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COBEM 2019
25th International Congress of Mechanical Engineering
APPLICATION OF THE HYBRID-MIXED FINITE ELEMENT METHOD WITH STABILIZED NODAL ENRICHMENT ON 1D PROBLEM
Submission Author:
Rafaela Rodrigues Gomes , SP , Brazil
Co-Authors:
Rafaela Rodrigues Gomes, Wesley Góis, Luis Armando Piccino Navarro, José Vieira de Melo Neto
Presenter: Rafaela Rodrigues Gomes
doi://10.26678/ABCM.COBEM2019.COB2019-2065
Abstract
A new numerical method is proposed to estimate approximations of the displacements and stresses fields applying the Stabilized Generalized Finite Element Method (SGFEM) on Hybrid-Mixed Stress Formulation (HMSF) to a classical 1D structural mechanic problem – the bar problem under normal force. For the HMSF, three approximation fields are involved: stresses and displacement in the domain and displacement on the static boundary. In the combined HMSF-SGFEM approach the enrichment of stress and displacement domain field is provided by the product of the partition of unity (PoU) and a polynomials basis enrichment functions. The HMSF-SGFEM numerical simulation was implemented using MATLAB® routines. The performance of this new approach is illustrated and compared with classical Finite Element Method (FEM) by applying two discretized elements and the exact solution of this problem. The results show that combining these two nonconventional methods (HMSF-SGFEM) provided better matrix conditioning and a good convergence when is compared with the FEM results. In addition, considering both computational and numerical aspects, the HMSF-SGFEM can be easily extrapolated to 2D and 3D analysis of the elastic structural mechanics problems.
Keywords
Hybrid-Mixed Stress Formulation, Stabilized Generalized Finite Element Method, Nodal Enrichment, Structural Mechanics 1D Problem
