Computing The Stress Intensity Factors Of Cracks Using The Multi-regional Boundary Element Method Double-mapping Singular Elements

The Boundary Element Method is a very efficient numerical method, at present it has been wide-rangingly used in numerical computation of many engineering fields, and has been got good results. In this paper, the fundamental theory of the Boundary Element Method and the multi-regional computation method of the Boundary Element Method on a compositive region with different thickness or various materials are introduced, the formula of linear element is detailedly deduced. Then according to the characteristics of the Boundary Element Method, its application in the Fracture Mechanics is introduced, a special element— double-mapping singular element is emphatically discussed, in the computation of the stress intensity factors of two-dimensional crack tips, and the coefficient matrixes according to this element are deduced. This element can perfectlysimulate the r ^1/2 singularity of stress field and the r^1/2 characteristics ofdisplacement near to the crack tip, and has better accuracy. Computer programs are edited, several examples are computed. In order to be compared easily, the numerical computation of the Finite Element using ANSYS is carried out at the same time. The results generated from the two numerical computations are compared with the relative analytic solutions or other numerical solutions. The results indicate the accuracy of the Boundary Element Method using the singular element is very high. Moreover, from these computations, we can directly see that in the Boundary Element Method more less elements are needed than in the Finite Element Method in order to get the same accuracy, so the needed input data and the computation time are relatively more simple and more shorter. Thereby we also can directly realize the advantages of the Boundary Element Method.