A finite element interior-point implementation of tension field theory

Rooij, RM; Abdalla, Mostafa

doi:10.1016/j.compstruc.2015.01.007

Cited by 10 publications

(4 citation statements)

References 26 publications

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“…In the last stage, the shape of the wrinkled regions is quite complex due to the combination of excessive shearing and elongation. The obtained wrinkled regions are quite similar to those obtained in [de Rooij and Abdalla, 2015] with a slightly different material model. Finally, let us remark that it was not necessary to subdivide the final loading into smaller load steps.…”

Section: Annular Square Membrane Deformationsupporting

confidence: 83%

“…Its outer boundary of size Wout = 50 mm is fixed whereas the inner boundary, of size W in = 17.5 mm, is subjected to an in-plane torsion of angle 90 • and to an out-of-plane vertical displacement of amplitude tWout/2 for t = 0 to t = 1. Note that a similar example has been investigated in [de Rooij and Abdalla, 2015] with a Neo-Hookean model whereas we use here α = 3.5. In this setting, since we consider out-of-plane displacements, the displacement and deformation gradients G and F are in fact 3 × 2 matrices such that:…”

Section: Annular Square Membrane Deformationmentioning

confidence: 99%

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Applications of conic programming in non-smooth mechanics

Bleyer¹

2022

Preprint

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In the field of nonlinear mechanics, many challenging problems (e.g. plasticity, contact, masonry structures, nonlinear membranes) turn out to be expressible as conic programs. In general, such problems are non-smooth in nature (plasticity condition, unilateral condition, etc.), which makes their numerical resolution through standard Newton methods quite difficult. Their formulation as conic programs alleviates this difficulty since large-scale conic optimization problems can now be solved in a very robust and efficient manner, thanks to the development of dedicated interior-point algorithms. In this contribution, we review old and novel formulations of various non-smooth mechanics problems including associated plasticity with nonlinear hardening, nonlinear membranes, minimal crack surfaces and visco-plastic fluid flows.

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Section: Annular Square Membrane Deformationsupporting

confidence: 83%

Section: Annular Square Membrane Deformationmentioning

confidence: 99%

Applications of conic programming in non-smooth mechanics

Bleyer¹

2022

Preprint

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“…Based on the tension-field theory, several approaches appeared including the modified constitutive matrix approaches [91][92][93][94][95] and the modified deformation tensor approaches [96,97]. These models have been applied in finite element algorithms [98,99] and can predict in-plane wrinkling regions. However, the tension-field theory cannot obtain out-of-plane details of wrinkles and their evolutionary features; therefore, it is usually not suitable for accurate membrane deformation calculation in spaceborne antenna analysis.…”

Section: Mechanics Of Wrinkles Andmentioning

confidence: 99%

A Review on the Development of Spaceborne Membrane Antennas

Liu

et al. 2022

Space Sci Technol

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The membrane antenna technology is a very promising approach to obtain large aperture with light weight and low stowed volume. In the past decades, extensive studies have been carried out on active and passive membrane antennas. However, the practical spaceborne applications are rare due to many challenges, e.g., the surface accuracy maintenance, the on-orbit reliability, and the environmental compatibility. This paper summarizes the history and state-of-art progresses on spaceborne membrane antennas. Curved surface reflectors, conformal active membrane antennas, planar array membrane antennas, and planar reflectarray membrane antennas have been introduced, respectively. Radiofrequency design, deploying mechanism, material, experiment, application, and analysis method have been presented. By concluding the advantages and challenges of the current membrane antennas, this paper is aimed at providing a perspective of the existing problems and future trend of spaceborne membrane antennas.

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“…Without employing a wrinkling model, the compressive strength of the rib is overestimated. We therefore incorporated a wrinkling model based on the tension field theory to measure the difference in rib deformations and therefore PHF and complementary energy. Running the optimization with the wrinkling model was unsuccessful because of the sensitive numerical behavior of the model, ie, mesh quality and load magnitude have a drastic influence on the convergence behavior.…”

Section: Efficient Designs Are Multidisplinary Compromisesmentioning

confidence: 99%

Ram‐air kite airfoil and reinforcements optimization for airborne wind energy applications

2019

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We present a multidisciplinary design optimization method for the profile and structural reinforcement layout of a ram‐air kite rib. The aim is to minimize the structural elastic energy and to maximize the traction power of a ram‐air kite used for airborne wind energy generation. Because of the large deformations occurring during flight, a fluid‐structure interaction (FSI) routine is included in the optimization, which determines the actual deformed rib geometry and its corresponding aerodynamic characteristics. A qualitative comparison between FSI inclusion and exclusion in the optimization is given. Discrepancies in airfoil profile and structural layout are observed.

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A finite element interior-point implementation of tension field theory

Cited by 10 publications

References 26 publications

Applications of conic programming in non-smooth mechanics

Applications of conic programming in non-smooth mechanics

A Review on the Development of Spaceborne Membrane Antennas

Ram‐air kite airfoil and reinforcements optimization for airborne wind energy applications

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