摘要
本文通过定义节点领域和单元延拓域,引入了单元外邻近节点的信息,并利用数值微分的方法将节点转角变量θx,θv用节点邻域内的一组节点挠度Wi(i=0,1,…,m)的线性组合表示,从而使薄板弯曲单元的节点变最由三个削减到一个,考虑到边界节点可能要保留某些转角变量,总自由度数乃可以减少一半以上,这样进行分析计算所需的计算机CPU时间和存储空间都节省了一半左右。这种延拓有限元法的单元刚度矩阵及等效载荷等都可以由相应的经典有限元法经变换矩阵变换得到,所以具有方法简单、适应性强和计算效率高等特点。
A class of Extend Finite Element Method (EFEM) has been discussed in the paper. The concept of nodal neighbouring region and extended element region are defined. The nodal values on neighbouring elements are introduced to define the internal displacements in the element.lt improves the continuity and accuracy. The nodal slopes θx, θy are substituted by the numerical derivatives in the nodal neighbouring region. The riodel parameters are reduced from three to one. Considering the reservation of some nodal slopes in the boundary,the total number of degrees of freedom can be decreased more than a half. Thus the CPU time involved in obtaining the results is saved a lot. A series of numerical examples for plate bending are analyzed. The results demonstrate good accuracy and efficiency for all cases considered.
