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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Vydané v:Journal of applied mechanics and technical physics Ročník 58; číslo 6; s. 1123 - 1129
Hlavní autori: Kaloerov, S. A., Koshkin, A. A.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Moscow Pleiades Publishing 01.11.2017
Springer Nature B.V
Predmet:
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
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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 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.
AbstractList 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.
Author Kaloerov, S. A.
Koshkin, A. A.
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Cites_doi 10.1016/S0020-7683(02)00335-9
10.1115/1.2900850
10.1007/978-1-4419-5915-7
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Keywords anisotropic plate
generalized least squares method
bending of plates
complex potentials
moment intensity factor
elastic inclusions
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Kaloerov, Dobryak (CR7) 2006; 2
Lekhnitskii (CR1) 1938; 2
Kaloerov (CR15) 2007; 43
Stashchuk (CR13) 1993
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Kosmodamianskii (CR4) 1976
Lekhnitskii (CR2) 1968
Kaloerov, Avdyushina, Mironenko (CR10) 2013
Grilitskii, Opanasovich, Tisovskii (CR12) 1982; 46
S. A. Kaloerov (1082_CR6) 1998
S. A. Kaloerov (1082_CR10) 2013
S. G. Lekhnitskii (1082_CR1) 1938; 2
S. A. Hwu (1082_CR8) 1993; 60
S. A. Kaloerov (1082_CR15) 2007; 43
D. V. Grilitskii (1082_CR12) 1982; 46
S. A. Kaloerov (1082_CR5) 2012; 4
V. B. Meglinskii (1082_CR3) 1967; 3
G. E. Forsythe (1082_CR14) 1977
C. Hwu (1082_CR9) 2010
S. G. Lekhnitskii (1082_CR2) 1968
S. A. Kaloerov (1082_CR7) 2006; 2
N. G. Stashchuk (1082_CR13) 1993
A. S. Kosmodamianskii (1082_CR4) 1976
M. C. Hsieh (1082_CR11) 2002; 39
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SubjectTerms 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
Title Solving the Problem of Bending of Multiply Connected Plates with Elastic Inclusions
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