基于单位分解的新型有限元方法研究

本文对基于单位分解概念的新型有限元方法具有一些新的特点进行了研究。这些新的特点包括自由度全部定义在单元顶点上，不同于传统的非协调和协调P型有限元方法自由度主要定义在单位区域内，因此很便于P型方法的实施；网格畸变度对解的不敏感性较传统有限元有了很大改进。此外，Dirichlet边界条件的处理与有限元是完全相同的，非常便利。论文分析了几个平面弹性问题：R.L.Tayor高阶分片试验和受拉弯剪切的平面悬臂梁，Cook悬臂T形板等，得到了满意的数值结果。

Study on partition of unit FEM

In this paper, some new characteristics of partition of unitFEM are studied, including:1) all freedoms are defined on the model vertex nodes, which is different from the conventional confirm and nonconfirm FEM in which freedoms are mainly defined in field so that implementation of P\|shape method is easier.2) The solution of problem is not sensitive with mesh distortion. In addition, Dirichlet boundary condition can be treated with same way as FEM. Several numerical examples about plane elastic problem are analyzed in this paper, which are R.L. Tayor high patch test problem and tensioned, bend, sheared plane cantilever beam problem, Cook membrane problem etc. Satisfactory numerical results are obtained.