Geometrically nonlinear analysis of the stability of the stiffened plate taking into account the interaction of eigenforms of buckling
The aims of this work are a detailed consideration in a geometrically nonlinear formulation of the stages of the equilibrium behavior of a compressed stiffened plate, taking into account the interaction of the general form of buckling and local forms of wave formation in the plate or in the reinforc...
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Peoples’ Friendship University of Russia (RUDN University)
2021-12-01
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Online Access: | http://journals.rudn.ru/structural-mechanics/article/viewFile/26182/19279 |
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doaj-2a2602f12f104b5fa344742e26393db42021-04-05T11:55:45ZengPeoples’ Friendship University of Russia (RUDN University)Structural Mechanics of Engineering Constructions and Buildings1815-52352587-87002021-12-0117131810.22363/1815-5235-2021-17-1-3-1819965Geometrically nonlinear analysis of the stability of the stiffened plate taking into account the interaction of eigenforms of bucklingGaik A. Manuylov0Sergey B. Kositsyn1Irina E. Grudtsyna2Russian University of TransportRussian University of TransportRussian University of TransportThe aims of this work are a detailed consideration in a geometrically nonlinear formulation of the stages of the equilibrium behavior of a compressed stiffened plate, taking into account the interaction of the general form of buckling and local forms of wave formation in the plate or in the reinforcing ribs, comparison of the results of the semi-analytical solution of the system of nonlinear equations with the results of the numerical solution on the Patran-Nastran FEM complex of the problem of subcritical and postcritical equilibrium of a compressed stiffened plate. Methods. Geometrically-nonlinear analysis of displacement fields, deformations and stresses, calculation of eigenforms of buckling and construction of bifurcation solutions and solutions for equilibrium curves with limit points depending on the initial imperfections. An original method is proposed for determining critical states and obtaining bilateral estimates of critical loads at limiting points. Results. An algorithm for studying the equilibrium states of a stiffened plate near critical points is described in detail and illustrated by examples, using the first nonlinear (cubic terms) terms of the potential energy expansion, the coordinates of bifurcation points and limit points, as well as the corresponding values of critical loads. The curves of the critical load sensitivity are plotted depending on the value of the initial imperfections of the total deflection. Equilibrium curves with characteristic bifurcation points of local wave formation are constructed using a numerical solution. For the case of action of two initial imperfections, an algorithm is proposed for obtaining two-sided estimates of critical loads at limiting points.http://journals.rudn.ru/structural-mechanics/article/viewFile/26182/19279geometrically nonlinear equilibrium equationsbifurcation pointslimit pointsinteraction of formsreinforced platecritical stresses |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Gaik A. Manuylov Sergey B. Kositsyn Irina E. Grudtsyna |
spellingShingle |
Gaik A. Manuylov Sergey B. Kositsyn Irina E. Grudtsyna Geometrically nonlinear analysis of the stability of the stiffened plate taking into account the interaction of eigenforms of buckling Structural Mechanics of Engineering Constructions and Buildings geometrically nonlinear equilibrium equations bifurcation points limit points interaction of forms reinforced plate critical stresses |
author_facet |
Gaik A. Manuylov Sergey B. Kositsyn Irina E. Grudtsyna |
author_sort |
Gaik A. Manuylov |
title |
Geometrically nonlinear analysis of the stability of the stiffened plate taking into account the interaction of eigenforms of buckling |
title_short |
Geometrically nonlinear analysis of the stability of the stiffened plate taking into account the interaction of eigenforms of buckling |
title_full |
Geometrically nonlinear analysis of the stability of the stiffened plate taking into account the interaction of eigenforms of buckling |
title_fullStr |
Geometrically nonlinear analysis of the stability of the stiffened plate taking into account the interaction of eigenforms of buckling |
title_full_unstemmed |
Geometrically nonlinear analysis of the stability of the stiffened plate taking into account the interaction of eigenforms of buckling |
title_sort |
geometrically nonlinear analysis of the stability of the stiffened plate taking into account the interaction of eigenforms of buckling |
publisher |
Peoples’ Friendship University of Russia (RUDN University) |
series |
Structural Mechanics of Engineering Constructions and Buildings |
issn |
1815-5235 2587-8700 |
publishDate |
2021-12-01 |
description |
The aims of this work are a detailed consideration in a geometrically nonlinear formulation of the stages of the equilibrium behavior of a compressed stiffened plate, taking into account the interaction of the general form of buckling and local forms of wave formation in the plate or in the reinforcing ribs, comparison of the results of the semi-analytical solution of the system of nonlinear equations with the results of the numerical solution on the Patran-Nastran FEM complex of the problem of subcritical and postcritical equilibrium of a compressed stiffened plate. Methods. Geometrically-nonlinear analysis of displacement fields, deformations and stresses, calculation of eigenforms of buckling and construction of bifurcation solutions and solutions for equilibrium curves with limit points depending on the initial imperfections. An original method is proposed for determining critical states and obtaining bilateral estimates of critical loads at limiting points. Results. An algorithm for studying the equilibrium states of a stiffened plate near critical points is described in detail and illustrated by examples, using the first nonlinear (cubic terms) terms of the potential energy expansion, the coordinates of bifurcation points and limit points, as well as the corresponding values of critical loads. The curves of the critical load sensitivity are plotted depending on the value of the initial imperfections of the total deflection. Equilibrium curves with characteristic bifurcation points of local wave formation are constructed using a numerical solution. For the case of action of two initial imperfections, an algorithm is proposed for obtaining two-sided estimates of critical loads at limiting points. |
topic |
geometrically nonlinear equilibrium equations bifurcation points limit points interaction of forms reinforced plate critical stresses |
url |
http://journals.rudn.ru/structural-mechanics/article/viewFile/26182/19279 |
work_keys_str_mv |
AT gaikamanuylov geometricallynonlinearanalysisofthestabilityofthestiffenedplatetakingintoaccounttheinteractionofeigenformsofbuckling AT sergeybkositsyn geometricallynonlinearanalysisofthestabilityofthestiffenedplatetakingintoaccounttheinteractionofeigenformsofbuckling AT irinaegrudtsyna geometricallynonlinearanalysisofthestabilityofthestiffenedplatetakingintoaccounttheinteractionofeigenformsofbuckling |
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