Mathematical Model of Elastic Closed Flexible Shells with Nonlocal Shape Deviations

Олевский, Виктор Исаакович; Olevska, Yu. B.

doi:10.7546/jgsp-50-2018-57-69

Cited by 7 publications

(4 citation statements)

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“…To predict the rock mass behavior at various stage of excavating, the preliminary numerical simulation should be carried out taking into account all possible changes in rock structure (Vladyko, Kononenko, & Khomenko, 2012;Pivnyak, Dychkovskyi, Smirnov, & Cherednichenko, 2013;Pivnyak, Dychkovskyi, Bobyliov, Cabana, & Smoliński, 2018). To apply adequate mathematical modeling (Shashenko, Gapieiev, Solodyankin, 2009;Olevskyi & Olevska, 2018) for studying the stress-strain state of surrounding rocks, we need a correct estimation of mechanical properties.…”

Section: Rock Mass Mechanical Characteristics Estimationmentioning

confidence: 99%

Implementation of probabilistic approach to rock mass strength estimation while excavating through fault zones

Babets¹,

Sdvyzhkova²,

Shashenko³

et al. 2019

Min. miner. depos.

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Purpose. The paper addresses the rock mass state estimation while excavating a cross-heading through the area of regional fault "Bohdanivskyi" based on probabilistic approach to assessing the rock strength.Methods. The boundaries and fault zone extension are specified based on geological service database. This hazardous fault area has been confirmed, and the expected water inflow and methane emission have been identified based on the probe holes drilled ahead of the advancing face. To assess the strength of rocks, the statistical strength theory is used. Numerical simulation is performed using finite element method that is well-tested in geomechanical problems. Findings.The technique of rock mass strength estimation using structural factor based on statistical strength theory has been implemented to improve the adequacy of mathematical modeling. Numerical simulation of geomechanical processes based on finite element method and Hoek-Brown failure criterion is carried out. The changes of rock stress-strain state while excavating the cross-heading through various sites of the fault zone are determined depending on the level of rock disintegration.Originality. New regularities of rock mass behavior within the fault area are determined based on developed technique of rock strength assessment considering the rock mass disintegration and watering.Practical implications. Estimation of rock failure has resulted in designing the combination of support systems comprising metal sets, rockbolts and shotcrete.

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Section: Rock Mass Mechanical Characteristics Estimationmentioning

confidence: 99%

Implementation of probabilistic approach to rock mass strength estimation while excavating through fault zones

Babets¹,

Sdvyzhkova²,

Shashenko³

et al. 2019

Min. miner. depos.

View full text Add to dashboard Cite

show abstract

“…The method was tested a longitudinal cross section of a radioimage obtained with the help of aperture synthesis in intermediate radiation zone in order to estimate the distance to the reflector. Such approach can be used in order to estimate the shape of conductive objects instead of the standard laser interferometry [24]. The radar images are usually processed with the help of Fourier transform or Fourier series, which may lead to difficulties during the calculation process [25].…”

Section: Testing On Real Datamentioning

confidence: 99%

Approaches for improvement of reliability of the Prony’s method computation

Drobakhin,

Olevskyi

2023

J. Phys.: Conf. Ser.

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Parametric spectral analysis methods such as the Prony’s method can estimate the frequencies and amplitudes of a signal, conforming to their model, with great precision. At the same time, the addition of noise to the signal can lead to a complete model breakdown which leads to erroneous parameter values. This is especially true for the impulse noise. The article explores several possible algorithms which can be applied to the Prony’s method in order to refine the results and make them more noise resistant. Such algorithms include signal segmentation methods where the results of each segment processing influence the final estimate as well as the conceptually related method of point skipping. An approach based on the use of non-Euclidean norms as a measure of the linear algebraic equation system’s solution quality is developed and tested. Initially, the methods are applied to model digital signals, comprised of harmonic components with varying complex frequencies and amplitudes. Additive white Gaussian and impulse noise is added to the model signals. The results are then applied to the noisy results of a real-life synthetic aperture synthesis experiment obtained in the intermediate zone of radiation.

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“…The field of mathematical physics approximation is experiencing rapid development, with the theory of approximation being the most prominent area of progress [1,6,7]. Traditionally, the focus has been on approximation techniques that utilize polynomials [8,9] and trigonometric functions [6,7,10]. One particularly successful type of approximation technique is the use of fractional rational functions [8,11,12].…”

Section: Introductionmentioning

confidence: 99%

Raster image processing using 2D Padé-type approximations

Olevskyi,

Olevska,

Olevskyi

et al. 2023

J. Phys.: Conf. Ser.

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We have developed a method called the two-dimensional Padé-type approximants method, which can be used to reduce the Gibbs phenomenon in the harmonic two-dimensional Fourier series. This method can be applied to both monochrome and color raster images. To do this, we implement the generalized two-dimensional Padé approximation proposed by Chisholm. In this approach, we select the range of frequency values on the integer grid according to the Vavilov method. We propose a definition of a Padé-type functional and provide examples of its application to simple discontinuous templates represented as raster images. Through this study, we are able to draw conclusions about the practical usage and advantages of the Padé-type approximation. We demonstrate that the Padé-type approximant effectively eliminates distortions associated with the Gibbs phenomenon, and it is visually more appropriate than the Fourier approximant. Additionally, the application of the Padé-type approximation reduces the number of parameters without sacrificing precision.

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Mathematical Model of Elastic Closed Flexible Shells with Nonlocal Shape Deviations

Cited by 7 publications

References 0 publications

Implementation of probabilistic approach to rock mass strength estimation while excavating through fault zones

Implementation of probabilistic approach to rock mass strength estimation while excavating through fault zones

Approaches for improvement of reliability of the Prony’s method computation

Raster image processing using 2D Padé-type approximations

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