МЕТОД НАЧАЛЬНЫХ ФУНКЦИЙ В РАСЧЕТЕ ИЗГИБА ЗАЩЕМЛЕННОЙ ПО КОНТУРУ ТОНКОЙ ОРТОТРОПНОЙ ПЛАСТИНКИ

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МЕТОД НАЧАЛЬНЫХ ФУНКЦИЙ В РАСЧЕТЕ ИЗГИБА ЗАЩЕМЛЕННОЙ ПО КОНТУРУ ТОНКОЙ ОРТОТРОПНОЙ ПЛАСТИНКИ. / Goloskokov, Dmitry P.; Matrosov, Alexander V.

In: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, Vol. 17, No. 4, 2021, p. 330-344.

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

BibTeX

@article{c8d712c932e248dda96bddfb4fa7f743,

title = "МЕТОД НАЧАЛЬНЫХ ФУНКЦИЙ В РАСЧЕТЕ ИЗГИБА ЗАЩЕМЛЕННОЙ ПО КОНТУРУ ТОНКОЙ ОРТОТРОПНОЙ ПЛАСТИНКИ",

abstract = "In this paper, the method of initial functions (MIF) is used to solve the problem of bending an orthotropic plate clamped along all four sides, under the influence of a normal load uniformly distributed over its surface. The solution is obtained in the form of an exponential series with unknown coefficients. The algorithm of the method is such that on two opposite sides the boundary conditions (equality to zero of displacements and angles of rotation) are satisfied exactly, while on a pair of two other opposite sides the boundary conditions are satisfied with an arbitrary degree of accuracy by the collocation method. All studies were carried out using the Maple analytical computing system. This system allows you to perform calculations with an arbitrary mantissa in the representation of real numbers. Calculations with a long mantissa overcome one of the main disadvantages of the MIF: the computational instability of its algorithm, which arises under certain parameters of the problem. The computational stability of the obtained solution is investigated, as well as the stress-strain state in the neighbourhood of the corner points of the plate. It is shown that the moments and shear forces tend to zero when approaching the corners of the plate with a single change in sign.",

keywords = "Bending of a thin plate, Clamped plate, Computer algebra, Maple, Method of initial functions, Orthotropic plate",

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

year = "2021",

doi = "10.21638/11701/SPBU10.2021.402",

language = "русский",

volume = "17",

pages = "330--344",

journal = " ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ",

issn = "1811-9905",

publisher = "Издательство Санкт-Петербургского университета",

number = "4",

}

RIS

TY - JOUR

T1 - МЕТОД НАЧАЛЬНЫХ ФУНКЦИЙ В РАСЧЕТЕ ИЗГИБА ЗАЩЕМЛЕННОЙ ПО КОНТУРУ ТОНКОЙ ОРТОТРОПНОЙ ПЛАСТИНКИ

AU - Goloskokov, Dmitry P.

AU - Matrosov, Alexander V.

PY - 2021

Y1 - 2021

N2 - In this paper, the method of initial functions (MIF) is used to solve the problem of bending an orthotropic plate clamped along all four sides, under the influence of a normal load uniformly distributed over its surface. The solution is obtained in the form of an exponential series with unknown coefficients. The algorithm of the method is such that on two opposite sides the boundary conditions (equality to zero of displacements and angles of rotation) are satisfied exactly, while on a pair of two other opposite sides the boundary conditions are satisfied with an arbitrary degree of accuracy by the collocation method. All studies were carried out using the Maple analytical computing system. This system allows you to perform calculations with an arbitrary mantissa in the representation of real numbers. Calculations with a long mantissa overcome one of the main disadvantages of the MIF: the computational instability of its algorithm, which arises under certain parameters of the problem. The computational stability of the obtained solution is investigated, as well as the stress-strain state in the neighbourhood of the corner points of the plate. It is shown that the moments and shear forces tend to zero when approaching the corners of the plate with a single change in sign.

AB - In this paper, the method of initial functions (MIF) is used to solve the problem of bending an orthotropic plate clamped along all four sides, under the influence of a normal load uniformly distributed over its surface. The solution is obtained in the form of an exponential series with unknown coefficients. The algorithm of the method is such that on two opposite sides the boundary conditions (equality to zero of displacements and angles of rotation) are satisfied exactly, while on a pair of two other opposite sides the boundary conditions are satisfied with an arbitrary degree of accuracy by the collocation method. All studies were carried out using the Maple analytical computing system. This system allows you to perform calculations with an arbitrary mantissa in the representation of real numbers. Calculations with a long mantissa overcome one of the main disadvantages of the MIF: the computational instability of its algorithm, which arises under certain parameters of the problem. The computational stability of the obtained solution is investigated, as well as the stress-strain state in the neighbourhood of the corner points of the plate. It is shown that the moments and shear forces tend to zero when approaching the corners of the plate with a single change in sign.

KW - Bending of a thin plate

KW - Clamped plate

KW - Computer algebra

KW - Maple

KW - Method of initial functions

KW - Orthotropic plate

UR - http://www.scopus.com/inward/record.url?scp=85124258190&partnerID=8YFLogxK

U2 - 10.21638/11701/SPBU10.2021.402

DO - 10.21638/11701/SPBU10.2021.402

M3 - статья

AN - SCOPUS:85124258190

VL - 17

SP - 330

EP - 344

JO - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

JF - ВЕСТНИК САНКТ-ПЕТЕРБУРГСКОГО УНИВЕРСИТЕТА. ПРИКЛАДНАЯ МАТЕМАТИКА. ИНФОРМАТИКА. ПРОЦЕССЫ УПРАВЛЕНИЯ

SN - 1811-9905

IS - 4

ER -

ID: 93274778