Solving the Problem of Bending of Multiply Connected Plates with Elastic Inclusions

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 an overdeterm...

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Bibliographic Details
Published in:Journal of applied mechanics and technical physics Vol. 58; no. 6; pp. 1123 - 1129
Main Authors: Kaloerov, S. A., Koshkin, A. A.
Format: Journal Article
Language:English
Published: Moscow Pleiades Publishing 01.11.2017
Springer Nature B.V
Subjects:
Anisotropic plates
Apexes
Applications of Mathematics
Bending moments
Classical and Continuum Physics
Classical Mechanics
Complex variables
Elastic anisotropy
Elastic properties
Fluid- and Aerodynamics
Inclusions
Linear algebra
Mathematical Modeling and Industrial Mathematics
Mechanical Engineering
Physics
Physics and Astronomy
Strain
anisotropic plate
generalized least squares method
bending of plates
complex potentials
moment intensity factor
elastic inclusions
ISSN:0021-8944, 1573-8620
Online Access:Get full text
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Summary: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 an overdetermined 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 found 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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ISSN:0021-8944
1573-8620
DOI:10.1134/S0021894417060190