Изгиб ребристой пластины при сложном нагружении

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Изгиб ребристой пластины при сложном нагружении. / Goloskokov, Dmitry P.; Matrosov, Alexander.

в: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya, Том 17, № 2, 2021, стр. 120-130.

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

Author

Goloskokov, Dmitry P. ; Matrosov, Alexander. / Изгиб ребристой пластины при сложном нагружении. в: Vestnik Sankt-Peterburgskogo Universiteta, Prikladnaya Matematika, Informatika, Protsessy Upravleniya. 2021 ; Том 17, № 2. стр. 120-130.

BibTeX

@article{1f0b7f49a3724c07a7bf41acb4b75289,

title = "Изгиб ребристой пластины при сложном нагружении",

abstract = "The article considers the problem of a rectangular plate, supported by a cross system of stiffening ribs, bending. In addition to the transverse load, the plate is subjected to forces in its plane, transmitted through the ribs. An analytical solution to the boundary value problem for the resolving differential equation with respect to the normal deflection of the plate, describing the deformation of a rectangular plate supported by stiffeners, is obtained. The solution is presented in the form of series in combinations of regular and special discontinuous functions, which converge quickly and lead to a simple computational algorithm. The influence of the ribs is taken into account in the equation in the form of additional terms containing factors with a delta function. This approach allows us to get rid of a number of assumptions regarding the interaction of the plate with its reinforcing elements. The use of the apparatus of generalized functions when modeling objects of this type simplifies the boundary conditions (there are no conditions for conjugation of various structural elements), but at the same time the differential equations become more complicated. The problem is reduced to the so-called partially degenerate equations. Development of analytical methods that allow obtaining exact solutions of differential equations of this type, and their introduction into computational practice, is one of the urgent tasks of the mechanics of objects with disturbed regularity.",

keywords = "Dirac function, Fourier series, Heaviside function, Mathematical model, Numerical-analytical methods, Orthogonal series, Plate, Special discontinuous functions, Stiffeners, special discontinuous functions, orthogonal series, plate, numerical-analytical methods, mathematical model, stiffeners",

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

year = "2021",

doi = "10.21638/11701/SPBU10.2021.202",

language = "русский",

volume = "17",

pages = "120--130",

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

issn = "1811-9905",

publisher = "Издательство Санкт-Петербургского университета",

number = "2",

}

RIS

TY - JOUR

T1 - Изгиб ребристой пластины при сложном нагружении

AU - Goloskokov, Dmitry P.

AU - Matrosov, Alexander

PY - 2021

Y1 - 2021

N2 - The article considers the problem of a rectangular plate, supported by a cross system of stiffening ribs, bending. In addition to the transverse load, the plate is subjected to forces in its plane, transmitted through the ribs. An analytical solution to the boundary value problem for the resolving differential equation with respect to the normal deflection of the plate, describing the deformation of a rectangular plate supported by stiffeners, is obtained. The solution is presented in the form of series in combinations of regular and special discontinuous functions, which converge quickly and lead to a simple computational algorithm. The influence of the ribs is taken into account in the equation in the form of additional terms containing factors with a delta function. This approach allows us to get rid of a number of assumptions regarding the interaction of the plate with its reinforcing elements. The use of the apparatus of generalized functions when modeling objects of this type simplifies the boundary conditions (there are no conditions for conjugation of various structural elements), but at the same time the differential equations become more complicated. The problem is reduced to the so-called partially degenerate equations. Development of analytical methods that allow obtaining exact solutions of differential equations of this type, and their introduction into computational practice, is one of the urgent tasks of the mechanics of objects with disturbed regularity.

AB - The article considers the problem of a rectangular plate, supported by a cross system of stiffening ribs, bending. In addition to the transverse load, the plate is subjected to forces in its plane, transmitted through the ribs. An analytical solution to the boundary value problem for the resolving differential equation with respect to the normal deflection of the plate, describing the deformation of a rectangular plate supported by stiffeners, is obtained. The solution is presented in the form of series in combinations of regular and special discontinuous functions, which converge quickly and lead to a simple computational algorithm. The influence of the ribs is taken into account in the equation in the form of additional terms containing factors with a delta function. This approach allows us to get rid of a number of assumptions regarding the interaction of the plate with its reinforcing elements. The use of the apparatus of generalized functions when modeling objects of this type simplifies the boundary conditions (there are no conditions for conjugation of various structural elements), but at the same time the differential equations become more complicated. The problem is reduced to the so-called partially degenerate equations. Development of analytical methods that allow obtaining exact solutions of differential equations of this type, and their introduction into computational practice, is one of the urgent tasks of the mechanics of objects with disturbed regularity.

KW - Dirac function

KW - Fourier series

KW - Heaviside function

KW - Mathematical model

KW - Numerical-analytical methods

KW - Orthogonal series

KW - Plate

KW - Special discontinuous functions

KW - Stiffeners

KW - special discontinuous functions

KW - orthogonal series

KW - plate

KW - numerical-analytical methods

KW - mathematical model

KW - stiffeners

UR - http://www.scopus.com/inward/record.url?scp=85111962806&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/ddb4bcfb-e36a-35da-b5cd-4bf4f74bbd71/

U2 - 10.21638/11701/SPBU10.2021.202

DO - 10.21638/11701/SPBU10.2021.202

M3 - статья

AN - SCOPUS:85111962806

VL - 17

SP - 120

EP - 130

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

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

SN - 1811-9905

IS - 2

ER -

ID: 84671585