Three dimensional hybrid‐<scp>Trefftz</scp> stress finite elements for plates and shells

Martins, P. H. C.; Bussamra, Flávio Luiz de Silva; Neto, Eliseu Lucena

doi:10.1002/nme.5715

Cited by 6 publications

(6 citation statements)

References 34 publications

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“…To introduce geometric nonlinearities to the model, first consider the fundamental relations governing the elastic response for equilibrium, constitutive and compatibility equations [32], respectively:…”

Section: Nastran®mentioning

confidence: 99%

Static loads evaluation in a flexible aircraft using high-fidelity fluid–structure iteration tool (E2-FSI): extended version

Verri

Bussamra

Morais

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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This paper presents a fluid-structure iteration method applied as a study case to a conventional transport aircraft with wing aspect ratio of 12. It evaluates the nonlinear structure effect on the calculation of static limit loads. The numerical tool presented herein is named E2-FSI, which stands for nonlinear high-fidelity static fluid-structure iteration, developed for high flexibility static aeroelastic evaluations. A discussion about the use and the applicability of high-fidelity static fluid-structure iteration for the calculation of static loads is presented as part of the conclusion, for both current and future conventional transport aircraft.

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Section: Nastran®mentioning

confidence: 99%

Static loads evaluation in a flexible aircraft using high-fidelity fluid–structure iteration tool (E2-FSI): extended version

Verri

Bussamra

Morais

et al. 2020

J Braz. Soc. Mech. Sci. Eng.

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“…The main advantage of using this harmonic set of polynomials as approximation functions lies in its full completeness for every desired degree of approximation n, as shown by Wang et al (2012) and Martins et al (2018).…”

Section: Homogeneous Harmonic Polynomialsmentioning

confidence: 99%

“…Homogeneous Harmonic Polynomial (HHP) functions derived from the Pascal's pyramid of polynomials proposed by Wang (2002) are applied to the Papkovitch-Neuber solution of the Navier equation to derive a complete set of 3-D stress and displacement bases. This procedure was applied with success to the analysis of plates and shells with hybrid-Trefftz elements by Martins et al (2018).…”

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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“…Consequently, the resulting formulation allows accurate and efficient numerical solution to be obtained. In this regards, notable contributions are the hybrid Trefftz element for Mindlin-Reissner plates proposed by Cen et al, 23 the hybrid plates by Teixeira de Freitas and Tiago, 24 the plate and shell elements by Martins et al 25 and the FE for bending analysis by Rezaiee-Pajand and Karkon. 26,27 The Trefftz method has also been used by Horak et al 28 within isogeometric formulations.…”

Section: Introductionmentioning

confidence: 99%

An efficient isostatic mixed shell element for coarse mesh solution

Madeo

Liguori

Zucco

et al. 2020

Numerical Meth Engineering

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A novel mixed shell finite element (FE) is presented. The element is obtained from the Hellinger-Reissner variational principle and it is based on an elastic solution of the generalized stress field, which is ruled by the minimum number of variables. As such, the new FE is isostatic because the number of stress parameters is equal to the number of kinematical parameters minus the number of rigid body motions. We name this new FE MISS-8. MISS-8 has generalized displacements and rotations interpolated along its contour and drilling rotation is also considered as degree of freedom. The element is integrated exactly on its contour, it does not suffer from rank defectiveness and it is locking-free. Furthermore, it is efficient for recovering both stress and displacement fields when coarse meshes are used. The numerical investigation on its performance confirms the suitability, accuracy, and efficiency to recover elastic solutions of thick-and thin-walled beam-like structures. Numerical results obtained with the proposed FE are also compared with those obtained with isogeometric high-performance solutions. Finally, numerical results show a rate of convergence between h 2 and h 4 .

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Three dimensional hybrid‐Trefftz stress finite elements for plates and shells

Cited by 6 publications

References 34 publications

Static loads evaluation in a flexible aircraft using high-fidelity fluid–structure iteration tool (E2-FSI): extended version

Static loads evaluation in a flexible aircraft using high-fidelity fluid–structure iteration tool (E2-FSI): extended version

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

An efficient isostatic mixed shell element for coarse mesh solution

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