An enhanced scaled boundary finite element method for linear elastic fracture

作者：Egger Adrian W; Chatzi Eleni N^*; Triantafyllou Savvas P

来源：Archive of Applied Mechanics, 2017, 87(10): 1667-1706.

DOI：10.1007/s00419-017-1280-7

• Scaled boundary finite element method (SBFEM)
• Extended finite element method (XFEM)
• Linear elastic fracture mechanics (LEFM)
• Stress intensity factors (SIFs)
• Block Hamiltonian Schur decomposition (HSchur)
• Superconvergent patch recovery theory (SPR)

A blocked Hamiltonian Schur decomposition is herein proposed for the solution process of the scaled boundary finite element method (SBFEM), which is demonstrated to comprise a robust simulation tool for linear elastic fracture mechanics (LEFM) problems. By maintaining Hamiltonian symmetry, increased accuracy is achieved, resulting in higher rates of convergence and reduced computational toll, while the former need for adoption of a stabilizing parameter and, inevitably user supervision, is alleviated. The method is further enhanced via adoption of superconvergent patch recovery theory in the formulation of the stress intensity factors (SIFs). It is shown that in doing so, superconvergence, and in select cases ultraconvergence, is succeeded in the SIFs calculation. Based on these findings, a novel error estimator for the SIFs within the context of SBFEM is proposed. To investigate and assess the performance of SBFEM in the context of LEFM, the method is contrasted against the finite element method and the extended finite element method variants. The comparison, carried out in terms of computational toll and accuracy for a number of applications, reveals SBFEM as a highly performant method.

• 出版日期2017-10