Splitting method and hybrid-Trefftz formulation for multisite damage analysis in two-dimensional domains

Argôlo, Higor Sérgio Dantas de; Proença, Sérgio Persival Baroncini

doi:10.1016/j.ijsolstr.2016.10.030

Cited by 3 publications

(1 citation statement)

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“…In crack analysis, singular stress fields and stress concentration problems were analyzed using LC and Airy functions (Bussamra et al, 2014) and Kaczmarczyk and Pearce (2009), respectively. In multisite cracked solids, Chebyshev functions were applied in a nodal framework (Argôlo and Proença, 2016).…”

Section: Introductionmentioning

confidence: 99%

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

Businaro

Bussamra

2020

Lat. Am. j. solids struct.

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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.

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Section: Introductionmentioning

confidence: 99%