On numerical solving a rigid inclusions problem in 2D elasticity

Rudoy, E. M.

doi:10.1007/s00033-016-0764-6

Cited by 17 publications

(9 citation statements)

References 33 publications

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“…Dong and Lee [4] studied the problem of double periodic arrangement of cracks /rigid line inclusions in infinite isotropic plane media by using the boundary integral equation method. Rudoy [5] considered the two‐dimensional elastic problem of rigid inclusion with arbitrary shape and size by variational method. Jobin [6] solved the elastic field of two rigid line inclusions embedded in a finite matrix by boundary element method.…”

Section: Introductionmentioning

confidence: 99%

Circular inclusion problem of two‐dimensional decagonal quasicrystals with interfacial rigid lines under concentrated force

Zhai

Ding

et al. 2021

Z Angew Math Mech

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The plane problem of two-dimensional decagonal quasicrystals with a rigid circular arc inclusion was investigated under infinite tension and concentrated force. Based on complex representations of stresses and displacements of two-dimensional decagonal quasicrystals, the above problem is transformed into Riemann boundary problem by using the analytic continuation principle of complex functions. The general solutions of two-dimensional decagonal quasicrystals under the action of plane concentrated force and infinite uniform tension are derived. The closed solutions of complex potential functions in several typical cases are obtained, and the formula of singular stress field at the tip of rigid line inclusions is given. The results show that the stress field at the tip of circular arc rigid line inclusions has singularity of oscillation under plane load. Numerical examples are given to analyze the effects of inclusion radius, different inclusions, the coupling coefficient and phason field parameter on stress singularity coefficients.

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Section: Introductionmentioning

confidence: 99%

Circular inclusion problem of two‐dimensional decagonal quasicrystals with interfacial rigid lines under concentrated force

Zhai

Ding

et al. 2021

Z Angew Math Mech

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“…The features of mechanical properties and geometric parameters of inclusions can affect the initiation and propagation of a crack. At present, active studies of problems for various models of elastic bodies containing rigid inclusions and cracks with both linear and nonlinear boundary conditions are being carried out, and we refer the reader, for example, to [1][2][3][4][5][6][7][8][9][10][11]. Using the universality of the methods of the calculus of variations, various problems for bodies with rigid inclusions have been successfully formulated and investigated, see, for example, [1,[12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

On a Limiting Passage as the Thickness of a Rigid Inclusions in an Equilibrium Problem for a Kirchhoff-Love Plate with a Crack

Lazarev

Semenova

Романова

2021

Journal of Siberian Federal University. Mathematics &Amp; Physics

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The paper considers equilibrium models of Kirchhoff-Love plates with rigid inclusions of two types. The first type of inclusion is described by three-dimensional sets, the second one corresponds to a cylindrical rigid inclusion, which is perpendicular to the plate’s median plane in the initial state. For both models, we suppose that there is a through crack along a fixed part of the inclusion’s boundary. On the crack non-penetration conditions are prescribed which correspond to a certain known configuration bending near the crack. The uniqueness solvability of a new problems for a Kirchhoff-Love plate with a flat rigid inclusion is proved. It is proved that when a thickness parameter tends to zero, the problem for a flat rigid inclusion can be represented as a limiting task for a family of variational problems concerning the inclusions of the first type. A solvability of an optimal control problem with a control given by the size of inclusions is proved

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“…В [4] получено полное асимптотическое разложение решения задачи равновесия двухмерного упругого тела, содержащего тонкое включение, в окрестности вершины тонкого включения, рассмотрены случаи с отслоением и без отслоения. В работе [5] выполнено численное исследование равновесия плоского упругого тела с системой жестких включений, найдено распределение напряжений в теле. В [6] проведен численный счет равновесия двухслойной конктрукции со сквозной трещиной.…”

Section: Introductionunclassified

A problem of glueing of two Kirchhoff–Love plates

Pyatkina¹

2019

Sib. Elektron. Mat. Izv.

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An equilibrium problem of two parallel elastic plates is considered in the paper. The plates are located without a gap and have the same size and shape. They are clamped at their edges and joined to each other along a straight interval. The deflections of the plates satisfy the nonpenetration condition. The case is considered when at the contact surface of the plates not only the lateral load from another plate, but also additional elastic force acts. It is assumed that this elastic force acts both in contact plane and orthogonal to it, and its value is characterized by a so-called damage parameter. Two extreme cases are studied when the parameter equals zero or tends to infinity. The first case corresponds to contact without friction of two plates. The second one corresponds to equilibrium of two-layer plate. The strong convergence of the solutions sequence of equilibrium problem of two plates with elastic force acting at the contact surface to the solutions of extreme problem is proved when the damage parameter tends to zero or to infinity. For the case of the contact without friction singular solution is found near the tip of the interval along which the plates are glued.

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On numerical solving a rigid inclusions problem in 2D elasticity

Cited by 17 publications

References 33 publications

Circular inclusion problem of two‐dimensional decagonal quasicrystals with interfacial rigid lines under concentrated force

Circular inclusion problem of two‐dimensional decagonal quasicrystals with interfacial rigid lines under concentrated force

On a Limiting Passage as the Thickness of a Rigid Inclusions in an Equilibrium Problem for a Kirchhoff-Love Plate with a Crack

A problem of glueing of two Kirchhoff–Love plates

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