Accuracy improvement of XFEM using Wilson's incompatible element technique

ABSTRACT

Based on the extended finite element method (XFEM) and Wilson incompatible element technique, an incompatible extended finite element method (IXFEM) is presented to deal with the cracked bending problems in this study. The additional displacement modes of Wilson's incompatible element are introduced into the approximation of the XFEM. The internal degrees of freedom induced by additional models are condensed to improve efficiency. Derivation of the equilibrium equations of the IXFEM is performed. Several examples are employed to validate the capabilities of the proposed method. The influence of bending degree on the performance of proposed method is studied by changing the crack length. The numerical results indicate that the stress and displacement solutions of the IXFEM show a slight oscillation. The IXFEM achieves better convergence rate and computational accuracy compared with the traditional XFEM for the bending problems.

KEYWORDS:

• Incompatible element
• XFEM
• crack
• bending problem
• convergence rate

Funding

Funding was provided by the National Natural Science Foundations of China (11502286), Natural Science Foundations of Tianjin (17JCQNJC02600), and Fundamental Research Funds for the Central Universities (3122017021 and 3122017034).