Korn's Inequalities for Junctions of Spatial Bodies and Thin Rods

Назаров, С. А.

doi:10.1002/(sici)1099-1476(199702)20:3<219::aid-mma854>3.0.co;2-c

Cited by 38 publications

(12 citation statements)

References 11 publications

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“…The geometric conditions 3 • and 4 • have already been stated in [24] in the derivation of asymptotically sharp Korn inequalities and in [11,26,27] in the asymptotic analysis of elastic junctions. In both cases, these conditions provide some specific properties of the objects to be studied.…”

Section: Discussionmentioning

confidence: 99%

Elliptic boundary value problems in hybrid domains

Назаров

2004

Funct Anal Its Appl

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We derive asymptotic transmission conditions at points where segments are attached to a three-dimensional body. These conditions result in a formally self-adjoint problem on a hybrid set with properties similar to those of standard boundary value problems. In particular, the problem has a zero index and possesses a variational statement. If the systems of differential equations have a special form, then the operator of the problem is realized as a self-adjoint extension of the "decoupled" operators of the problems on the body and the segments. From this viewpoint, we interpret the results of asymptotic analysis of coupled thin and solid bodies.

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Section: Discussionmentioning

confidence: 99%

Elliptic boundary value problems in hybrid domains

Назаров

2004

Funct Anal Its Appl

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“…19) where the constant c is independent of the vector field u and the parameters γ > 0, h ∈ (0, h 0 ].…”

Section: H/2)mentioning

confidence: 99%

Korn Inequalities for a Reinforced Plate

Назаров

Slutskij

Sweers

2010

J Elast

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“…Асимптотическая точность та кого неравенства достигается введением в L<i-нормы смещений и их производных добавочных весовых множителей -степеней параметра h и расстояний до торцов стержня. Для тонких цилиндрических областей подобные неравенства получены в [36], [33] (изотропное распределение весовых множителей) и в [32], [34] (анизо тропное распределение, выделяющее направление вдоль оси стержня). В этом па раграфе весовое неравенство Корна обобщается на случай криволинейного стерж ня при дополнительных предположениях о его геометрии.…”

Section: = -(4m D^(1) + D^(0) }L()unclassified