An exact analytical solution for a free-supported micropolar rectangle by the method of initial functions

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An exact analytical solution for a free-supported micropolar rectangle by the method of initial functions. / Matrosov, Alexander V.

в: Zeitschrift fur Angewandte Mathematik und Physik, Том 73, № 2, 74, 14.03.2022.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{3de576fe771e4512b257c4c40cfeaf7d,

title = "An exact analytical solution for a free-supported micropolar rectangle by the method of initial functions",

abstract = "In this work, the method of initial functions for a micropolar medium under conditions of plane strain has been developed. In a Cartesian rectangular coordinate system, the solution of the differential equilibrium equations in displacements of the micropolar isotropic theory of elasticity in the form of a linear combination of the stress-strain state (SSS) components defined on the line x = 0 (initial functions) with coefficients in operator form is constructed. The choice of initial functions in the form of trigonometric series makes it possible to solve the boundary problem of deformation of a micropolar rectangle (h x l) with arbitrary boundary conditions on the sides x = 0, h and the type of free support on the sides y = 0, l. The obtained solution was used to study the SSS of a rectangle made of human bone considered as an isotropic micropolar material. The results of the SSS study, depending on the size of the rectangle, are presented. The limiting dimensions at which the SSS values of the components differ by 5% from the values of the corresponding components calculated according to the classical theory of elasticity are determined.",

keywords = "Free supported, Method of initial functions, Micropolar rectangle, Size effect, ELASTICITY, COMPACT-BONE, TORSION, PLATE",

author = "Matrosov, {Alexander V.}",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.",

year = "2022",

month = mar,

day = "14",

doi = "10.1007/s00033-022-01714-y",

language = "English",

volume = "73",

journal = "Zeitschrift fur Angewandte Mathematik und Physik",

issn = "0044-2275",

publisher = "Birkh{\"a}user Verlag AG",

number = "2",

}

RIS

TY - JOUR

T1 - An exact analytical solution for a free-supported micropolar rectangle by the method of initial functions

AU - Matrosov, Alexander V.

PY - 2022/3/14

Y1 - 2022/3/14

N2 - In this work, the method of initial functions for a micropolar medium under conditions of plane strain has been developed. In a Cartesian rectangular coordinate system, the solution of the differential equilibrium equations in displacements of the micropolar isotropic theory of elasticity in the form of a linear combination of the stress-strain state (SSS) components defined on the line x = 0 (initial functions) with coefficients in operator form is constructed. The choice of initial functions in the form of trigonometric series makes it possible to solve the boundary problem of deformation of a micropolar rectangle (h x l) with arbitrary boundary conditions on the sides x = 0, h and the type of free support on the sides y = 0, l. The obtained solution was used to study the SSS of a rectangle made of human bone considered as an isotropic micropolar material. The results of the SSS study, depending on the size of the rectangle, are presented. The limiting dimensions at which the SSS values of the components differ by 5% from the values of the corresponding components calculated according to the classical theory of elasticity are determined.

AB - In this work, the method of initial functions for a micropolar medium under conditions of plane strain has been developed. In a Cartesian rectangular coordinate system, the solution of the differential equilibrium equations in displacements of the micropolar isotropic theory of elasticity in the form of a linear combination of the stress-strain state (SSS) components defined on the line x = 0 (initial functions) with coefficients in operator form is constructed. The choice of initial functions in the form of trigonometric series makes it possible to solve the boundary problem of deformation of a micropolar rectangle (h x l) with arbitrary boundary conditions on the sides x = 0, h and the type of free support on the sides y = 0, l. The obtained solution was used to study the SSS of a rectangle made of human bone considered as an isotropic micropolar material. The results of the SSS study, depending on the size of the rectangle, are presented. The limiting dimensions at which the SSS values of the components differ by 5% from the values of the corresponding components calculated according to the classical theory of elasticity are determined.

KW - Free supported

KW - Method of initial functions

KW - Micropolar rectangle

KW - Size effect

KW - ELASTICITY

KW - COMPACT-BONE

KW - TORSION

KW - PLATE

UR - http://www.scopus.com/inward/record.url?scp=85126254349&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/2d014bf2-349a-307b-921c-804e3273ef94/

U2 - 10.1007/s00033-022-01714-y

DO - 10.1007/s00033-022-01714-y

M3 - Article

AN - SCOPUS:85126254349

VL - 73

JO - Zeitschrift fur Angewandte Mathematik und Physik

JF - Zeitschrift fur Angewandte Mathematik und Physik

SN - 0044-2275

IS - 2

M1 - 74

ER -

ID: 93637462