[RETRACTED ARTICLE] On the sparsity of linear systems of equations for a new stress basis applied to three-dimensional Hybrid-Trefftz stress finite elements

Abstract

Hybrid-Trefftz finite elements have been applied to the analysis of several types of structures successfully. It is based on two different sets of approximations applied simultaneously: stresses in the domain and displacements on its boundary. This method presents very large linear systems of equations to be solved. To overcome this issue, most authors have been careful in the choice of the approximation fields in order to have highly sparse linear systems. The natural choice for the stress basis has been linearly independent, hierarchical and orthogonal polynomials which typically result in more than 90% of sparsity in 3-D finite elements. Functions derived from associated Legendre and Chebyshev orthogonal polynomials have been used with success for this purpose. In this work the non-orthogonal polynomials available in the Pascal pyramid are proposed to derive a harmonic and complete set of polynomial basis as an alternative to the above-cited functions. Numerical tests show this basis produces accurate results. No significant differences were found when comparing the sparsity of the linear system of equations for both functions.

Keywords:
hybrid-Trefftz; sparsity; Finite Element Method; stress element

Graphical Abstract

The journal editors and authors agreed to fully retract the article:

Businaro, Felipe Alvarez, & Bussamra, Flávio Luiz de Silva. (2020). On the sparsity of linear systems of equations for a new stress basis applied to three-dimensional Hybrid-Trefftz stress finite elements. Latin American Journal of Solids and Structures, 17(7), e307. Epub September 28, 2020. https://doi.org/10.1590/1679-78256124

This is due to several unnoticed and unintentional problems with the formulae presented in multiple places and pages across the whole article that were caused at the copyediting stage after the author's intermediary and final proof.

Marcílio Alves
Editor-in-chief

Edited by

Editor:

Marco L. Bittencourt.

Publication Dates

• Publication in this collection
  28 Sept 2020
• Date of issue
  2020

History

• Received
  19 May 2020
• Reviewed
  11 Aug 2020
• Accepted
  30 Aug 2020
• Published
  02 Sept 2020