 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 11223 |
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| N. P. Tyutyunnikov and F. N. Shklyarchuk, "Analysis of a strengthened weakly conical shell using a complete system of orthogonal functions on an arbitrary contour of its transverse cross-section," Mech. Solids. 43 (4), 623-634 (2008) |
| Year |
2008 |
Volume |
43 |
Number |
4 |
Pages |
623-634 |
| DOI |
10.3103/S0025654408040109 |
| Title |
Analysis of a strengthened weakly conical shell using a complete system of orthogonal functions on an arbitrary contour of its transverse cross-section |
| Author(s) |
N. P. Tyutyunnikov (Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993, Russia, nicpet@list.ru)
F. N. Shklyarchuk (Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993, Russia, shklyarchuk@list.ru) |
| Abstract |
Thin-walled weakly conical and cylindrical shells with arbitrary open, simply or multiply closed contour of transverse cross-sections strengthened by longitudinal elements (such as stringers and longerons) are used in the design of wings, fuselages, and ship hulls. To avoid significant deformations of the contour, such structures are stiffened by transverse elements (such as ribs and frames).
Various computational models and methods are used to analyze the stress-strain states of such compound structures. In particular, the ground stress-strain states in bending, transverse shear, and twisting of elongated structures are often analyzed with the use of the theory of thin-walled beams [1] based on the hypothesis of free (unconstrained) warping and bending of the contour of transverse cross-sections. In general, the computations with the contour warping and bending constraints caused by the variable load distribution, transverse stiffening elements, and the difference in the geometric and rigidity parameters of the shell cells are usually performed by the finite element method or the superelement (substructure) method [2, 3].
In several special cases (mainly for separate cells of cylindrical and weakly conical shells located between transverse stiffening elements, with the use of some additional simplifying assumptions), efficient variation methods for computations in displacements [4–8] and in stresses [9] were developed, so that they reduce the problem to a system of ordinary differential equations. In the one-and two-term approximations, these methods permit obtaining analytic solutions, which are convenient in practical computations. But for shells with multiply closed contours of transverse cross-sections and in the case of exact computations by using the Vlasov variational method [4], difficulties are encountered in choosing the functions representing the warping and bending of the contour of transverse cross-sections. In [10], in computations of a cylindrical shell with simply closed undeformed contour of the transverse section, warping was represented in the form of expansions in the eigenfunctions orthogonal on the contour, which were determined by the method of separation of variables from a special integro-differential equation. In [11], a second-order ordinary differential equation of Sturm-Liouville type was obtained; its solutions form a complete system of orthogonal functions with orthogonal derivatives on an arbitrary open simply or multiply closed contour of a membrane cylindrical shell stiffened by longitudinal elements. The analysis of such a shell with expansion of the displacements in these functions leads to ordinary differential equations that are not coupled with each other.
In the present paper, by using the method of separation of variables, we obtain differential and the corresponding variational equations for numerically determining complete systems of eigenfunctions on an arbitrary contour of a discretely stiffened membrane weakly conical shell and a weakly conical shell with undeformed contour. The obtained systems of eigenfunctions are used to reduce the problem of deformation of shells of these two types to uncoupled differential equations, which can be solved exactly. |
| Received |
30 April 2008 |
| Link to Fulltext |
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