广义有限元及其应用

基于传统有限元理论，吸收数值流形方法中有限覆盖技术，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，给出了广义四结点等参单元的有限元列式，结合算例探讨了广义有限元的数值实施措施，针对复杂结构形式，提出广义有限元与传统有限元的联合运用，从而解决计算交和精度这一问题，算例结果表明了本文方法的合理性。

Generalized finite element and its application

Based on the conventional finite element, by use of the finite cover technique in the numerical manifold method, the Lagrange interpolation space for displacement of each node is expanded to a function expansion with any number of generalized displacements, and formulae of generalized four-node iso-parametric finite element are given. In combination with numerical examples, the numerical measures for generalized finite element are discussed. Besides, the generalized finite element is also combined with the conventional finite element for treatment of complicated structures, improving the efficiency and precision of computation. The results of numerical examples show that the method is rational.