Mechanics of Solids (about journal) Mechanics of Solids
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IssuesArchive of Issues2002-6pp.105-113

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Total articles in the database: 3546
In Russian (. . ): 1998
In English (Mech. Solids): 1548

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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
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