| Summary: | 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. It is shown that in doing so, superconvergence, and in select cases ultraconvergence, is succeeded in the Stress Intensity Factors (SIFs) calculation. Based on these findings, a novel error estimator for the stress intensity factors within the context of SBFEM is proposed.
To investigate and assess the performance of SBFEM in the context of linear elastic fracture mechanics, the method is contrasted against the Finite Element Method (FEM) and the eXtended Finite Element Method (XFEM) variants. The comparison, carried out in terms of computational toll and accuracy for a number of applications, reveals SBFEM as a highly performant method.
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