 | | 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 |
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| L. S. Rybakov, "Linear theory of an elastic prismatic framework," Mech. Solids. 36 (4), 83-93 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
4 |
Pages |
83-93 |
| Title |
Linear theory of an elastic prismatic framework |
| Author(s) |
L. S. Rybakov (Moscow) |
| Abstract |
The rigorous linear discrete-continuous analysis
of a regular prismatic framework (closed or open) is presented
for the case of static elastic deformation.
The framework is a three-dimensional system
of two mutually orthogonal sets of
rods which are spatially deformable and are rigidly attached to each other.
The elastic axes of the rods lie on a common prismatic surface the cross
section of which is a regular polygon (for a closed framework) or
a part of this polygon (for an open framework). The axes of the
rods of one of the sets coincide with the edges of the surface, whereas the
axes of the rods of the other set coincide with the sides of
regular polygons. The external forces acting on the framework are
arbitrary.
Using the sewing method [1-2], we exactly reduce the original
discrete-continuum problem to a discrete problem. For
this problem, we obtain the complete
system of governing partial difference equations with constant
coefficients expressed in
terms of the generalized nodal displacements and angles of rotation,
total strains, and initial internal forces and torques in the rods.
This system involves the geometrical, physical, and static relations,
as well as compatibility equations for the total strains.
Within the framework of the theory constructed,
two alternative statements of the
problem are presented- in terms of the generalized nodal displacements
and in terms of the initial internal forces in the rods. Possible
generalizations of these statements are indicated.
The former statement is illustrated by the exact
closed-form solution obtained for the problem of deformation of an
infinite closed prismatic framework subjected to a radial
cyclically symmetric nodal loading. The theory presented is a
discrete analogue of the theory of circular
cylindrical shells and follows from the moment theory of elasticity.
It should be emphasized that the results presented in the paper are valid
only if the rods do not buckle under
compression. This assumption is reasonable from the standpoint of
the linear theory which allows the determination of only
subcritical stress-strain state of an elastic system. The static
elastic stability of the framework in question needs
a special study. |
| Sections |
1. L. S. Rybakov, "On a theory of a plane regular
truss-type elastic structure," Izv. AN. MTT [Mechanics of Solid], No. 5,
pp. 171-179, 1995.
2. L. S. Rybakov, "Elastic analysis of a plane regular latticed
structure," Izv. AN. MTT [Mechanics of Solid], No. 1, pp. 198-207, 1996.
3. L. S. Rybakov, "Linear theory of a plane orthogonal lattice,"
Izv. AN. MTT [Mechanics of Solid], No. 4, pp. 174-189, 1999.
4. F. D. Gakhov, Boundary Value Problems [in Russian], Nauka, Moscow,
1977.
5. S. P. Timoshenko and S. Woinowsky-Krieger, Plates and
Shells [Russian translation], Nauka, Moscow, 1966. |
| Received |
12 April 1999 |
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