 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4760 |
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| V. V. Chekhov, "On optimality of physically nonlinear fully-stressed structures," Mech. Solids. 37 (6), 105-113 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
6 |
Pages |
105-113 |
| Title |
On optimality of physically nonlinear fully-stressed structures |
| Author(s) |
V. V. Chekhov (Zhukovskii) |
| Abstract |
We consider discrete models of fully-stressed (in one special case of
loading) structures having a given geometry and consisting of several
materials. Sufficient conditions of optimality and convergence of the
stress ratio algorithm are obtained for such structures, with their
physical nonlinearity being taken into account. These conditions can be
used for choosing the materials ensuring the optimality and the
convergence, without design calculations or stress state analysis. For
structures made of arbitrary materials, the optimality condition obtained
here can be utilized for heuristic evaluation of the lower bound of the
level of stresses which should take place in the optimal design
(without finding the design itself), and to indicate some fully-stressed
members of an optimally designed structure. The design corresponding to
this lower bound can be obtained by the same means as a fully-stressed
design and may appear to be closer to the optimal design than the latter.
As an illustration, we consider the problem of designing a beam made of
two materials and working in transverse bending. |
| References |
| 1. | N. V. Banichuk, Introduction to Structural Optimization [in Russian],
Nauka, 1986. |
| 2. | R. Razani, "Behavior of a an equistressed structure and its
relation to the minimal weight structure," Raketn. Tekhn., Vol. 3, No. 12,
pp. 115-124, 1965. |
| 3. | E. K. Lipin, V.M. Frolov, V. V. Chedrik, and A. N. Shanygin,
"An algorithm of optimization of load-bearing structures relative to
the strength conditions with compensation for violated constraints,"
Uchen. Zap. TSAGI, Vol. 19, No. 1, pp. 58-66, 1988. |
| 4. | C. Fleury, "An efficient optimality criteria approach
to the minimum weight design of elastic structures,"
Computers and Structures, Vol. 11, No. 3, pp. 163-173, 1980. |
| 5. | I. M. Rabinovich, Principles of Framework Structural Mechanics [in Russian],
Gosstroiizdat, Moscow, 1960. |
| 6. | S. V. Selyugin,
"Optimization of physically nonlinear structures," in N. Olhoff and
G. Rozvany (Editors), Proceedings of the 1st World Congr. of Structural and
Multidisciplinary Optimization. Goslar. Germany, pp. 637-444,
Pergamon Press, Oxford, 1995. |
| 7. | L. M. Kachanov, Fundamentals of the Theory of Plasticity [in Russian],
Nauka, Moscow, 1969. |
| 8. | S. V. Selyugin and V. V. Chekhov, Calculation of reasonable
parameters for physically nonlinear structures,"
Trudy TSAGI, Vol. 2698, pp. 85-95, 1998. |
| 9. | R. J. Melosh, "Convergence in fully-stressed designing,"
AGRARD C.P., 36-70, P. 7-1-7-15, 1970. |
| 10. | A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of
Functions and Functional Analysis [in Russian], Nauka, Moscow, 1968. |
|
| Received |
27 June 2000 |
| << Previous article | Volume 37, Issue 6 / 2002 | Next article >> |
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