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所发展的广义节点有限元法是将传统有限元法中的节点广义化 ,在不增加节点个数的前提下 ,仅通过提高广义节点插值函数的阶次 ,达到提高有限元解精度的目的 .传统有限元法是这种方法当广义节点阶数退化为 0时的特例 .主要讨论了这一新方法的高阶形式 .重点分析了广义节点阶次的提高对计算精度以及计算量的影响 ,并与低阶方法以及传统有限元法进行了比较 .对受弯悬臂梁和半无限平面受集中力作用两个算例的数值分析表明 :1)广义节点阶次的提高可明显地提高计算精度 ;2 )为达到同一精度 ,高阶方法所需计算量要小于低阶方法和传统有限元法 ;3 )随着广义节点阶次的提高 ,单元间的应力不连续性能得到明显改善
The developed generalized node finite element method is to generalize the nodes in the traditional finite element method. Without increasing the number of nodes, the resolution of the finite element solution can be improved only by increasing the order of the interpolation function of generalized nodes. The traditional finite element method is a special case of this method when the generalized node order is degenerated to 0. The high order form of this new method is mainly discussed, and the influence of the improvement of generalized node order on the calculation accuracy and computation is analyzed. And compared with the lower-order method and the traditional finite element method.Numerical analysis of two cases of concentrated beams subjected to bending and semi-infinite plane shows that: 1) The improvement of generalized node order can obviously improve the calculation accuracy ; 2) to achieve the same precision, the computational complexity of the higher-order method is less than that of the lower-order method and the traditional finite element method; 3) With the increase of generalized node order, the stress discontinuity between cells can be significantly improved