Eventos Anais de eventos
COBEM 2019
25th International Congress of Mechanical Engineering
IMPROVING THE POLYNOMIAL REPRODUCIBILITY FOR THE PARTITION OF UNITY IN THE Ck -GENERALIZED FEM
Submission Author:
Mateus Afonso Garbuio , PR
Co-Authors:
Mateus Afonso Garbuio, Diego Amadeu Torres
Presenter: Mateus Afonso Garbuio
doi://10.26678/ABCM.COBEM2019.COB2019-0827
Abstract
In this work, an improvement on the polynomial reproducibility of the Ck-Generalized Finite Element Method (Ck-GFEM) is achieved by assigning a polynomial basis to its Partitions of Unity (PoU) via Moving Least Squares (MLS). The construction of the weighting functions is similar to the conventional Ck-GFEM, while employing a polynomial basis alternatively to the Shepard functions when building the PoU. A study considering the one-dimensional elastostatic problem is presented, producing approximations by the present method and conventional FEM with Lagrangian shape functions for comparison. Extrinsic enrichment, as in the conventional GFEM, is also used. Numerical results in the form of relative errors in the L 2 norms and the convergence rates are presented. The results suggest that the intrinsic enrichment via MLS improves the approximation in the context of Ck-GFEM without the need of an extrinsic enrichment, while being able to better approximate regular fields if compared to the conventional Lagrangian shape functions, and keeping the arbitrariness of the parameters h, p and k as in original Ck-GFEM
Keywords
Moving Least Squares Method, Intrinsic Enrichment, Extrinsic Enrichment, Smoothness, Generalized Finite Element Method
