Bending of clamped orthotropic thin plates

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Bending of clamped orthotropic thin plates : polynomial solution. / Goloskokov, Dmitriy P.; Matrosov, Alexander V.

In: Mathematics and Mechanics of Solids, Vol. 27, No. 11, 11.2022, p. 2498-2509.

Research output: Contribution to journal › Article › peer-review

Author

Goloskokov, Dmitriy P. ; Matrosov, Alexander V. / Bending of clamped orthotropic thin plates : polynomial solution. In: Mathematics and Mechanics of Solids. 2022 ; Vol. 27, No. 11. pp. 2498-2509.

BibTeX

@article{9fb899942a8a4172a96214762a137bf0,

title = "Bending of clamped orthotropic thin plates: polynomial solution",

abstract = "In this paper, we study the bending of a clamped thin orthotropic plate by the Bubnov–Galerkin method. Special-type polynomials constructed on the basis of classical Jacobi polynomials and satisfying the clamped conditions are used as basis functions. The “quasi-orthogonality” property of first and second derivatives of the polynomials allows us to immediately write out the formula for the deflection of the plate in the form of a series, by analogy with the Navier method for a free-supported isotropic plate. This solution approximates well the displacement of the plate, but the series for moments and shear forces do not give reliable results. The refusal of using the “quasi-orthogonality” property of the polynomials leads to the solution of an infinite system of linear algebraic equations for finding unknown coefficients of series. The resulting series give reliable results for both displacements and moments and shear forces. The convergence of the series for displacement is very good, but it worsens for shearing forces and bending moments.",

keywords = "analytical solution, bending of a clamped plate, Bubnov-Galerkin method, Jacobi polynomials, orthogonal polynomials, Orthotropic plate",

author = "Goloskokov, {Dmitriy P.} and Matrosov, {Alexander V.}",

note = "Publisher Copyright: {\textcopyright} The Author(s) 2022.",

year = "2022",

month = nov,

doi = "10.1177/10812865221075280",

language = "English",

volume = "27",

pages = "2498--2509",

journal = "Mathematics and Mechanics of Solids",

issn = "1081-2865",

publisher = "SAGE",

number = "11",

}

RIS

TY - JOUR

T1 - Bending of clamped orthotropic thin plates

T2 - polynomial solution

AU - Goloskokov, Dmitriy P.

AU - Matrosov, Alexander V.

N1 - Publisher Copyright: © The Author(s) 2022.

PY - 2022/11

Y1 - 2022/11

N2 - In this paper, we study the bending of a clamped thin orthotropic plate by the Bubnov–Galerkin method. Special-type polynomials constructed on the basis of classical Jacobi polynomials and satisfying the clamped conditions are used as basis functions. The “quasi-orthogonality” property of first and second derivatives of the polynomials allows us to immediately write out the formula for the deflection of the plate in the form of a series, by analogy with the Navier method for a free-supported isotropic plate. This solution approximates well the displacement of the plate, but the series for moments and shear forces do not give reliable results. The refusal of using the “quasi-orthogonality” property of the polynomials leads to the solution of an infinite system of linear algebraic equations for finding unknown coefficients of series. The resulting series give reliable results for both displacements and moments and shear forces. The convergence of the series for displacement is very good, but it worsens for shearing forces and bending moments.

AB - In this paper, we study the bending of a clamped thin orthotropic plate by the Bubnov–Galerkin method. Special-type polynomials constructed on the basis of classical Jacobi polynomials and satisfying the clamped conditions are used as basis functions. The “quasi-orthogonality” property of first and second derivatives of the polynomials allows us to immediately write out the formula for the deflection of the plate in the form of a series, by analogy with the Navier method for a free-supported isotropic plate. This solution approximates well the displacement of the plate, but the series for moments and shear forces do not give reliable results. The refusal of using the “quasi-orthogonality” property of the polynomials leads to the solution of an infinite system of linear algebraic equations for finding unknown coefficients of series. The resulting series give reliable results for both displacements and moments and shear forces. The convergence of the series for displacement is very good, but it worsens for shearing forces and bending moments.

KW - analytical solution

KW - bending of a clamped plate

KW - Bubnov-Galerkin method

KW - Jacobi polynomials

KW - orthogonal polynomials

KW - Orthotropic plate

UR - http://www.scopus.com/inward/record.url?scp=85124266203&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/39d4c03a-9a18-3598-a9df-d209e6124bc5/

U2 - 10.1177/10812865221075280

DO - 10.1177/10812865221075280

M3 - Article

AN - SCOPUS:85124266203

VL - 27

SP - 2498

EP - 2509

JO - Mathematics and Mechanics of Solids

JF - Mathematics and Mechanics of Solids

SN - 1081-2865

IS - 11

ER -

ID: 93274853