A numerical comparison of the uniformly valid asymptotic plate equations with a 3D model: Clamped rectangular incompressible elastic plates

Wang, Fan‐Fan; Dai, Hui–Hui; Giorgio, Ivan

doi:10.1177/10812865211025583

Cited by 17 publications

(4 citation statements)

References 40 publications

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“…Based the above-mentioned works, we found that the majority of researchers used an analytical solution to investigate the behavior of homogeneous and FGM nanostructures. Such analytical solutions, however, are very limited when the geometry, gradation of materials properties, boundary conditions, and loading conditions become even more complicated [57][58][59][60][61]. To this end, numerical methods such as finite element method (FEM), isogeometric analysis (IGA), and meshless methods (MMs) represent valid alternatives to analyze the complex behavior of size-dependent continuum FGM nanostructures.…”

Section: Introductionmentioning

confidence: 99%

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Belarbi

Houari

et al. 2022

Mathematics and Mechanics of Solids

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This work studies the size-dependent free vibration response of functionally graded (FG) nanoplates using a layerwise theory. The proposed model supposes not only a higher-order displacement field for the core but also the first-order displacement field for the two face sheets, thereby maintaining an interlaminar displacement continuity among layers. Unlike the conventional layerwise models, the number of variables is kept fixed and does not increase for an increased number of layers. This is a very important feature compared to conventional layerwise models and facilitates significantly the engineering analyses. The material properties of the FG nanoplate are graded continuously through the thickness direction in accordance with a power-law function. The Eringen’s nonlocal elasticity theory is here adopted to relax the continuum axiom required in classical continuum mechanics and hence hopeful to capture the small size effects of naturally discrete nanoplates. The equations of motion of the problem are obtained via a classical Hamilton’s principle. The present layerwise model is implemented with a computationally efficient C0- continuous isoparametric serendipity elements and applied to solve a large-scale discrete numerical problem. The robustness and reliability of the developed finite element model are demonstrated by a comparative evaluation of results against predictions from literature. The comparative studies show that the proposed finite element model is: (a) free of shear locking, (b) accurate with a fast rate convergence for both thin and thick FG nanoplates, and (c) excellent in terms of numerical stability. Moreover, a detailed parametric analysis checks for the sensitivity of the vibration response of FG nanoplates to the aspect ratio, length-to-thickness ratio, nonlocal parameter, boundary conditions, power-law index, and modes shapes. Referential results are also reported, for the first time, for natural frequencies of FGM nanoplates which will serve as benchmarks for further computational investigations.

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Section: Introductionmentioning

confidence: 99%

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Belarbi

Houari

et al. 2022

Mathematics and Mechanics of Solids

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“…The extraction of waterproof rock pillars of a specific thickness in underwater mining is crucial for ensuring safety in subaqueous mining operations. According to the thickness-span ratio theory [38], a critical criterion to prevent the rupture of these pillars is that the ratio of their height to the stope span must exceed 0.5:…”

Section: Estimation Of the Isolation Layer Thickness Of The Similar M...mentioning

confidence: 99%

Fractal Evolution Characteristics of Isolation Layers in a Submarine Gold Mine: A Case Study

Chen,

Li,

Lin

et al. 2024

Minerals

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The establishment of an isolation layer in submarine mining has been a persistent challenge. In the context of this research, we conducted a similarity simulation test to preliminarily assess the interaction between the thickness and extent of the isolation layer. Subsequently, we introduce an innovative approach that integrates fractal theory and the Bonded Block Model (BBM) to simulate undersea isolation layer mining. The validation of this method relies on on-site borehole scanning and displacement monitoring, which depict the intricate fractal evolution of fractures and predict the optimal thickness of the isolation layer. Our findings affirm the robustness and validity of this method. Evaluation of the fractal dimensions of fractures reveals that a critical threshold of 1.7 is essential to prevent structural failure of the isolation layer, while a limit of 1.5 is necessary to avoid significant water ingress. Remarkably, the correlation dimension of the settlement time series closely aligns with the fractal dimension of the fractures, underscoring the feasibility of ensuring the safety of isolation layer mining through real-time settlement monitoring.

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“…This nonlinearity dependence on the external loads rather than the plate/membrane intrinsic properties, such as plate dimensions and material properties, leads to a problem called as ''a hierarchy of two-dimensional models'' [37]. This hierarchy problem is overcome by the uniformly valid asymptotic plate theory developed by Dai and his collaborators [38,39]. The expression of ''uniformly valid'' means that the asymptotic plate theory is independent on the external loads [38,39].…”

Section: Model Developmentmentioning

confidence: 99%

“…This hierarchy problem is overcome by the uniformly valid asymptotic plate theory developed by Dai and his collaborators [38,39]. The expression of ''uniformly valid'' means that the asymptotic plate theory is independent on the external loads [38,39]. Furthermore, an (implicit) assumption in the von Ka´rma´n plate model is the linear elasticity as indicated by equation (1).…”

Section: Model Developmentmentioning

confidence: 99%

The pull-in instability and eigenfrequency variations of a graphene resonator under electrostatic loading

Zhang

Zhao

2022

Mathematics and Mechanics of Solids

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A continuum membrane model is presented to describe the pull-in instability and eigenfrequency variations of a graphene resonator under an electrostatic loading. The pull-in instability leads to the device failure and the eigenfrequency variation determines its frequency tuning range, which are among the most important aspects in a micro/nanomechanical resonator design. The von Kármán kinematic assumptions are used for the membrane large deflection. The geometric nonlinearity resulting from a large deflection and the physical nonlinearity resulting from an electrostatic loading are the two competing mechanisms: the geometric nonlinearity stiffens the membrane structure and the physical nonlinearity softens it. The effects of these two competing mechanisms together with the initial tensile strain on the pull-in instability and eigenfrequency variations are vividly demonstrated. With the aim of achieving a higher accuracy, a multimodal computation method together with its convergence study and error analysis is also presented.

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A numerical comparison of the uniformly valid asymptotic plate equations with a 3D model: Clamped rectangular incompressible elastic plates

Cited by 17 publications

References 40 publications

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Nonlocal vibration of functionally graded nanoplates using a layerwise theory

Fractal Evolution Characteristics of Isolation Layers in a Submarine Gold Mine: A Case Study

The pull-in instability and eigenfrequency variations of a graphene resonator under electrostatic loading

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