Virtual elements for a shear-deflection formulation of Reissner–Mindlin plates

Veiga, L. da; Mora, David; Rivera, Gonzalo

doi:10.1090/mcom/3331

Cited by 40 publications

(9 citation statements)

References 52 publications

(72 reference statements)

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“…Moreover, low-level rock strata fracturing can influence high-level rock strata fracturing, causing additional drastic mine pressure behaviors [4]. Among the existing studies on reasonable initial and periodic fracturing span and intensity of hard roofs, many scholars have proposed the adoption of "Reissner thick plate" theory [5,6], "Vlasov plate" theory [7,8], and "long beam" theory [9,10], which provide a precious theoretical basis for hard roof control. However, the calculation and analytical results obtained using a single theory somewhat deviate from engineering practice when the complexity of overlying strata collapse on fully mechanized caving faces in multi-stratum hard roofs, the different structural characteristics of the overlying strata at the fracture of each stratum of the hard roof, and the varying stress environments are altogether considered.…”

Section: Introductionmentioning

confidence: 99%

Influence Characteristics of Double-Stratum Hard Roof Movement in a Fully Mechanized Top Coal Caving on the Working Resistance of Supports

Shi¹,

Yin²,

Li³

et al. 2020

JESTR

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In the traditional mechanical models of hard roof, multiple hard rock strata are usually taken as the overall critical stratum to analyze its movement instability characteristics while the mutual effect between two hard rock strata is neglected, so it's difficult for theoretical analysis results to realize the accurate prediction of mine pressure behaviors. The reasonable prediction of mine pressure behaviors on a fully mechanized caving face with multiple hard rock strata is ensured further by considering the geological conditions of the 1307 working face mine in Zhaoxian Coal Mine in the Yonglong Coalfield Mine area in China, a mechanical model of a hard roof structure with high and low strata (double strata) was proposed in this study, and the periodic instability step of the high-and low-level hard roofs and the change laws of support resistance on the working face were also determined. Then, the theoretical calculation results were verified according to field measurement data. Results indicate that fracturing instability does not simultaneously occurred in the high and low strata of the hard roof, as the instability steps are 106 m and 18 m, and the corresponding working resistances of the hydraulic support are 63 MPa and 37 MPa, respectively. Meanwhile, the onsite-measured mine pressure data suggest that the major-cycle cyclic weighting step is approximately 101 m, while the continuous step is approximately 12 m. The minor-cycle cyclic weighting step is within 15-25 m, the continuous step is approximately 2 m, and the peak working resistances of the hydraulic support on the average are 42.3 MPa and 36.8 MPa, respectively, so the on-site monitoring data basically accorded with the theoretical analysis results, thus verifying the scientificity of the constructed mechanical model. This study provides a theoretical reference on the safe mining of the fully mechanized caving face of a multi-stratum hard roof.

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Section: Introductionmentioning

confidence: 99%

Influence Characteristics of Double-Stratum Hard Roof Movement in a Fully Mechanized Top Coal Caving on the Working Resistance of Supports

Shi¹,

Yin²,

Li³

et al. 2020

JESTR

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“…Although the VEM is very recent, it has been applied to a large number of problems; for instance, VEM for Stokes, Brinkman, Cahn-Hilliard, plates bending, advection-diffusion, Helmholtz, parabolic, and hyperbolic problems have been introduced in [4,5,15,17,24,19,21,26,27,30,51,54,55,56], VEM for spectral problems in [18,37,42,44], VEM for linear and non-linear elasticity in [6,9,13,36,57], whereas a posteriori error analysis have been developed in [16,20,28,43].…”

Section: Introductionmentioning

confidence: 99%

A virtual element method for a nonlocal FitzHugh–Nagumo model of cardiac electrophysiology

Anaya

Bendahmane

Mora

et al. 2019

IMA Journal of Numerical Analysis

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We present a Virtual Element Method (VEM) for a nonlocal reaction-diffusion system of the cardiac electric field. To this system, we analyze an H 1 (Ω)-conforming discretization by means of VEM which can make use of general polygonal meshes. Under standard assumptions on the computational domain, we establish the convergence of the discrete solution by considering a series of a priori estimates and by using a general L p compactness criterion. Moreover, we obtain optimal order space-time error estimates in the L 2 norm. Finally, we report some numerical tests supporting the theoretical results.

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“…Although VEM is very recent, it has been applied to a large number of problems; for instance, to Stokes, Brinkman, Cahn-Hilliard, plates bending, advection-diffusion, Helmholtz, parabolic, and hyperbolic problems have been introduced in [3,4,12,15,23,16,24,25,28,41,44,45,46]. Regarding VEM for linear and non-linear elasticity we mention [7,11,31,48], for spectral problems [14,32,38,40], whereas a posteriori error analysis for VEM have been developed in [13,19,26,39].…”

Section: Introductionmentioning

confidence: 99%

A priori and a posteriori error estimates for a virtual element spectral analysis for the elasticity equations

Mora

Rivera

2018

IMA Journal of Numerical Analysis

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We present a priori and a posteriori error analysis of a Virtual Element Method (VEM) to approximate the vibration frequencies and modes of an elastic solid. We analyze a variational formulation relying only on the solid displacement and propose an H 1 (Ω)-conforming discretization by means of VEM. Under standard assumptions on the computational domain, we show that the resulting scheme provides a correct approximation of the spectrum and prove an optimal order error estimate for the eigenfunctions and a double order for the eigenvalues. Since, the VEM has the advantage of using general polygonal meshes, which allows implementing efficiently mesh refinement strategies, we also introduce a residual-type a posteriori error estimator and prove its reliability and efficiency. We use the corresponding error estimator to drive an adaptive scheme. Finally, we report the results of a couple of numerical tests that allow us to assess the performance of this approach.Key words: virtual element method, elasticity equations, eigenvalue problem, a priori error estimates, a posteriori error analysis, polygonal meshes 2000 MSC: 65N25, 65N30, 70J30, 76M25.Cτ := 2µ S τ + λ S tr(τ )I, where λ S and µ S are the Lamé coefficients, which we assume constant.We introduce the following bounded bilinear forms:Then, the eigenvalue problem above can be rewritten as follows:Problem 2. Find (λ, w) ∈ R × V, w = 0, such that a(w, v) = λb(w, v) ∀v ∈ V.

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Virtual elements for a shear-deflection formulation of Reissner–Mindlin plates

Cited by 40 publications

References 52 publications

Influence Characteristics of Double-Stratum Hard Roof Movement in a Fully Mechanized Top Coal Caving on the Working Resistance of Supports

Influence Characteristics of Double-Stratum Hard Roof Movement in a Fully Mechanized Top Coal Caving on the Working Resistance of Supports

A virtual element method for a nonlocal FitzHugh–Nagumo model of cardiac electrophysiology

A priori and a posteriori error estimates for a virtual element spectral analysis for the elasticity equations

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