Solving the Problem of Bending of Multiply Connected Plates with Elastic Inclusions
S. A. Kaloerov, A. A. Koshkin
Donetsk National University, Donetsk, 83001, Ukraine
Keywords: анизотропная плита, изгиб плит, упругие включения, коэффициенты интенсивности моментов, комплексные потенциалы, обобщенный метод наименьших квадратов, anisotropic plate, bending of plates, elastic inclusions, moment intensity coefficients, complex potentials, generalized least squares method
Abstract
This paper describes a method for determining the strain state of a thin anisotropic plate with elastic arbitrarily arranged elliptical inclusions. Complex potentials are used to reduce the problem to determining functions of generalized complex variables, which, in turn, comes down to a undetermined system of linear algebraic equations, solved by singular expansions. This paper presents the results of numerical calculations that helped establish the influence of rigidity of elastic inclusions, distances between inclusions, and their geometric characteristics on the bending moments occurring in the plate. It is certain that the specific properties of distribution of moments near the apexes of linear elastic inclusions, characterized by moment intensity coefficients, occur only in the case of sufficiently rigid and elastic inclusions.
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