Non-homogeneous density functions to strengthen rectangular partially hinged plates

A. Falocchi

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Non-homogeneous density functions to strengthen rectangular partially hinged plates

A. Falocchi

Analysis of PDEs · Submitted 17 Feb 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The analysis is in accordance with some results obtained studying the corresponding eigenvalue problem in terms of maximization of the ratio of specific eigenvalues.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,112 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.07 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.41 · mentions code or data availability 0.02.

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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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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider a non-homogeneous partially hinged rectangular plate having structural engineering applications.	contribution 0.50	0.44	0.03	asserted 0.92
s1	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.	method 0.77	0.78	0.04	asserted 0.83
s2	We treat different configurations of load and we study which density function is optimal for our aims.	contribution 0.74	0.92	0.10	asserted 0.82
s3	The analysis is in accordance with some results obtained studying the corresponding eigenvalue problem in terms of maximization of the ratio of specific eigenvalues.	method 0.69	0.48	0.11	asserted 0.65
s4	Some numerical experiments complete the analysis.	method 0.81	0.89	0.03	asserted 0.90

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Original abstract

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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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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The numerical computation of the gap function in [ref] is obtained truncating the Fourier series at a certain $N≥1$, integer; we compute the weighted eigenvalues and eigenfunctions of [ref], exploiting the explicit information we have in the case $p≡1$, see [ref] , and adopting the same numerical procedure described in [ref] .

Maximizing the ratio of eigenvalues of non-homogeneous partially hinged plates · $L^2(Ω)$ external forcing terms · 1.00

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Here we compare the density functions proposed in [ref] and we observe that $p(x,y)$ optimal for [ref] are optimal also with respect to the reduction of the gap function.

Maximizing the ratio of eigenvalues of non-homogeneous partially hinged plates · Introduction · 0.97

Cites as support 1 paper

More precisely, in [ref] the authors proved theoretically that optimal weights $p(x,y)$ in increasing or reducing the first torsional or longitudinal eigenvalue must be of bang-bang type, i.e. [equation] for a suitable set $S⊂Ω$, $0<α<1<β$ and $χ_S$ is the characteristic function of $S$.

Maximizing the ratio of eigenvalues of non-homogeneous partially hinged plates · The choice of the weight function $p∈𝒫_L^∞^α,β$ · 0.96

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