An exact and efficient X-FEM-based reanalysis algorithm for quasi-static crack propagation

Abstract

• A specific and exact reanalysis algorithm is suggested to analysis crack propagation problem based on X-FEM. • Compared with the popular reanalysis algorithm, the displacement and stress can be obtained more accurately. • Local stiffness matrix updating strategy is suggested to achieve the modified stiffness matrix . • Cholesky factorization of stiffness matrix allows efficient updating. • Compared with classical X-FEM, the efficiency of suggested method is significantly improved. This study suggests a specific reanalysis algorithm termed decomposed updating reanalysis (DUR) for quasi-static linear crack propagation based on the extended finite element method (X-FEM). It is well known that the number of iterative steps is usually very large during X-FEM simulation procedures because a small crack increment is required to improve the accuracy of the simulation. However, according to the features of the X-FEM, the small crack increment only influences the nearby elements and only leads the local change of the stiffness matrix at each iterative step. Therefore, the DUR method is proposed to accelerate the X-FEM solving process by only calculating the changed part of the equilibrium equations. Moreover, the local updating strategy can efficiently update the modified stiffness matrix and the Cholesky factorization. Compared with other reanalysis algorithms, such as combined approximations (CA), the DUR method is more accurate. Numerical examples demonstrate that the DUR method improves the efficiency of the X-FEM significantly with a high accuracy.