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The BIE Analysis Of The Berger Equation

J. Sládek, V. Sládek
Published 1983 · Mathematics

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SummaryAn iterative solution of the nonlinear integro-differential Berger equation by the boundary integral equation method is proposed. The fundamental solution of the linearized Berger equation is used. Both formulations of the problem through the physical and non-physical quantities are given. The proposed method of solution is applied to numerical computation of the finite deflection of a thin circular plate under a concentrated load. An analytical solution of the linearized Berger equation in the case of rotationally symmetrical problem is found.ÜbersichtBine iterative Lösung der nichtlinearen integrodifferentialen Gleichungen von Berger mittels der Methode der Integralgleichungen wird vorgelegt. Die fundamentale Lösung der linearisierten Gleichungen von Berger wird angewendet. Zwei alternative Formulierungen des Problems mit physikalischen und nichtphysikalischen Größen sind angeführt. Die vorgelegte Lösungsmethode wird zur numerischen Berechnung der Durchbiegung einer mittels Einzellast belasteten, dünnen Kreisplatte angewendet. Fur den Fall eines rotationssymmetrischen Problems wurde eine analytische Lösung der linearisierten Bergerschen Gleichungen gefunden.

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