Some solutions of minimaxmax problems for the torsional displacements of rectangular plates

Antunes, Pedro R. S.; Gazzola, Filippo

doi:10.1002/zamm.201800065

Cited by 7 publications

(3 citation statements)

References 24 publications

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“…This idea is confirmed by [5, Theorem 4.1-4.2] when the weights p are symmetric with respect to y as in our case. This result and others in [2] seem to suggest that odd loads are favourite in attaining the maximum (3.3).…”

Section: Gap Functionsupporting

confidence: 70%

Non-homogeneous density functions to strengthen rectangular partially hinged plates

Falocchi¹

2020

Preprint

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We consider a non-homogeneous partially hinged rectangular plate having structural engineering applications. In order to study possible remedies for torsional instability phenomena we consider the gap function as a measure of the torsional performances of the plate. We treat different configurations of load and we study which density function is optimal for our aims. The analysis is in accordance with some results obtained studying the corresponding eigenvalue problem in terms of maximization of the ratio of specific eigenvalues. Some numerical experiments complete the analysis.

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Section: Gap Functionsupporting

confidence: 70%

Non-homogeneous density functions to strengthen rectangular partially hinged plates

Falocchi¹

2020

Preprint

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“…The constant Ed 3 12(1−ν 2 ) in front of the biharmonic operator ∆ 2 represents the rigidity of the plate. In order to have a more detailed picture on the recent literature on rectangular plates and applications in models for decks of bridges, we quote [6,16,17,20,22] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

An orthotropic plate model for decks of suspension bridges

Ferrero¹

2021

Preprint

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The main purpose of the present paper is to compare two different kinds of approaches in modeling the deck of a suspension bridge, the first one consisting in looking at the deck as a rectangular plate and the second one as a beam concerning vertical deflections and as a rod concerning torsional deformations. Throughout this paper we will refer to the model corresponding to the second approach as the beam-rod model. In our discussion, we observe that the beam-rod model has more degrees of freedom if compared with the isotropic plate model. For this reason the beam-rod model is supposed to be more appropiate to describe the behavior of the deck of a realistic suspension bridge. A possible strategy to make the plate model more efficient could be to relax the isotropy condition with a more general condition of orthotropy, which is expected to increase the degrees of freedom in view of the larger number of elastic constants. In this new setting, it becomes more meaningful comparing the two approaches.Basic results are proved for the suggested problem, from existence and uniqueness of solutions to spectral properties. We suggest realistic values for the elastic parameters thus obtaining with both approaches similar responses in the static and dynamic behavior of the deck. This can be considered as a preliminary article since many work has still to be done with the perspective of formulating models for a complete suspension bridge which take into account not only the deck but also the action on it of cables and hangers. With this perspective, a section is devoted to open questions dealing with possible future developments.

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“…The constant Ed 3 12(1−ν 2 ) in front of the biharmonic operator ∆ 2 represents the rigidity of the plate. For more details on recent literature about rectangular plates and applications in models for decks of bridges, we quote [5,10,11,13,15,16,18] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A note on an orthotropic plate model describing the deck of a bridge

Ferrero¹

2021

Preprint

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The purpose of this work is to develop a model for a rectangular plate made of an orthotropic material. If compared with the classical model of the isotropic plate, the relaxed condition of orthotropy increases the degrees of freedom as a consequence of the larger number of elastic parameters, thus allowing to better describe rectangular plates having different behaviors in the two directions parallel to the edges of the rectangle.We have in mind structures like decks of bridges where the rigidity in the direction of their length does not necessarily coincide with the one in the direction of its width.We introduce some basic notions from the theory of linear elasticity, having a special attention for the theory of orthotropic materials. In particular we recall the Hooke's law in its general setting and we explain how it can be simplified under the orthotropy assumption.Following the approach of the Kirchhoff-Love model, we obtain the bending energy of an orthotropic plate and from it the corresponding equilibrium equation when the plate is subject to the action of a vertical load. Accordingly, we write the kinetic energy of the plate which combined with the bending energy gives the complete Lagrangian; classical variational methods then produces the equation of motion.

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Some solutions of minimaxmax problems for the torsional displacements of rectangular plates

Cited by 7 publications

References 24 publications

Non-homogeneous density functions to strengthen rectangular partially hinged plates

Non-homogeneous density functions to strengthen rectangular partially hinged plates

An orthotropic plate model for decks of suspension bridges

A note on an orthotropic plate model describing the deck of a bridge

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