Research On The Algorithm Of The Extended Finite Element Method On CB Shell And Sub-Interfacial Fracture Problems

Crack propagating along a curved or rough path in planes or curved surfaces is a common phenomenon in many kinds of engineering fields. Due to the complicity of the problem, theoretical method is incapable of dealing with it, the cost of experimental is large and the numerical research is hard to solve it. So it has been a great challenging work. The extended finite element method (X-FEM) is a novel computational method which has been proposed to solve this problem and it exhibits great accuracy and efficiency when dealing with arbitrary propagation of the cracks with complicated shape.On the basis of 2D X-FEM, a new X-FEM algorithm on the continuum-based shell element (CB shell element) is established in this thesis. A program of 2D and CB shell X-FEM is developed, which is applied to several problems of planar discontinuities and arbitrary crack propagation in shells, respectively. Besides, sub-interfacial crack growth in bi-materials is also studied.A program for 2D arbitrary crack propagation is developed based on the algorithm of X-FEM. With the enriched shape functions which have the jumping property in the crack-crossing element and singular property in the tip-embedded element, cracks independent of the mesh can be captured and the stress field around the crack tip can be calculated accurately. The maximum circumferential stress criterion is used for predicting the direction and speed of crack propagation and the interaction integral is used for calculating the stress intensity factors. Several problems of planar discontinuities are simulated such as mixed-mode crack propagation, interface between two materials and the interaction between cracks and holes. Computational results are compared with the experimental data, analytical answer and other computational results which use the standard FEM. This proves the capability of X-FEM and the program.Sub-interfacial crack growth in bi-materials is also simulated with the program. The computed crack path and phase angle are the same with those obtained in the experiment. Further research reveals the effect on the equilibrium state of mode-I crack propagation made by the material inhomogeneity, loading asymmetry and the initial crack length. The experience formula has been developed to guide the experimental researches.Besides, a new X-FEM algorithm on CB shell element is established and the program of shell fracture is developed based on it. Arbitrary crack propagation in curved surfaces is able to be computed and the variation of the shell thickness can be considered. As the enriched shape functions are constructed in the body element, the situation of crack not perpendicular to the mid-face of the shell can be conveniently considered. The formula for calculating three-dimensional stress intensity factors and 3D maximum energy release rate criterion is used in the program.