Elastoplastic state of thin-walled cylindrical shells with elleptcal hole on the lateral face

Mulyar, V. P.; Storozhuk, E. À.; Chemyshenko, I. S.

doi:10.1007/bf02700658

Int Appl Mech

1997

DOI: 10.1007/bf02700658

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Elastoplastic state of thin-walled cylindrical shells with elleptcal hole on the lateral face

V. P. Mulyar

E. À. Storozhuk

I. S. Chemyshenko

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Cited by 4 publications

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“…where [ ] K is the global stiffness matrix; { } g is the column vector of nodal variables; and { } F is the column vector of load [3]. The use of the oblique frame (1) calls for the appropriate transformation of mathematical operators in the FEM: derivatives, surface elements, and arc elements [8].…”

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“…Solution Technique. To solve two-dimensional problems, we will use the numerical technique developed in [1][2][3]; it is based on the finite-element method (FEM). A system of linear governing equations follows from the variational Lagrange equation in matrix form From the stationarity conditions for the total energy of the shell (2), we derive a system of governing equations, which can be written in a matrix form as…”

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On the stress distribution in a spherical shell with an off-center curvilinear hole

Mulyar

2006

Int Appl Mech

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A numerical analysis is made of the joint effect of two factors of asymmetry-ellipticity and eccentricity-on the stress distribution near a free hole in a spherical shell. The nature of deformation is determined by the predominant factor. Whether there are "fixed" points on the graphs of stress distribution around a small hole at which they intersect depends on how rigidly the outer edge is fixed. As the rigidity of fixation is increased, the points smear Introduction. The asymmetric stress-strain state (SSS) near curvilinear holes (cutouts) in isotropic [4,6,9,10] and composite [4,5,8,11] plates and shells is of theoretical and practical interest: the results of a stress-strain analysis would allow us to evaluate the stress and strain of various thin-walled structural members under various kinds of loads.Numerical stress-strain analyses were performed mainly for thin-walled spherical caps with a central elliptical hole [4,5,8,10,11].As pointed out in [1,7], in the off-center case, numerical results are mainly available only for a circular hole, with the emphasis being on the stress distribution around the bridge between the outer and inner edges, which does not give an accurate account of the maximum stresses. Most publications employ special orthogonal coordinate frames and address simply connected stress-concentration problems for elastic isotropic shells. Such problems for elastoplastic shells were analyzed in [6, 10] and for shells made of nonlinear elastic composites in [8].Note that the paper [5], where the SSS of elastic orthotropic laminates with an elliptic hole was analyzed, gives specific results only for a special case (a circular hole).Specific simply and doubly connected problems for spherical shells with a central circular hole or with two circular holes were solved in [6].We will examine the joint effect of two factors of asymmetry (ellipticity and eccentricity) on the SSS only for a rigidly fixed shell with finite mechanical and geometrical parameters.Nowadays, stress-strain studies of doubly and multiply connected thin-walled structural members are of interest. The same applies to the stress-strain analysis of spherical shells (bottoms). We will discuss below results from a stress-strain analysis of elastic isotropic spherical shells with an off-center curvilinear (elliptical or circular) hole.1. Problem Formulation. Let us consider a thin isotropic nonclosed spherical shell of radius R and thickness h with an off-center [7] curvilinear (elliptical, circular) hole. The shell is a doubly connected domain (Fig. 1); its boundaries are the outer and inner edges of the shell. The shell is subjected to surface forces { } { , , } p p p p T = 1 2 3 . The inner boundary can be free, fixed,

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On the stress distribution in a spherical shell with an off-center curvilinear hole

Mulyar

2006

Int Appl Mech

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“…Of considerable interest is the nonaxisymmetric deformation of shells weakened by an elliptic hole. Solutions for spherical and cylindrical shells with an elliptic free hole are presented in [1,8,11,12].We will analyze the stress-strain state of an elastoplastic flexible spherical shell with an elliptic hole reinforced with a thin curvilinear element (a rod or a ring) of given stiffness. We will use the method developed in [11,21] and numerical results to examine the effect of the nonlinearity and stiffness of the reinforcement on the distribution of stresses (strains, displacements) around a reinforced hole in a shell subjected to surface pressure.…”

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Elastoplastic state of flexible spherical shells with a reinforced elliptic hole

2008

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The elastoplastic state of a thin spherical shell weakened by an elliptic hole is analyzed. Finite deflections are considered. The hole is reinforced with a thin ring. The shell is made of an isotropic homogeneous material. The load is internal pressure. A relevant problem is formulated and solved numerically with allowance for physical and geometrical nonlinearities. The distribution of stresses, strains, and displacements along the elliptic boundary and in the zone of their concentration is studied. The stress-strain state of the shell near the hole is analyzed Introduction. The stress distribution in thin-walled shells of revolution made of isotropic (metal) and anisotropic (composite) materials and weakened by a curvilinear (circular) hole is studied in [2, 3, 5, 7, 20, etc.]. The major results were obtained by solving boundary-value problems in the linear elastic axisymmetric case. Structural members (plates, shells) with circular holes either free or reinforced with a rigid inclusion were considered in most cases. Some boundary-value problems for shells with a curvilinear (circular, elliptic) nonreinforced hole were solved in physically nonlinear [1,7,15,16] or geometrical nonlinear [7,19] formulations. Numerical results on stress concentration in thin-walled shells were obtained in [7, 11, 16-18, 21, etc.] making joint allowance for nonlinear factors (elastoplastic strains and finite deflections). The elastoplastic state of shells of various shapes with circular holes reinforced with a thin elastic element (ring) is studied in [4,10,13,14]. Of considerable interest is the nonaxisymmetric deformation of shells weakened by an elliptic hole. Solutions for spherical and cylindrical shells with an elliptic free hole are presented in [1,8,11,12].We will analyze the stress-strain state of an elastoplastic flexible spherical shell with an elliptic hole reinforced with a thin curvilinear element (a rod or a ring) of given stiffness. We will use the method developed in [11,21] and numerical results to examine the effect of the nonlinearity and stiffness of the reinforcement on the distribution of stresses (strains, displacements) around a reinforced hole in a shell subjected to surface pressure.1. Consider a thin-walled isotropic spherical shell of radius R and thickness h weakened by an elliptic (circular) hole and subjected, in the general case, to surface ({p} = {p 1 , p 2 , p 3 } Ò ) and boundary ({m b } = {T b , S b , Q b , Ì b } Ò ) static loads. Let high levels of loading cause the shell to deform plastically near the hole and undergo large (finite) deflections comparable to the thickness of the shell, but smaller than all the other linear dimensions. We also assume that the properties and stress-strain curve of the shell's material are known from experiments.The midsurface of the shell is described [11] in a geographical coordinate system (y, v) with the origin at the center of the hole, and its geometry is described in a global Cartesian coordinate system (X, Y, Z) with the origin at the center of the sph...

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“…The stress distribution ( / ) K h P s j s = along the elliptic boundary is shown by plots [8,18], which are indicative of the efficiency of the numerical method and quite accurate solution of the problem for a shell of complex geometry.…”

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“…The method was validated by comparing the numerical solution of a linear elastic problem [8] and experimental data [18] for a cylindrical shell with the following characteristics: …”

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Inelastic deformation of flexible cylindrical shells with an elliptic hole

2007

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The elastoplastic state of isotropic homogeneous cylindrical shells with elliptic holes and finite deflections under internal pressure is studied. Problems are formulated and numerically solved taking into account physical and geometrical nonlinearities. The distribution of stresses (displacements, strains) along the boundary of the hole and in the zone of their concentration is analyzed. The data obtained are compared with the numerical solutions of the physically nonlinear, geometrically nonlinear, and linear problems. The stress-strain state of cylindrical shells in the neighborhood of the elliptic hole is analyzed with allowance for nonlinear factors Introduction. The distribution of stresses (strains, displacements) in isotropic and anisotropic, simply and multiply connected structural members (shells, plates) has mostly been studied for the elastic range of deformation [1, 3, 5-7, 9, 10]. The major results have been obtained in solving static linear elastic problems for thin and nonthin shells with curvilinear (circular, elliptic, etc.) holes (cutouts) under surface and edge loads. The use was made of theories of shells based on hypotheses on structural members made of traditional metallic and advanced composite materials. To formulate and solve problems of this class, variational, numerical, and analytic methods were used.Physically nonlinear problems that deal with nonlinear elastic, plastic, and creep strains in members (isotropic or orthotropic) of shell structures of positive or zero Gaussian curvature with curvilinear holes are solved in [4, 6, 7, 12, 14, etc.]. The distribution of stress/strain components around an elliptic hole is studied in [3, 5-8, 11, 17] by solving boundary-value problems and taking into account the physical nonlinearity of materials (metals, composites).Also of interest are two-dimensional nonlinear problems of stress concentration around elliptic (noncircular) holes in isotropic cylindrical shells with both physical and geometrical (finite, large deflections) nonlinearities. Such studies are even more important in connection with calculations for high levels of loads (surface pressure, axial forces, edge forces, moments).The present paper discusses results, obtained by the method developed in [2] and presented in support of its applications [14,16,18], from a numerical analysis of the elastoplastic stress-strain state around an elliptic hole in a flexible cylindrical shell under a surface load. We will examine the influence of physical (plastic deformations) and geometrical (finite deflections) nonlinearities on the distribution of stresses and strains in the zone of their concentration in a shell under internal pressure of given magnitude.

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Elastoplastic state of thin-walled cylindrical shells with elleptcal hole on the lateral face

Cited by 4 publications

References 1 publication

On the stress distribution in a spherical shell with an off-center curvilinear hole

On the stress distribution in a spherical shell with an off-center curvilinear hole

Elastoplastic state of flexible spherical shells with a reinforced elliptic hole

Inelastic deformation of flexible cylindrical shells with an elliptic hole

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