含裂纹Reissner板的有限元分析

提出了裂纹尖端区域有限元计算分析的一种新方法.首先用Reissner型板的裂纹尖端位移场计算奇异单元的刚度矩阵;其次完成奇异单元的广义位移向量对应的刚度矩阵向节点位移向量对应的刚度矩阵的转换,使奇异单元可以直接参与总刚度矩阵的组集;最后解除了裂纹尖端奇异单元的位移的相关性,得到独立的节点位移向量对应的总刚度矩阵.该方法直接引入Reissner型板裂纹尖端位移场,不仅减少了单元的划分,较好地模拟了裂纹尖端的奇异性,而且避免了在奇异单元和常规单元之间建立过渡单元,使裂纹尖端区域的计算在理论和计算上都得到了较大的简化.

New Finite Element Method to Analyze Crack Tip of Plate Structure

In this paper a new finite element method to analyze the crack tip is proposed. Firstly the stiffness matrixes of the singular elements are completed on the base of the displacement field near the crack tip of the Reissner plate. Then the stiffness matrix of the singular element corresponding with the broad sense displacements is transformed into the stiffness matrix corresponding with the node displacements, so the latter can join the total stiffness directly. Finally the relativity between the displacements of the two singular elements is relieved, and the final stiffness is advanced. The new method, employing the transforming of the displacement and the conservation of the strain energy focuses the calculation on the singular elements. So it not only decreases the quantity of the elements in the filed of the fracture, but also simulates the singularity of the crack tip, and the calculation near the crock tip is simplified not only in the theory but also in the calculation.