Williams Element With Generalized DOF For Structural Fracture Analysis

This dissertation mainly has researched one new finite element method in the structural fracture analysis which is called Williams element with generalized DOR The computational format of FEM with Williams element and the corresponding Fortran 90 procedure has been established about theâ… -â…¡-mixed mode, mode I and mode II crack problems .The results calculated by Williams element was analyzed and compared with the singular element studied in the dissertation.The main research and the contribution of the thesis are as follows:1. Based on the linear elastic fracture mechanics and isoparametric element theory, singular element on the structural fracture analysis has been established and the homologous Fortran 90 procedure has been compiled. The stress intensity factor (SIF) are analyzed and calculated emphatically about theâ… -â…¡-mixed mode, modeâ…¡crack problems.2. The Williams element with generalized DOF are developed forâ… -â…¡-mixed mode, modeâ… and modeâ…¡crack problems, and respective Fortran 90 procedure are organized. The influence of the radial discretizing ratio, radial partition number in singular domain and the number of the terms of the Williams expansions on computing precision of SIF is illustrated, their design values are presented. The relationship between between SIF and the diffirent a/w and varing h/w about mode I and modeâ…¡crack problems has analyzed emphatically, respecatively. The sensitive question of the strss intensity factor on the singular area size in the singular domain are proposed, and the scope of the best singular area size around the crack tip are shown. The correctional formula of Originally analytic solution about stress intensity factor for modeâ… and modeâ…¡crack problems are presented. The theoretical analysis and the example analysis indicated that the Williams element with generalized DOF is one kind of numerical method with high efficiency, high accuracy, clear principle, simple unit structure, and it is prospective very much in the structural fracture problem analysis.