Refined gradient theory of scale-dependent superthin rods

Lurie, S. A.; Kuznetsova, E. L.; Rabinskii, L. N.; Popova, E. I.

doi:10.3103/s002565441502003x

Cited by 7 publications

(5 citation statements)

References 13 publications

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“…The result of solving the spectral problem can be a set of eigenvalues and eigenvectors of a discrete analogue of the original problem, while the smallest positive value is taken as critical. Similar problems with the study of temperature effects were considered in works (Knyazeva et al, 2007;Riedlbauer et al, 2012;Keller et al, 2013;Lurie et al, 2015;Formalev and Kolesnik, 2018;Rabinsky and Tushavina, 2019a;Rabinskiy and Tushavina, 2019b;Formalev and Kolesnik, 2019).…”

Section: Resultsmentioning

confidence: 78%

Validation of Methodology for Modeling Effects of Loss of Stability in Thin-Walled Parts Manufactured Using SLM Technology

Dobryanskiy¹,

Rabinskiy²,

Tushavina³

2019

PTQ

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Additive manufacturing technologies make it possible to manufacture any product in layers based on a 3D computer model, but this issue is understudied. Therefore, this paper considers the problem of describing the effects of buckling arising in the three-dimensional printing of products containing elements whose length significantly exceeds their thickness or the characteristic size of the cross section. The behavior of these elements, from the point of view of material mechanics, can be described using models of plates or beams. In this study, we compare the results of calculations obtained using the model of non-stationary thermal conductivity and thermos-elasticity with experimental data for a specific element of printed product in which stability loss occurs. It was concluded that, at the initial moments of time, the lowest critical impact coefficient is realized, which in turn makes it the most dangerous phenomenon. The possibility of changing print parameters and product geometry to exclude the mentioned effects has been investigated. The considered structural element may lose stability during the building process. The results of solving the spectral problem indicated that over time the value of the critical effect decreases and asymptotically tends to a fixed minimum value.

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Section: Resultsmentioning

confidence: 78%

Validation of Methodology for Modeling Effects of Loss of Stability in Thin-Walled Parts Manufactured Using SLM Technology

Dobryanskiy¹,

Rabinskiy²,

Tushavina³

2019

PTQ

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“…Thus, the abnormal non-physical increase of bending stiffness for the ultra-thin structures does not arise within the considered theory (see also refs. [36,49]).…”

Section: Pure Bending Of a Layermentioning

confidence: 99%

Variant of strain gradient elasticity with simplified formulation of traction boundary value problems

Lurie

Solyaev

2023

Z Angew Math Mech

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In this paper, we show that within the class of isotropic Mindlin‐Toupin gradient theories there exist a particular variant of the theory, which allows a completely simplified form of traction boundary value problems. This theory can be obtained assuming that the high‐grade part of the strain energy density depends only on the vector‐type quantities, that are the gradient of dilatation and the curl of small rotation. Such incomplete gradient theory becomes positive semi‐definite and at the same time it obeys the strong ellipticity conditions of the general Mindlin‐Toupin first strain gradient elasticity. Based on the variational approach it is shown that the equilibrium equations of the developed theory and its definition for the surface traction can be given only in terms of the total stresses (like in classical elasticity). Such formulation can be useful for derivation of the closed form solutions for the problems with traction‐type boundary conditions. Examples of the solutions for the problem of cylindrical bending and for the inplane crack tip fields are presented. It is shown that considered theory allows to obtain a regularized solution for the crack problems and at the same time it does not predict a non‐physical infinite increase of the material's rigidity under bending.

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“…Генерируемые модели структур с различным диаметром волокон будут подобны друг другу (с точностью до статистической ошибки) при выборе представительных фрагментов соответствующего размера. Поэтому для учета размерных эффектов при моделировании таких материалов, вероятно, следует привлекать неклассические модели балок и стержней, построенные, например, в рамках градиентной теории упругости [16][17][18]. Весьма перспективными при учете масштабных эффектов в задачах теплопроводности и термоупругости для рассматриваемых пористых систем могут оказаться модели, учитывающие свойства интерфейса элементов пористых структур [19,20].…”

Section: результаты расчетовunclassified

Methodology of Numerical Modelling of Mechanical Properties of the Porous Heat-Shielding Material Based on Ceramic Fibers

2016

PNRPU MB

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ния механических свойств волокнистых материалов в зависимости от объемного содержания пористости и ориентации волокон. В работе показано, что для достаточно больших фрагментов (40 мкм и более) предложенная методика позволяет получать стабильные прогнозы механических свойств с относительно небольшим разбросом значений вследствие статистического отличия рассматриваемых фрагментов.

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Refined gradient theory of scale-dependent superthin rods

Cited by 7 publications

References 13 publications

Validation of Methodology for Modeling Effects of Loss of Stability in Thin-Walled Parts Manufactured Using SLM Technology

Validation of Methodology for Modeling Effects of Loss of Stability in Thin-Walled Parts Manufactured Using SLM Technology

Variant of strain gradient elasticity with simplified formulation of traction boundary value problems

Methodology of Numerical Modelling of Mechanical Properties of the Porous Heat-Shielding Material Based on Ceramic Fibers

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