Investigations in the theory of thin shells with openings (review)

Guz, A. N.; Chernyshenko, I. S.; Chekhov, Val N.; Chekhov, V. N.; Shnerenko, K. I.

doi:10.1007/bf00895026

Cited by 8 publications

(9 citation statements)

References 118 publications

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“…A fairly large number of works are devoted to the methods of calculating shell structures made of composite materials and the study of stress concentration near holes. However, most of the studies were carried out within the framework of the classical Kirchhoff-Love hypothesis, which does not take into account interlayer and transverse shears characteristic of composite materials [1,2].…”

Section: Introductionmentioning

confidence: 99%

Stress-strain state of spherical shells with two unequal holes

et al. 2021

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This article presents the results of a numerical study of the stress concentration around two equal and unequal holes in an orthotropic spherical shell made of composite materials under the action of internal pressure. The influence of geometric (hole radii, shell thickness, distance between holes) characteristics, as well as material orthotropy and shear stiffness, on the stress state of spherical shells made of composite materials is studied. A numerical algorithm based on the finite element method has been developed and a software package has been implemented on a computer that allows solving the problem of stress concentration near two unequal holes in spherical shells made of composite materials.

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Section: Introductionmentioning

confidence: 99%

Stress-strain state of spherical shells with two unequal holes

et al. 2021

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“…Background and bibliography can be found in Ref. [1][2][3][9][10][11][12][13][14][15]. Although the basic equations and relations of the theory of shells were obtained long ago, until now analytical solutions to problems have been obtained only for some relatively simple classes of shells with predominantly canonical form.…”

Section: Introductionmentioning

confidence: 99%

Buckling and vibrations of the shell with the hole under the action of thermomechanical loads

Баженов

Krivenko

2020

OMTC

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The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling, and vibrations of thin thermoelastic inhomogeneous shells with complex-shaped midsurface, geometrical features throughout the thickness, under complex thermomechanical loading. The technique is based on the geometrically nonlinear equations of three-dimensional thermoelasticity, the finite element formulation of the problem in increments, and the use of the moment finite-element scheme. A thin shell is considered by this method as a threedimensional body. We approximate a shell by one spatial universal finite element (FE) throughout the thickness. The universal FE is based on an isoparametric spatial FE with polylinear shape functions for coordinates and displacements. The universal element has additional variable parameters introduced to expand its capabilities. The method of modal analysis of the shell is based on an approach that at each current stage of thermomechanical loading takes into account the stresses accumulated at the previous stages. The developed algorithm allows one to study geometric nonlinear deformation and buckling of elastic shells of an inhomogeneous structure with a thin and medium thickness, as well as to study small vibrations of the shells relative to the reference deformed state caused by static loading, taking into account large displacements and a prestressed state. An analysis of the stability and vibration of the spherical panel with the hole is carried out. The effect on the frequencies and mode shapes of the shell of the sequential action of thermal and mechanical loads is investigated.

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“…Methods and results of solving specific classes of physically and geometrically nonlinear problems for some metal shells are discussed in the monographs [20,32,38,42,67,70]. The issue of stress concentration in shells (plates) involving the development of methods of solving nonlinear problems is analyzed in the reviews [24,89,93,94].Note that most studies on nonlinear stress concentration in shells, including problem formulation, development of methods for solving certain classes of nonlinear problems, and analysis of calculated results were carried out by the authors of the present paper and their followers at the S. P. Timoshenko Institute of Mechanics. In solving specific classes of nonlinear…”

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confidence: 99%

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Nonlinear two-dimensional static problems for thin shells with reinforced curvilinear holes

2009

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Results on stress concentration in thin shells with curvilinear holes subject to plastic deformation and finite deflections are reviewed. The holes (circular, elliptical) are reinforced with thin-walled elements (rings, rods) of different stiffness. A numerical method of solving doubly nonlinear problems of statics for shells of complex geometry is outlined. The stress distribution near curvilinear holes in spherical, cylindrical, and conical shells under statical loading is studied. The numerical results are analyzed Introduction. Thin shells and plates are used as structural members in various fields of modern engineering. In most cases, they have complex geometry (geometry variations, holes, notches, and inclusions of various shapes) for the purposes of design or technology. High loads on structural members made of homogeneous isotropic materials (metals, alloys) may cause structural changes (plastic or creep strains) near stress concentrators and microcracks, which may lead to failure of structural members and then the whole structure. There are also large or finite displacements or strains in the zone of high stresses. One of the basic and most important tasks in the mechanics of shell structures is to analyze the distribution of stresses and strains in structural members of complex form. Therefore, in designing and manufacturing load-bearing structures or their elements with high strength and minimum weight, the need arises to take into account the real operation conditions of structural members and the real properties of structural materials (plastic strains) and their deformation (large or finite displacements).Results of theoretical and experimental analysis of the stress distribution in shells (plates) obtained by solving linear elastic boundary-value problems (linear Hooke's law, small displacements, strains) are discussed in a great many publications most fully generalized in the monographs [2,21,22,25,26,58,65]. They mainly discuss solutions of linear (elastic) problems for thin (spherical, cylindrical, conical, etc.) shells weakened by curvilinear holes of various shapes and made of advances metallic materials.The available theoretical and applied results on the stress distribution in thin and nonthin anisotropic (composite) shells made of materials obtained by solving linear elastic problems (generalized Hooke's law; Kirchhoff-Love or Timoshenko hypotheses) are presented in [27,50].To solve this class of problems in linear elastic formulation, analytic, variational, and numerical methods are used. Methods and results of solving specific classes of physically and geometrically nonlinear problems for some metal shells are discussed in the monographs [20,32,38,42,67,70]. The issue of stress concentration in shells (plates) involving the development of methods of solving nonlinear problems is analyzed in the reviews [24,89,93,94].Note that most studies on nonlinear stress concentration in shells, including problem formulation, development of methods for solving certain classes of nonlinear problems, a...

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Investigations in the theory of thin shells with openings (review)

Cited by 8 publications

References 118 publications

Stress-strain state of spherical shells with two unequal holes

Stress-strain state of spherical shells with two unequal holes

Buckling and vibrations of the shell with the hole under the action of thermomechanical loads

Nonlinear two-dimensional static problems for thin shells with reinforced curvilinear holes

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