Inelastic Deformation of Flexible Spherical Shells with Two Circular Openings

Guz, A. N.; Storozhuk, E. À.; Chernyshenko, I. S.

doi:10.1023/b:inam.0000041395.63200.aa

Cited by 18 publications

(24 citation statements)

References 7 publications

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“…The stresses at the point C ( , ) r r = = 0 θ π , which is closest to the contour of the second hole, vary insignificantly compared with the case of a shell under internal pressure [13]. Thus, when the shell is loaded by axial tensile forces (even for closely spaced holes (~, ) l = 2 3 ), the point B located in the section ( , / ) r r = = 0 2 θ π on the inside surface ( . )…”

Section: The Matrices Of Linear Operations Of Differentiation and [ ]mentioning

confidence: 96%

“…A numerical method for solving nonlinear static problems for arbitrary thin shells of complex geometry with regard for geometrical (finite or large deflections) or/and physical (plastic strains) nonlinearity is outlined in [12]. This paper also proposes an algorithm for approximate solution of doubly nonlinear two-dimensional boundary-value problems of stress concentration in multiply connected shells.Specific numerical results have been obtained in [13,14] in studying the elastoplastic stress-strain state near two circular holes in spherical and cylindrical flexible shells under uniform surface load (internal pressure) of given intensity. These results were used to study the influence of physical and geometrical nonlinearities on the stress (strain) concentration in shells, depending on the distance between the holes.…”

mentioning

confidence: 99%

“…Specific numerical results have been obtained in [13,14] in studying the elastoplastic stress-strain state near two circular holes in spherical and cylindrical flexible shells under uniform surface load (internal pressure) of given intensity. These results were used to study the influence of physical and geometrical nonlinearities on the stress (strain) concentration in shells, depending on the distance between the holes.…”

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confidence: 99%

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Elastoplastic Deformation of Flexible Cylindrical Shells With Two Circular Holes under Axial Tension

Storozhuk

Chernyshenko

2005

Int Appl Mech

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The elastoplastic state of thin cylindrical shells with two circular holes under axial tension is analyzed considering finite deflections. The distributions of stresses along the contours of the holes and in the zone of their concentration are studied by solving doubly nonlinear boundary-value problems. The solution obtained is compared with the solutions that account for either physical nonlinearity (plastic deformations) and geometrical nonlinearity (finite deflections) alone and with a numerical solution of the linearly elastic problem. The stress-strain state near the two holes is analyzed depending on the distance between the holes and the nonlinear factors accounted for Stress distribution in multiply connected elastic isotropic shells (plates) was studied in [3, 4, 9, 11, etc.]. The basic theoretical and experimental results have been obtained by solving linearly elastic problems for shallow and deep thin-walled shells with two and more curvilinear or rectangular holes.Physically and geometrically nonlinear problems of stress (strain or displacement) distribution in various multiply connected thin shells under static loads (surface pressure, boundary forces, or bending moments) of high intensity were addressed in [1, 3-10, 12, etc.]. A numerical method for solving nonlinear static problems for arbitrary thin shells of complex geometry with regard for geometrical (finite or large deflections) or/and physical (plastic strains) nonlinearity is outlined in [12]. This paper also proposes an algorithm for approximate solution of doubly nonlinear two-dimensional boundary-value problems of stress concentration in multiply connected shells.Specific numerical results have been obtained in [13,14] in studying the elastoplastic stress-strain state near two circular holes in spherical and cylindrical flexible shells under uniform surface load (internal pressure) of given intensity. These results were used to study the influence of physical and geometrical nonlinearities on the stress (strain) concentration in shells, depending on the distance between the holes.Expanding upon the earlier studies [12,14], we will present numerical solutions of nonlinear problems for cylindrical shells subjected to boundary forces (axial tension) and weakened by two curvilinear (circular) holes.1. We will analyze the elastoplastic state of thin-walled flexible cylindrical shell having two circular holes with centers on a common generatrix. The shell is subject to axial tensile forces of given intensity P P = ⋅ 0 3 10 N/m (Fig. 1). These forces are assumed to induce plastic strains in the stress-concentration regions of the shell, which is made of an isotropic homogeneous material. The normal displacements become comparable to or exceed the thickness of the shell [3,12], yet remain small compared with the other linear dimensions. Considering certain boundary conditions at the contours of the holes, we will analyze the stress-strain state of a complex flexible shell with certain geometrical and physicomechanical parameters, taking plastic s...

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Section: The Matrices Of Linear Operations Of Differentiation and [ ]mentioning

confidence: 96%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Elastoplastic Deformation of Flexible Cylindrical Shells With Two Circular Holes under Axial Tension

Storozhuk

Chernyshenko

2005

Int Appl Mech

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“…The stress distribution in a spherical shell with two equal circular holes undergoing finite deflections at the elastoplastic stage of deformation was studied in [90,91]. The shell is under internal pressure p p = × 0 5 10 Pa (Fig.…”

Section: Spherical Shell With Two Circularmentioning

confidence: 99%

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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“…For thin-walled isotropic spherical and cylindrical shells with two circular holes, such results are presented in [6,[14][15][16][17].…”

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Stress distribution in physically and geometrically nonlinear thin cylindrical shells with two holes

Storozhuk

Chernyshenko

2005

Int Appl Mech

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The elastoplastic state of thin cylindrical shells weakened by two circular holes is analyzed. The centers of the holes are on the directrix of the shell. The shells are made of an isotropic homogeneous material and subjected to internal pressure of given intensity. The distribution of stresses along the hole boundaries and over the zone where they concentrate (when the distance between the holes is small) is analyzed using approximate and numerical methods to solve doubly nonlinear boundary-value problems. The data obtained are compared with the solutions of the physically nonlinear (plastic strains taken into account) and geometrically nonlinear (finite deflections taken into account) problems and with the numerical solution of the linearly elastic problem. The stress-strain state near the two holes is analyzed depending on the distance between them and the nonlinearities accounted for Introduction. Stress, strain, and strength analyses of isotropic and anisotropic structural members (plates and shells) of complex geometry, including multiple connectivity, under static and dynamic loads are still of importance. Of heightened interest are nonaxisymmetric problems for thin and nonthin shells and plates of various outlines and shapes under high surface and boundary loads. Solving such static and dynamic problems, in both linear and nonlinear formulations, involves severe mathematical and computational difficulties.Efficient methods developed to solve linearly elastic boundary-value problems for multiply connected shells (weakened by two or more curvilinear holes or notches) are outlined in [1,2,6,7,[11][12][13].Concrete numerical results have been obtained for metal and composite shells of spherical, cylindrical, conical, and other shapes subjected to static surface loads, axial forces, and a system of boundary forces and moments. Note that the publications [2,6,7,12] present results for elastic isotropic and orthotropic cylindrical shells with two equal or unequal circular holes (their centers are on a common generatrix or directrix) and with a finite number of circular holes, and for periodic cases.It should also be emphasized that two-dimensional static problems for shells (plates) of various shapes and purposes with a curvilinear (circular or elliptic) hole or a notch of various geometries (simply and doubly connected domains) have mostly been solved considering only the elastic stage of deformation or only geometrical (finite deflections) or physical (plastic or creep strains) nonlinearities [6,7,9,11,13]. The principles and methods of theoretical and experimental analysis of stress concentration in load-bearing structural members were developed with an eye toward solving two-dimensional boundary-value problems in various formulations [3-8, 10, 11]. Isolated results were obtained by solving nonlinear problems for shells with both finite (large) deflections and plastic strains [6,7,13].As regards nonlinear problems for multiply connected thin shells, there are only isolated theoretical results. For thin-walled...

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Inelastic Deformation of Flexible Spherical Shells with Two Circular Openings

Cited by 18 publications

References 7 publications

Elastoplastic Deformation of Flexible Cylindrical Shells With Two Circular Holes under Axial Tension

Elastoplastic Deformation of Flexible Cylindrical Shells With Two Circular Holes under Axial Tension

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

Stress distribution in physically and geometrically nonlinear thin cylindrical shells with two holes

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