVATION COMPUTATION FOR UNDERGROUND ENGINEERING
地下工程开挖计算的广义有限元法

Based on the conventional finite element,Lagrange type interpolation space of displacements on each node is extended to an arbitrary function expansion with any variable number of generalized displacements. The accuracy of the numerical computations is improved only through increasing the order of interpolation functions without increasing the number of nodes. Three-dimensional generalized isoparameteric element of eight nodes and one-dimensional generalized bar element are established. The formulae of generalized shape function and the element displacement formulation are given. The strain matrix,stiffness matrix and load vector of element are formulated. In response to the excavation problem of underground engineering,the combined usage of conventional finite element with generalized finite element is suggested. The generalized finite element is applied to the surrounding rock mass of excavation boundary and the anchored rock mass. The conventional finite element is applied to the rock mass far from excavation boundary. Not only the computation precision,but also the computation efficiency is improved. The numerical implement programs of generalized finite element are discussed. From the computational examination questions as well as the engineering example,the numerical results indicate the advantage of generalized finite element. The proposed method is rational for analysis and computations of underground engineering.