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MECSOL 2022
8th International Symposium on Solid Mechanics
An Investigation of Hierarchical Blending Elements in G/XFEM for Linear Elasticity
Submission Author:
Erik da Rosa Rodriguez , RS , Brazil
Co-Authors:
Erik da Rosa Rodriguez, Oscar Alfredo Garcia de Suarez, Rodrigo Rossi
Presenter: Erik da Rosa Rodriguez
doi://10.26678/ABCM.MECSOL2022.MSL22-0044
Abstract
This work investigates the interpolation behavior of blending elements, characterized by the non-fulfillment of partition of unity property leading to unwanted terms in the approximation and degrading the convergence rate. To deal with this issue, a hierarchical polynomial enrichment approach in blending elements is used and compared with classical XFEM, being verified by an analytical solution of a bi-material cantilever beam with a third-order displacement field, a classic engineering case, widely used in various industrial segments. The hierarchical XFEM is compared with the classical XFEM through the values of the relative error norms, convergence rate, and the local behavior of the approximate field in blending elements for two opposite material configurations with a known analytical solution. The results show that the hierarchical term enhances the approximated local field in blending elements to compensate for the unwanted terms and better approximates the local field than classical XFEM.
Keywords
XFEM, blending elements, weak discontinuity, hierarchical shape functions
