裂缝分析的叠单元法研究

RESEARCH ON SUPERPOSED ELEMENT METHOD FOR CRACK ANALYSIS

裂缝是影响结构正常工作性态的重要因素。提出裂缝分析的叠单元法,首先,对于含裂缝的结构,将其离散成不含裂缝的整体网格和裂缝附近区域的局部网格,整体网格和局部网格相互独立。然后,将整体网格和局部网格叠加,在局部网格覆盖范围内,直接采用有限单元法;在局部网格覆盖范围以外,则以整体网格为准,在完整单元上直接采用有限单元法,在残缺单元上采用数值流形技术。最后,在局部网格边界面上施加罚刚度,以实现其与整体网格的耦合。算例分析结果表明,该方法前处理较简单,计算精度较高,适合于裂缝动态扩展过程模拟。

Crack is the key factor of structures for the normal operation. A superposed element method（SEM） is proposed for crack analysis. Firstly, the structure containing cracks is divided into two independent meshes. One is the global mesh without cracks, and the other is the local mesh of the crack together with its adjacent zone. Then, the global mesh and the local mesh are superposed together： the finite element format is adopted for the local mesh Outside of the coverage of the local mesh, the finite element format is adopted for the complete elements： and the numerical manifold technology is adopted for the incomplete elements on the basis of the global mesh. Finally, in order to couple with the global mesh, the penalty stiffness coefficients are adopted at the boundary of local mesh. The case studies show that the preprocessing of the SEM is quite simple, and its calculation precision is relatively high. The proposed method is suitable for the dynamic simulation of crack propagation process.