A selfsimilar problem on the action of a sudden load on the boundary of an elastic half-space

Куликовский, А. Г.; Свешникова, Е.И.

doi:10.1016/0021-8928(85)90105-4

Cited by 16 publications

(11 citation statements)

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“…10). Nevertheless, it must be emphasised that in certain regions of the initial parameters, a solution within the framework of the model considered here can only be constructed using admissible discontinuities and is not identical with the solution obtained earlier.…”

Section: Non-linear Quasi-transverse Waves In Composite Mediamentioning

confidence: 92%

Self-similar asymptotics of wave problems and the structures of non-classical discontinuities in non-linearly elastic media with dispersion and dissipation

Chugainova¹

2007

Journal of Applied Mathematics and Mechanics

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Section: Non-linear Quasi-transverse Waves In Composite Mediamentioning

confidence: 92%

Self-similar asymptotics of wave problems and the structures of non-classical discontinuities in non-linearly elastic media with dispersion and dissipation

Chugainova¹

2007

Journal of Applied Mathematics and Mechanics

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“…Solutions of a piston problem were analyzed in [15,Chapter 5], [17,Section 7.4.7], [22,23]. For fixed initial values U 1 , U 2 , the whole u 1 , u 2 plane is divided into domains in such a way that, if boundary values u * 1 , u * 2 belong to one of them, then a definite combination of Riemann waves and shocks gives the solution.…”

Section: Riemann and Shock Waves Solution Of Piston Problemmentioning

confidence: 99%

On the Nonuniqueness of Solutions to the Nonlinear Equations of Elasticity Theory

2006

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One-dimensional selfsimilar problems for waves in an elastic half-space generated by a sudden change of the boundary stress (the "piston" problem) and problems of disintegration of an arbitrary discontinuity are considered. For the case when small-amplitude waves are generated in a medium with small anisotropy a qualitative analysis shows that these problems have nonunique solutions when it is assumed that the solutions involve Riemann waves and evolutionary discontinuities. The above-mentioned problems are considered as limits of properly formulated problems for visco-elastic media when the viscosity tends to zero or (what is the same) that time tends to infinity. It is numerically found that all above-mentioned inviscid solutions can represent the asymptotics of visco-elastic solutions. The type of asymptotics depends on those details of the visco-elastic problem formulation which are absent when formulating inviscid selfsimilar problems. Similar considerations are made for elastic media with dispersion along with dissipation which are manifested in small-scale processes. In such media the number of available asymptotics (as t → ∞) for the above-mentioned solutions depends on a relation between dispersion and dissipation and can be large. Thus, two possible causes for the nonuniqueness of solutions to the equations of elasticity theory are investigated.

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“…В работах [29], [30] построено решение сформулированной автомодельной задачи. Решение состоит из последовательности автомодельных волн Рима-на и ударных волн, следующих в порядке убывания скорости.…”

Section: ударные волныunclassified

“…Решение состоит из последовательности автомодельных волн Рима-на и ударных волн, следующих в порядке убывания скорости. Построенное решение принципиально различается для сред с κ > 0 и κ < 0 и зависит от па-раметра анизотропии g. В [29] отмечено, что у автомодельной задачи о вне-запном изменении напряжений на границе упругого полупространства (задачи о поршне) в некоторой области параметров, характеризующих задачу (обла-сти неединственности), могут существовать два решения. Геометрия области неединственности зависит от параметров U α , g, κ.…”

Section: ударные волныunclassified

“…Неединственность решения была обнаружена при фактическом построении решения задачи [21], [29]. Однако можно предвидеть ее появление и дать до-98 А. Г. КУЛИКОВСКИЙ, А. П. ЧУГАЙНОВА статочный признак неединственности, не получая полного решения, а восполь-зовавшись видом диаграммы эволюционности [31].…”

Section: ударные волныunclassified

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Классические И Неклассические Разрывы В Решениях Уравнений Нелинейной Теории Упругости

Куликовский¹,

Chugainova²

2008

Uspekhi Mat. Nauk

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A selfsimilar problem on the action of a sudden load on the boundary of an elastic half-space

Cited by 16 publications

References 0 publications

Self-similar asymptotics of wave problems and the structures of non-classical discontinuities in non-linearly elastic media with dispersion and dissipation

Self-similar asymptotics of wave problems and the structures of non-classical discontinuities in non-linearly elastic media with dispersion and dissipation

On the Nonuniqueness of Solutions to the Nonlinear Equations of Elasticity Theory

Классические И Неклассические Разрывы В Решениях Уравнений Нелинейной Теории Упругости

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