Stability of Cylindrical Shells Made of Fibrous Composites with One Symmetry Plane

2007

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A solution is obtained to describe the stability and initial postbuckling behavior of cylindrical shells made of composites with one plane of symmetry. The solution is based on the Donnell-Mushtari-Vlasov nonlinear theory of anisotropic shells and Koiter's theory of buckling and postbuckling behavior. Calculated results are presented for boron plastic shells with reinforcement of different types under external pressure. It is shown that the conventional model of a composite as an orthotropic material is erroneous for many types of reinforcement Keywords: stability, initial postbuckling behavior, composite material, cylindrical shell, different types of reinforcement, external pressureIntroduction. Most studies on the stability of shells made of composite materials modeled a composite as an orthotropic material [2,3,5]. This model is justified for the most popular shell making techniques; however, there are cases where it was not proved to be applicable [4]. One example is a fiber-reinforced composite layer that, being orthotropic within its own layers, deforms as an anisotropic body with one symmetry plane when the reinforcement directions are not aligned with the coordinate axes of the shell. Analytic and numerical methods of stability analysis of shells with a similar kind of anisotropy were developed in [6][7][8][15][16][17][18][19]. Note that all results on the initial postcritical behavior of composite shells apply only to orthotropic materials [3].In what follows, we will study the relationship of the initial postcritical behavior and sensitivity of shells to geometrical imperfections and deviations of composites from orthotropy. To this end, we will use the above-mentioned technique, which is based on the Donnell-Mushtari-Vlasov (DMV) theory of anisotropic shells [1] and Budiansky's version [12] of Koiter's asymptotic theory of buckling and postbuckling behavior.1. DMV Equations. Consider shells of constant thickness t consisting of N layers, also of constant thickness t k . Each layer is an anisotropic body with one symmetry plane coinciding with the mid-surface. The elastic relations for laminated anisotropic shells can be written in the following form accurate to an extent sufficient for the engineering theory of shells:

Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Stability and initial postbuckling behavior of anisotropic cylindrical shells under external pressure

Semenyuk

2007

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“…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.…”

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confidence: 66%

“…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.…”

Section: Introductionmentioning

confidence: 99%

“…The curves represent the critical external pressure q cr depending on the angle b and the arrangement of the principal directions of elasticity. Solid curves 1, 2, 3, and 4 and dashed curves 1a, 2a, 3a, and 4a represent the cases where the parameters Â 16 and Â 26 are neglected and are taken into account, respectively. Curves 1, 2, 3, and 4 correspond to b = 85, 80, 75, 65.…”

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confidence: 99%

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

2007

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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...

Stability of axially compressed cylindrical shells made of reinforced materials with specific fiber orientation within each layer

Semenyuk

2006

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A technique for stability analysis of anisotropic cylindrical shells is developed. It permits us to examine the cases of reinforcement where the elastic axes of layers do not coincide with the coordinate axes of the shell. The solution is obtained using the mixed equations of the Donnell-Mushtari-Vlasov theory of shells. The deflection and force functions are approximated by trigonometric series. Single-layer and multilayer cylindrical shells with fiber orientation of two types are analyzed for stability. It is revealed that when layers are few, failure to incorporate the direction of fibers in layers into the design model results in highly inaccurate values of critical loads Keywords: stability of anisotropic cylindrical shells, Donnell-Mushtari-Vlasov theory of shells, axial compression, fiber orientation within layers, two types of fiber orientation, deflection and force functions, critical loadIntroduction. The influence of the reinforcement configuration of composite materials on the stability of cylindrical shells is the subject of many studies [2-6]. The basic conclusion made there is that optimal structures can be obtained with reinforcing elements making some angles ϕ i with the coordinate lines within each layer. These angles depend on the mechanical properties of the material components, on the acting loads, etc. In some cases, however, calculated data may appear rather inaccurate because of the limitation of the design model used. Most authors suppose that the reinforced material has three planes of symmetry, i.e., is orthotropic. Such a high order of symmetry is typical of a quite narrow class of materials; hence incorrect results produced by orthotropic models that neglect the orientation of fibers within each layer.The pioneering studies of filament-wound shells attempted to develop a design technique that would describe the deformation of composites with one plane of elastic symmetry [3,5]. However, the approximate formulation of stability problems adversely affected the accuracy of the results. Some of the shortcomings were eliminated in [9]. The technique proposed in [10] for stability analysis of composite shells of revolution with one plane of elastic symmetry is based on the discrete-orthogonalization method. The stability equations used in [8,10] are exact within the framework of Euler's static criterion and are widely applicable. However, they are rather difficult to solve by the technique in question, which hinders parametric analysis. The analytic solution, found in [7], to the stability problem for anisotropic cylindrical shells under torsion is free from this disadvantage, but is applicable only to one class of shells and boundary conditions. We will use such a solution below to analyze the typical features of buckling of anisotropic laminated cylindrical shells made of materials with one plane of symmetry and subjected to axial compression. The assumed level of symmetry allows us to describe the deformation of a composite made by winding matrix-impregnated filaments at a certain angle,...