Extension of the scaled boundary finite element method to treat implicitly defined interfaces without enrichment

摘要

In this paper, the scaled boundary finite element method (SBFEM) is extended to solve the second order elliptic equation with discontinuous coefficients and to treat weak discontinuities. The salient feature of the proposed technique is that: (a) it requires only the boundary to be discretized and (b) does not require the interface to be discretized. The internal boundaries are represented implicitly by the level set method and the zero level sets are used to identify the different regions. In the regions containing the interface, edges along the boundary are assigned different material properties based on their location with respect to the zero level set. A detailed discussion is provided on the implementation aspects, followed by a few example problems in both two and three dimensions to show the robustness, accuracy and effectiveness of the proposed approach in modelling materials with interfaces. The proposed technique can easily be integrated to any existing finite element code. (C) 2019 Elsevier Ltd. All rights reserved.