Study On The Extended Finite Element Method Based On The State Vector

Hamilton system has significant advantages in the study of mechanical problems. The convergent rate of the Semi-analytical method about Hamilton state vector equations is faster than that of the conventional finite element method and the Semi-analytical method has higher calculation precision, which leads to the rapid development of the theory of elastic mechanics under the Hamilton system. However, when dealing with discontinuity problems like cracks and holes, this theory will not only decrease the accuracy but intensify the computation. The core of extended finite element method(XFEM) is to deal with regional discontinuity with the expanded shape function. XFEM has unique superiority in analyzing discontinuous problems. In order to take the full advantages of Hamilton state vector equations and XFEM, this thesis combines both of them to analyze a crack and its extension problems in linear elastic fracture mechanics. The main contents are organized as follows:First, based on the semi-analytical solution of the Hamilton state vector equation and XFEM, the XFEM with a shape function of discontinuity for Hamilton method was deduced. The method and formulas to solve stress intensity factor(SIF) were given in detail. And the XFEM program to calculate SIF was compiled based on Hamilton system.Second, according to the program compiled through MATLAB software, the SIF of slope crack model and double edge cracks model were computed. The accuracy and reliability of the program had been verified by contrast between the calculation results and the theoretical values.Last, the cracking angle was computed by the maximum hoop stress criterion in XFEM, the propagation paths of the single edge crack and double edge cracks were simulated by the program, and the results were analyzed.