Limit analysis of cracked structure by combination of extended finite element method with linear matching method

摘要

Linear matching method (LMM) is one of the effective numerical methods for the limit and shakedown analysis, which computes the converging upper series by solving iteratively linear elastic analysis with Young’s modulus varying in space. LMM, which is capable of implementing by using the commercial finite element packages such as ABAQUS and ANSYS has been widely used in the practical applications including fatigue, creep and composite analysis. Nevertheless, LMM could not ensure numerical accuracy for discontinuous problems such as crack analysis since it computes the mechanical quantities including stress, strain and displacement on the base of conventional finite element method, likewise other numerical methods for the limit and shakedown analysis. Meanwhile, extended finite element method (XFEM), recently proposed, is an attractive numerical method for the analysis of discontinuous problems which enriches finite element approximate space by some special functions. In this paper, authors proposed a very straightforward method for the limit analysis by the combination of XFEM with LMM. Numerical validation is done for two types of typical fracture specimens. Numerical examples show that the limit analysis by combining XFEM with LMM gives more accurate result compared with the one by combining of conventional finite element method with LMM. Furthermore, we demonstrated that the choice of enrichment region plays an important role in the improvement of numerical accuracy of our proposed method.