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Identification of the parameters of the stress-strain problem for a multicomponent elastic body with an inclusion. (English. Ukrainian original) Zbl 1272.74226

Int. Appl. Mech. 46, No. 4, 377-387 (2010); translation from Prik. Mekh., Kiev 46, No. 4, 14-24 (2010).
Summary: Explicit expressions for residual functional gradients are derived. They are used to identify, using gradient methods, the parameters of elastic problems for multicomponent bodies. The method employs the solutions of conjugate problems in the theory (developed by the authors) of optimal control of distributed multicomponent systems.

MSC:

74G75 Inverse problems in equilibrium solid mechanics
74E05 Inhomogeneity in solid mechanics
74B10 Linear elasticity with initial stresses
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[1] O. M. Alifanov, E. A. Artyukhin, and S. V. Rumyantsev, Extremal Methods for Solving Ill-Posed Problems [in Russian], Nauka, Moscow (1988). · Zbl 0657.35003
[2] V. S. Deineka, Optimal Control of Distributed Multicomponent Elliptic Systems [in Russian], Naukova Dumka, Kyiv (2005). · Zbl 1080.49001
[3] V. S. Deineka and N. A. Veshchunova, ”Identification of parameters of parabolic multicomponent systems: Numerical problem solving,” Komp. Matem., No. 1, 22–33 (2008).
[4] V. S. Deineka and N. A. Veshchunova, ”Numerical solution of inverse nonstationary heat-conduction problems for plates,” Komp. Matem., No. 2, 32–43 (2008).
[5] V. S. Deineka and I. V. Sergienko, Models and Methods for Solving Problems in Inhomogeneous Media [in Russian], Naukova Dumka, Kyiv (2001). · Zbl 0976.65097
[6] V. S. Deineka and I. V. Sergienko, Optimum Control of Distributed Inhomogeneous Systems [in Russian], Naukova Dumka, Kyiv (2003). · Zbl 1124.49300
[7] G. Duvaut and J.-L. Lions, Inequalities in Physics and Mechanics, Springer-Verlag, Berlin (1979). · Zbl 0331.35002
[8] O. C. Zienkiewicz, The Finite-Element Method in Engineering Science, McGraw-Hill, New York (1971). · Zbl 0237.73071
[9] A. D. Kovalenko, Basic Thermoelasticity [in Russian], Naukova Dumka, Kyiv (1970).
[10] J. L. Lions, Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, New York (1971).
[11] I. V. Sergienko and V. S. Deineka, ”Numerical solution of the dynamic problem of elasticity for bodies with concentrated masses,” Int. Appl. Mech., 40, No. 12, 1360–1370 (2004). · Zbl 1122.74406 · doi:10.1007/s10778-005-0041-4
[12] I. V. Sergienko and V. S. Deineka, ”Solving integrated inverse thermoelasticity problems,” J. Automat. Inf. Sci., 39, No. 10, 22–46 (2007). · Zbl 1153.35085 · doi:10.1615/JAutomatInfScien.v39.i10.20
[13] S. P. Timoshenko, A Course in the Theory of Elasticity [in Russian], Naukova Dumka, Kyiv (1972).
[14] V. D. Budak, A. Ya. Grigorenko, and S. V. Puzyrev, ”Solution describing the natural vibrations of rectangular shallow shells with varying thickness,” Int. Appl. Mech., 43, No. 4, 432–441 (2007). · Zbl 1150.74048 · doi:10.1007/s10778-007-0040-8
[15] Ya. M. Grigorenko and O. A. Avramenko, ”Stress–strain analysis of closed nonthin orthotropic conical shells of varying thickness,” Int. Appl. Mech., 44, No. 6, 635–643 (2008). · doi:10.1007/s10778-008-0081-7
[16] A. Ya. Grigorenko and T. L. Efimova, ”Using spline-approximation to solve problems of axisymmetric free vibration of thick-walled orthotropic cylinders,” Int. Appl. Mech., 44, No. 10, 1119–1127 (2008). · doi:10.1007/s10778-009-0128-4
[17] Ya. M. Grigorenko and S. N. Yaremchenko, ”Influence of orthotropy on displacementand stresses in nothin cylindrical shells with elliptic cross section,” Int. Appl. Mech., 43, No. 6, 654–661 (2007). · doi:10.1007/s10778-007-0064-0
[18] I. V. Sergienko and V. S. Deineka, Optimal Control of Distributed Systems with Conjugation Conditions, Kluwer, New York (2005). · Zbl 1080.49001
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