On the variational method in the theory of contact problems for nonlinearly elastic laminated bodies

Kuz'menko, V.I.

doi:10.1016/0021-8928(79)90184-9

Cited by 7 publications

(13 citation statements)

References 1 publication

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“…Then, analogously to [4], it is found, using the Ostrogradskii-Gauss theorem, that the real displacement ui(x, t) at time t corresponds to the value of the precise lower boundary at the set V(t) of the functional 1"2 ~l~) ' ' ""…”

Section: ~Xerhm (Kmentioning

confidence: 89%

“…Let subscripts ~ and T denote the normal and tangential components; the conditions at the surface Fk c may now be formulated [4] u~ (x, t) ~< ~ b) the actual contact area is not specified in advance, and so-called normal contact occurs in the absence of frictional force. Let subscripts ~ and T denote the normal and tangential components; the conditions at the surface Fk c may now be formulated [4] u~ (x, t) ~< ~ b) the actual contact area is not specified in advance, and so-called normal contact occurs in the absence of frictional force.…”

Section: F~=f~u ~U Kuf~mentioning

confidence: 99%

“…The Hilbert space H = Hl(~l) x HI(~2) • ... HI(~N) is now introduced, where Hl(~k) is a Hilbert space of vector functions (vl, v2, v3) defined in region ~k, which are summable in quadratic fomn together with the first derivatives [3,4]. The variational formulation of the given problem is now outlined.…”

Section: % (X T)iu~'~ (X T) --U$~ (X T) + A~ (X)] = 0; V" X ~ I'mentioning

confidence: 99%

“…In [4], on the basis of a variational formulation, the theorems of existence and uniqueness of the solution for a system of nonlinearly elastic bodies are proven. The results obtained may also be generalized for the given class of problems.…”

Section: St (V) --Y 5 ' A'jp:i 8q~" + 3/2k~8'2 § T" Wh (E= T) Dementioning

confidence: 99%

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Contact interaction of systems of bodies in conditions of creep of the material

Kuz'menko¹

1986

Soviet Applied Mechanics

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Section: ~Xerhm (Kmentioning

confidence: 89%

Section: F~=f~u ~U Kuf~mentioning

confidence: 99%

Section: % (X T)iu~'~ (X T) --U$~ (X T) + A~ (X)] = 0; V" X ~ I'mentioning

confidence: 99%

Section: St (V) --Y 5 ' A'jp:i 8q~" + 3/2k~8'2 § T" Wh (E= T) Dementioning

confidence: 99%

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Contact interaction of systems of bodies in conditions of creep of the material

Kuz'menko¹

1986

Soviet Applied Mechanics

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“…Representation of problem in variational formulation is taken from (Kuzmenko 1979). Let us introduce the Sobolev space:…”

Section: Variational Formulation Of the Problemmentioning

confidence: 99%

Coupled Problems of Interaction of Deformable Bodies and Liquid of High Pressure

Shumelchyk

Kuz'menko

2013

mech

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Nowadays the problems of interaction between solids and liquid under high and extremely high pressure are fairly relevant. So the main aim of presented research work is: creating the mathematical models and methods to investigate the interaction of bodies that include cracks filled with a compressible liquid or gas. The coupled problem of interaction of nonlinear elastic bodies and liquid of high pressure was considered. The pressure exerted by a liquid or gas present in the cavities of solids depends on the deformation of the body. In turn the deformation is caused by the pressure inside the cavity. The interaction between a deformable body and liquid is presented as a variational problem. The iterative splitting process of the coupled problem was proposed as well as the algorithm of numerical solution based on variational approach and finite element method. The software which allows calculating the stress state of an elastic body for some classes of problems was developed basing on the algorithm of splitting. The plane problem with cavity and solid stamp which imposes pressure on the boundary was considered and the numerical solution was computed using created software.

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Stability of a strip compressed by slabs

Kuz'menko¹

1994

Int Appl Mech

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On the variational method in the theory of contact problems for nonlinearly elastic laminated bodies

Cited by 7 publications

References 1 publication

Contact interaction of systems of bodies in conditions of creep of the material

Contact interaction of systems of bodies in conditions of creep of the material

Coupled Problems of Interaction of Deformable Bodies and Liquid of High Pressure

Stability of a strip compressed by slabs

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