Stability of multilayered shells of revolution with allowance for geometric nonlinearity of the subcritical state

Rasskazov, A. O.; Trach, V. M.; Gupalyuk, V. N.

doi:10.1007/bf02682182

Cited by 4 publications

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“…Methods of stability analysis of thin-walled structures made of materials with a high order of elastic symmetry (isotropic, orthotropic) are adequately elucidated in the literature [2,10,11]. Filament-wound structures constitute a large class of shell systems [5-9, 12].…”

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confidence: 99%

“…Layers are laid up at similar or different angles, depending on the expected loading conditions. Thus, such thin-walled structures may be assumed to be orthotropic [5][6][7][8][9][10][11][12], though this assumption fails in some cases [13].In [5,6], it was proposed to use a material with one plane of elastic symmetry as a design model for filament-wound cylindrical shells. Failure to account for anisotropy of this type in determining the subcritical stress-strain state reduced the reliability of the solution.…”

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Stability of conical shells made of composites with one plane of elastic symmetry

Trach

2007

Int Appl Mech

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The paper proposes a technique for stability analysis of anisotropic laminated thin shells of revolution made of a composite with one plane of symmetry. The technique is used for numerical analysis of truncated cones made of binder-impregnated filaments continuously wound along geodesic lines. It is shown that the effect of low symmetry on the critical loads depends not only on the number of laminas, but also on the cone angle Keywords: laminated shell of revolution, stability, external pressure, carbon plastic shell, effect of boundary conditions Introduction.Methods of stability analysis of thin-walled structures made of materials with a high order of elastic symmetry (isotropic, orthotropic) are adequately elucidated in the literature [2,10,11]. Filament-wound structures constitute a large class of shell systems [5-9, 12]. Their reinforcement, continuous tows or filaments impregnated with a binder, is generally wound on a mandrel of set form. Layers are laid up at similar or different angles, depending on the expected loading conditions. Thus, such thin-walled structures may be assumed to be orthotropic [5][6][7][8][9][10][11][12], though this assumption fails in some cases [13].In [5,6], it was proposed to use a material with one plane of elastic symmetry as a design model for filament-wound cylindrical shells. Failure to account for anisotropy of this type in determining the subcritical stress-strain state reduced the reliability of the solution.In [14][15][16][17][18], analytic and numerical methods were used to make more accurate account of the stress state of a shell made of a composite with one plane of elastic symmetry. They helped to obtain, using Euler's static criterion, new solutions to stability problems for cylindrical shells subject to axial compression, triaxial pressure, twisting and different types of boundary conditions.In what follows, we will outline a technique for stability analysis of truncated conical shells with process-induced anisotropy. The technique is based on the Runge-Kutta method with discrete orthogonalization [3,4,10]. The present paper continues study conducted in [14][15][16][17][18].1. Consider fiber-reinforced composite conical shells of varying thickness. The number of layers is finite. We will use Euler's static criterion. The shells are assumed to be thin and rather stiff. To determine the subcritical state and critical load, we will use the equations of classical theory. We choose orthogonal coordinate to describe the shells. The datum surface is a surface of revolution. The material of the shells has one plane of elastic symmetry. There is no separation and slippage between neighboring layers. It is assumed that the subcritical stress-strain state (SSS) incorporates geometrical nonlinearity. The shells are subject to triaxial external pressure or axial compression.The material of one-and two-layer filament-wound shells has one plane of elastic symmetry in the general case. For such materials, the elastic relations can be written, using the Kirchhof-Love theory of she...

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Stability of conical shells made of composites with one plane of elastic symmetry

Trach

2007

Int Appl Mech

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“…It is shown that shells with a great number of plies and different ply angles may be considered orthotropic Introduction. Methods for stability analysis of isotropic and orthotropic shells are well developed [2,6,8]. Shells made of fibrous composites are mostly classed as orthotropic [6,7].…”

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“…A method for determining the critical loads for thin-walled cylindrical shells with one plane of elastic symmetry is outlined in [8,14]. According to this method, the system of differential equations can be written in the following mixed form:…”

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Stability of cylindrical shells with one plane of elastic symmetry under axial compression and torsion

Trach

2006

Int Appl Mech

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A numerical technique is developed for stability analysis of laminated cylindrical shells with one plane of symmetry subject to axial compression and torsion. Shells filament-wound in directions other than the coordinate axes are considered as a special case. These shells are analyzed for stability under axial compression, external pressure, and torsion. It is shown that shells with a great number of plies and different ply angles may be considered orthotropic Introduction. Methods for stability analysis of isotropic and orthotropic shells are well developed [2,6,8]. Shells made of fibrous composites are mostly classed as orthotropic [6,7]. Engineering practice employs techniques that prevent low-symmetry behavior of reinforced materials. Note that the theory and methods of stability analysis of nonorthotropic shells have not yet been developed adequately. The pioneering and recent studies [1, 7, 11-14] on buckling of composite shells with special behavior evidence that deviations from orthotropy affect critical loads. This effect is generally adverse and should thus be thoroughly studied to ensure reliable behavior of composite shell structures.Continuing the study [14], we will outline a design method for and perform a stability analysis of cylindrical filament-wound shells subject to axial compression and torsion. In contrast to [13], our method is based on the discrete-orthogonalization method, which makes it possible to allow for the nonlinearity of the prebuckling state and to examine different boundary conditions. Note that a similar design method was used in [3-6, 10] to analyze the stress-strain state and free vibrations of anisotropic shells.1. Let us analyze filament-wound shells for static stability. To this end, we assume that the material of such structures possesses anisotropy and has one plane of elastic symmetry parallel to the mid-surface. We choose an orthogonal coordinate system to describe the shells. Assume also that they are thin, but rigid enough. We assign the surface of revolution to be the datum surface. The plies are perfectly bonded, i.e., do not separate and slip, are symmetric about the mid-surface, and have the same thickness and equal initial elastic constants. The ply angle ψ i can be different in two neighboring plies. The classical theory of shells is known to use the elasticity relations (instead of the generalized Hooke's law), which are integral forces N ij and moments M ij linearly expressed in terms of the tangential strains ε ij and bending strains k ij of the mid-surface. If we denote the tensile and flexural stiffnesses of the ith ply by C B t

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Rasskazov

2002

International Applied Mechanics

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Stability of multilayered shells of revolution with allowance for geometric nonlinearity of the subcritical state

Cited by 4 publications

References 2 publications

Stability of conical shells made of composites with one plane of elastic symmetry

Stability of conical shells made of composites with one plane of elastic symmetry

Stability of cylindrical shells with one plane of elastic symmetry under axial compression and torsion

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