Theory of Elasticity for Scientists and Engineers

Atanacković, Teodor M.; Guran, Ardéshir

doi:10.1007/978-1-4612-1330-7

Cited by 102 publications

(89 citation statements)

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“…The position of the point of the spherical layer in given by spherical coordinates: ρ -radial coordinate, ϕ -meridional coordinate, θ -circumferential coordinate. Equilibrium equations for the spherical layer have the form [1] ∂σ ρρ ∂ρ + 1 ρ ∂σ ρϕ ∂ϕ + 1 ρsinϕ…”

Section: Equilibrium Equations In Displacementsmentioning

confidence: 99%

“…For axisymmetrilc problem v = 0. The relations for deformations and displacements of the spherical layer are the following [1] ε ρρ = ∂w ∂ρ , ε ϕϕ = 1 ρ ∂u ∂ϕ + w ρ , ε θθ = cot ϕ u ρ + w ρ , ε ρϕ = 1 2…”

Section: Equilibrium Equations In Displacementsmentioning

confidence: 99%

“…Such model may be used, for example, to describe the changes of the stress strain state of the external human eye shell under intraocular injections. For isotropic spherical layer this problem, known as Lame problem, is discussed, for example, in [1]. For transverse isotropic spherical layer the analytical solution has been obtained in [2,3] and asymptotic solution in [4].…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic Analysis of Deformations of the Slightly Orthotropic Spherical Layer Under Normal Pressure

Smirnov¹,

Bauer²,

Венатовская³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. The deformation of the orthotropic spherical layer under normal pressure applied on the outer and inner surfaces is analyzed. The layer is assumed to be slightly orthotropic, it permits to apply asymptotic methods. The equations of zeroth and first approximations are derived. For the shell, which is much softer in the transverse direction than in the tangential plane, one gets singularly perturbed boundary value problem. Solving this problem in the zeroth approximation the asymptotic formula for the change of the relative layer thickness under normal pressure is obtained. Also the effect of Poisson ratio and the layer thickness on the deformation is studied. For the cases of the thick and thin layers the last formula may be simplified. The asymptotic results well agree with the exact solution. The developed formulas are used in analysis of the scleral shell under intraocular pressure and may also be used in solution of the inverse problem, i.e. in analysis of the stress-strain state of a human eye under injection. The solution of the problem helps to estimate the mechanical parameters of the sclera, i.e. to find the ratio of the tangential and transversal Young moduli using clinical data for the sclera thickness change.

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Section: Equilibrium Equations In Displacementsmentioning

confidence: 99%

Section: Equilibrium Equations In Displacementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Asymptotic Analysis of Deformations of the Slightly Orthotropic Spherical Layer Under Normal Pressure

Smirnov¹,

Bauer²,

Венатовская³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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“…We have used appropriate transformations, following Atanackovic et al [15], on the set of equations (1) to derive equations for micropolar porous cubic crystal. In the present case, we consider an infinite homogeneous plate of micropolar porous medium possessing cubic symmetry and of thickness 2d.…”

Section: Problem Formulation and Its Solutionmentioning

confidence: 99%

“…Using dimensionless variables defined by (15) in Eqs. (3)- (6) with the help of (7)- (14), after suppressing the primes the field equations reduce to …”

Section: Problem Formulation and Its Solutionmentioning

confidence: 99%

Study of circular crested waves in a micropolar porous medium possessing cubic symmetry

Kumar¹,

Panchal²

2011

Bulletin of the Polish Academy of Sciences: Technical Sciences

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Abstract. The paper is concerned with the propagation of circular crested Lamb waves in a homogeneous micpropolar porous medium possessing cubic symmetry. The frequency equations, connecting the phase velocity with wave number and other material parameters, for symmetric as well as antisymmetric modes of wave propagation are derived. The amplitudes of displacement components, microrotation and volume fraction field are computed numerically. The numerical results obtained have been illustrated graphically to understand the behavior of phase velocity and attenuation coefficient versus wave number of a wave.

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Correcting precipitation feature location in general circulation models

et al. 2014

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There is much evidence that precipitation responses to global warming involve wet regions becoming wetter and dry regions drier. This presents challenges for the interpretation of projections from general circulation models (GCMs) which have substantial biases in the location of precipitation features. While improving GCM simulated precipitation is the most desirable solution, adaptation and mitigation decisions must be made with the models already available. Many techniques have been developed to correct biases in grid point precipitation intensities, but few have been introduced to correct for location biases. Here, we describe a new technique for correcting the spatial and seasonal location of climatological precipitation features. We design this technique to respect the geometry of the problem (spherical spatial dimensions, with cyclic seasons), while conserving either precipitation intensities, or integrated precipitation amount. We discuss the mathematical basis of the technique and investigate its behaviour in different regimes. We find that the resulting warps depend smoothly on the most influential parameter, which determines the balance between smoothness and closeness of fit. We show that the technique is capable of removing more than half the RMS error in a model's climatology, obtaining consistently better results when conserving integrated precipitation. To demonstrate the ability of the new technique to improve simulated precipitation changes, we apply our transformations to historical anomalies and show that RMS error is reduced relative to GPCP's anomalies by approximately 10% for both types of warp. This verifies that errors in precipitation changes can be reduced by correcting underlying location errors in a GCM's climatology.

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Theory of Elasticity for Scientists and Engineers

Cited by 102 publications

References 0 publications

Asymptotic Analysis of Deformations of the Slightly Orthotropic Spherical Layer Under Normal Pressure

Asymptotic Analysis of Deformations of the Slightly Orthotropic Spherical Layer Under Normal Pressure

Study of circular crested waves in a micropolar porous medium possessing cubic symmetry

Correcting precipitation feature location in general circulation models

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