Abstract
The extended Finite Element Method (XFEM) is derived from the traditional finite element method for discontinuous problems. It can simulate the behavior of cracks, which significantly improves the ability of finite element methods to simulate geotechnical and geological disaster problems. The integration of discontinuous enrichment functions in weak form and the ill-conditioning of the system equations are two major challenges in employing the XFEM in engineering applications. A mixed integration scheme is proposed in this paper to solve these problems. This integration scheme has a simple form and exhibits both the accuracy of the subcell integration method and the well-conditioning of a smeared integration method. The correctness and effectiveness of the proposed scheme were verified through a series of element analyses and two typical examples. For XFEM numerical simulations with unstructured meshes and arbitrary cracks/interfaces, this method guarantees the convergence of nonlinear iterations and yields correct results.
Highlights
The extended Finite Element Method (XFEM) is an excellent numerical method that can visually simulate discontinuous cracks/interfaces and their evolution without mesh regeneration
The mixed scheme converged to the given minimum error limit after 69 iterations, as shown in Figure 19; the subcell scheme did not converge within the Newton iterations due to the illconditioning. These results prove that the mixed integration scheme exhibits good convergence stability for strongly nonlinear problems with unstructured meshes
This study introduced a smeared integration method that can integrate the weak form of elements with discontinuous enrichment without element splitting
Summary
The extended Finite Element Method (XFEM) is an excellent numerical method that can visually simulate discontinuous cracks/interfaces and their evolution without mesh regeneration. Table 2; Figure 7 present comparisons of the stiffness matrix condition numbers obtained using smeared and subcell integration with different penalty coefficients and partition ratios. The mixed scheme converged to the given minimum error limit after 69 iterations, as shown in Figure 19; the subcell scheme did not converge within the Newton iterations due to the illconditioning These results prove that the mixed integration scheme exhibits good convergence stability for strongly nonlinear problems with unstructured meshes
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
