Die Greensche Matrix für zwei aneinander reibungsfrei gleitende elastische Halbräume mit verschiedenen Laméschen Moduln

Jentsch, Lothar

doi:10.1002/zamm.19780580405

Cited by 5 publications

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References 4 publications

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“…7) and (2.8) and taking into account the homogeneous contact conditions on S we get b , E ' ( U ' , u') dx + IQ,T'(u2, u') dx = 0.Therefore, according to the relations (2.9) and (2.10) it holds thatDkuY + DjuT = 0, k, j = 1,2, 3, m = 1, 2. These equalities yield [17] um(x) = [am x x] + b", x E Om, m = 1,2, (2.1 1)where am and 6"' are three-dimensional constant vectors.From the regularity of the vector u2 at infinity it follows a2 = b2 = 0 that is Now equations (2.5) for u' imply that (u')+ = 0 on S and the uniqueness theorem for the interior Dirichlet (displacement) problem gives u ' ( x ) = 0, x E fil Theorem 2.2.…”

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confidence: 90%

Non‐classical interface problems for piecewise homogeneous anisotropic elastic bodies

Jentsch¹,

Natroshvili²

1995

Math Methods in App Sciences

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Communicated by E. MeisterTwo non-classical model interface problems for piecewise homogeneous anisotropic bodies are studied. In both problems on the contact surface jumps of the normal components of displacement and stress vectors are given. In addition, in the first problem (Problem H) the tangent components of the displacement vectors are given from both sides of the contact surface, while in the second one (Problem G ) the tangent components of the stress vectors are prescribed on the same surface. The existence and uniqueness theorems are proved by means of the boundary integral equation method, and representations of solutions by single layer potentials are established. In the investigation the general approach of regularization of the first kind of integral equations is worked out for the case of two-dimensional closed smooth manifolds. An equivalent global regularizer operator is constructed explicitly in the form of a singular integro-differential operator.

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confidence: 90%

Non‐classical interface problems for piecewise homogeneous anisotropic elastic bodies

Jentsch¹,

Natroshvili²

1995

Math Methods in App Sciences

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Green's contact functions for heat conduction of two half‐spaces and half‐planes with application to several boundary contact problems

Jentsch

1991

Math Methods in App Sciences

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Communicated by E. MeisterGreen's contact functions are constructed for two half-spaces and two half-planes for materials with different thermal conductivities. With the aid of these contact functions some bimetal problems are reduced to boundary integral equations along the outer boundary where only the boundary conditions are to be satisfied. The boundary integral operators are investigated in the plane case. They are Fredholm operators with index zero. The asymptotia of the density of the potentials, which depends on the material parameters and on the angles between the contact line and the outer boundary, is determined by the Mellin transform technique.

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Über ein ebenes Bimetallproblem mit einer speziellen Rißbildung

Jentsch

1986

Z Angew Math Mech

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Bewiesen werden Existenz‐ und Eindeutigkeitssätze für ebene Randkontaktaufgaben der Thermoelastostatik in einer geeigneten Klasse regulärer Vektoren. Die Materialkonstanten sind in den Teilgebieten D+ und D− von D, die längs des Geradenstücks S0 aneinandergrenzen, konstant aber verschieden. Als Randbedingung auf S = δD ist die Normalspannung und als Kontaktbedingung auf S0 sind auf beiden Ufern von S0 die tangentiellen Komponenten des Verschiebungsvektors sowie die Differenz der Normalkomponenten des Verschiebungsvektors und des Normalspannungsvektors an beiden Ufern vorgegeben. Das Problem wird mit Hilfe von partikulären Lösungen und einem Potentialansatz vom Typ der einfachen Schicht, dessen Kern der Kontakttensor der Elastostatik für zwei gekoppelte Halbebenen ist, auf ein singuläres Integralgleichungssystem mit feststehenden Singularitäten zurückgeführt. Dieses ist im Raum L2(S) noethersch und hat den Index Null.

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Die Greensche Matrix für zwei aneinander reibungsfrei gleitende elastische Halbräume mit verschiedenen Laméschen Moduln

Cited by 5 publications

References 4 publications

Non‐classical interface problems for piecewise homogeneous anisotropic elastic bodies

Non‐classical interface problems for piecewise homogeneous anisotropic elastic bodies

Green's contact functions for heat conduction of two half‐spaces and half‐planes with application to several boundary contact problems

Über ein ebenes Bimetallproblem mit einer speziellen Rißbildung

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