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- W2116763092 abstract "Methods of solution for the nonlinear stress tensor field equations of matter in the creeping motion state are analysed. For homogeneous matter in two space dimensions the problem proves to be equivalent to the construction of symmetrical tensor fields of constant eigenvalue ratio (1 − β)/(1 + β) and constant divergence g, where β and g are the internal friction parameter and the specific weight. A nonlinear second order differential equation remains if a modified Airy stress potential is introduced. This equation is solved generally for β21, g ≠ 0 and also for β2 = 1, g arbitrary. Physically, the corresponding stress fields describe weightless plastic matter and slowly moving anisotropic fluids respectively. For g ≠ 0 classes of new solutions are derived in the β2 = 1 case.Es werden Methoden zur Losung der nichtlinearen Feldgleichungen des Spannungstensors fur Materie im Zustand der Kriechbewegung untersucht. Fur homogene Materie in zwei Raumdimensionen ist das Losungsproblem gleichwertig zur Konstruktion von symmetrischen Tensorfeldern mit konstantem Eigenwertverhaltnis (1 - β)/(1 + β) und konstanter Divergenz g. Dabei sind β und g der Parameter der inneren Reibung und das spezifische Gewicht. Bei Einfuhrung eines modifizierten Airy-Spannungspotentials verbleibt eine nichtlineare Differentialgleichung zweiter Ordnung. Diese Gleichung wird fur die Falle β2 < 1, g = 0 und β2 = 1, g = 0 allgemein gelost. Physikalisch beschreiben diese Spannungsfelder schwereloses plastisches Material und langsam bewegte anisotrope Flussigkeiten. Fur g = 0 werden im Falle β2 = 1 neue Losungen hergeleitet." @default.
- W2116763092 created "2016-06-24" @default.
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- W2116763092 date "1990-01-01" @default.
- W2116763092 modified "2023-09-25" @default.
- W2116763092 title "Symmetrical Tensor Fields of Constant Eigenvalue Ratio and Solutions of the Stress Equations for Creeping Motion" @default.
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- W2116763092 doi "https://doi.org/10.1002/zamm.19900700102" @default.
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