Stability of Laminated Shells Made of Materials with one Plane of Elastic Symmetry

Trach, V. M.; Podvornyi, A. V.

doi:10.1023/b:inam.0000037305.78333.21

Cited by 14 publications

(19 citation statements)

References 6 publications

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“…This effect can be revealed only when the problem is solved by different methods. Apparently, the effects detected in [11][12][13] may also manifest themselves in this problem. …”

Section: Introductionmentioning

confidence: 97%

“…As in [9], the unknown functions are expanded into trigonometric series satisfying the hinged-support conditions. It should be noted that the numerical method proposed in [12,13] for shells with one plane of symmetry also applies to the case of loading under consideration. The importance of allowing for low orders of symmetry can be judged from [6,10], wherein it was established that not only quantitative but also qualitative effect of this factor on the natural vibrations of anisotropic bodies is significant.…”

Section: Introductionmentioning

confidence: 99%

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Stability of Cylindrical Composite Shells under Torsion

2005

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The stability of fiber-reinforced cylindrical shells under torsion is analyzed in the case where the principal directions of elasticity in the layers do not coincide with the coordinate directions. The solution to the linearized equations of the technical theory of anisotropic shells is obtained in the form of trigonometric series. It is shown that for some reinforcement configurations the critical loads may depend on the direction of the torsional moment. It is also established that the minimum (in absolute value) eigenvalue does not always correspond to the critical load. This fact should be taken into account not only in the case of torsion but also in more complicated cases of loading Keywords: stability, torsion, cylindrical shell, composite with one plane of symmetry, critical loads Introduction. Problems of stability of cylindrical shells under torsion differ from those under loading of other types in both formulation and solution methods. It is obvious that the direction of the torsional moment is of no importance for isotropic and orthotropic shells. The mathematical solution should account for the fact that the absolute value of the critical load is also independent of the torsion direction, but its sign may be either plus or minus. The buckling of a shell is only possible under compressive loads of one sign such as axial load or pressure. This fact is also incorporated into the formulation of the eigenvalue problem. It is for these two types of loading that the most accurate solutions of stability problems have been obtained [2,4,8]. Less attention was given in the literature to the problem of stability under torsion [4,8,9]. Among the available analytic solutions, the most accurate seems to be Batdorf's solution to the stability problem for an isotropic cylindrical shell under torsion [8,9]. Its characteristic equation has the critical load parameter raised to the second power. If we determined its minimum value, it would become possible to calculate two critical values of the torsional moment differed only by sign. There are approximate analytic solutions for orthotropic shells [4]. For materials of lower order of symmetry, no satisfactory analytic solution has been found yet.In this paper, we solve the stability problem for cylindrical shells filament-wound in directions different from the coordinate axes. As in [9], the unknown functions are expanded into trigonometric series satisfying the hinged-support conditions. It should be noted that the numerical method proposed in [12,13] for shells with one plane of symmetry also applies to the case of loading under consideration. The importance of allowing for low orders of symmetry can be judged from [6, 10], wherein it was established that not only quantitative but also qualitative effect of this factor on the natural vibrations of anisotropic bodies is significant.1. Consider shells with an odd number of homogeneous anisotropic layers that have at each point only one plane of elastic symmetry parallel to the mid-surface. From the formal viewpoint, the...

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“…This effect can be revealed only when the problem is solved by different methods. Apparently, the effects detected in [11][12][13] may also manifest themselves in this problem. …”

Section: Introductionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Stability of Cylindrical Composite Shells under Torsion

2005

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“…The above approach follows the same line, though is rather approximate. Figure 1 depicts solid curves 1 and 2 plotted by the exacter method from [8]. Quantitatively, the dashed and solid curves 1 and 2 differ significantly for N = 1 and somewhat less for N = 2.…”

Section: Solution Of Stability Problemmentioning

confidence: 98%

“…(3.1) and (3.3) hamper obtaining the closed-form solution. A numerical algorithm for solving such a problem was proposed in [8]. The approximate solution has the following form [3,4]:…”

Section: Solution Of Stability Problemmentioning

confidence: 99%

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

2005

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Cylindrical shells produced by single-layer or cross winding are analyzed for stability. An approximate analytical solution is proposed. It allows evaluating the effect of an unbalanced laminate on the critical values of the axial load, intensity of external pressure, and shear forces. It is shown that the effect of imbalance weakens with increase in the number of laminas. In each specific case, the number of laminas at which the material can be considered orthotropic is determined

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Effects of fiber anisotropy on the microbuckling loads for a fiber composite

Lapusta¹,

Wagner

2005

Int J Fract

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Stability of Laminated Shells Made of Materials with one Plane of Elastic Symmetry

Cited by 14 publications

References 6 publications

Stability of Cylindrical Composite Shells under Torsion

Stability of Cylindrical Composite Shells under Torsion

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

Effects of fiber anisotropy on the microbuckling loads for a fiber composite

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