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Optimal Control for 3D Elastic Body Motions
G.V. Kostin, V.V. Saurin
The initial-boundary problem for the linear theory of elasticity is considered.
Based on the method of integrodifferential relations a new dynamical variational
principle in which displacement, stress, and momentum functions are varied is
proposed and discussed [1–5]. To minimize the nonnegative functional under
initial, boundary, and partial differential constraints arising in this approach a
regular algorithm for approximation of the unknown functions is worked out. The
algorithm gives us the possibility to estimate explicitly the local and integral
quality of obtained numerical solutions. An effective numerical method for the
optimization problems of controlled motions of elastic bodies with quadratic
objective functionals is developed. As example, the 3D problems of optimal
longitudinal motions of a rectilinear elastic prism with a quadratic cross section are
considered for the terminal total mechanical energy to be minimized. The
numerical results and their error estimates are presented and discussed.
References
1. Kostin,G.V., Saurin,V.V.: Modeling of Controlled Motions of an Elastic Rod
by the Method of Integro-Differential Relations. J. of Computer and Systems
Sciences Int. 45(1), 56–63 (2006)
2. Kostin,G.V., Saurin,V.V.: The Optimization of the Motion of an Elastic Rod
by the Method of Integro-Differential Relations. J. of Computer and Systems
Sciences Int. 45(2), 217–225 (2006)
3. Kostin,G.V., Saurin,V.V.: Modeling and Optimization of Elastic System
Motions by the Method of Integro-Differential Relations. Doklady
Mathematics. 73(3), 469–472 (2006)
4. Kostin G.V., Saurin V.V.: The method of integrodifferential relations for linear
elasticity problems // Archive of Applied Mechanics. 76(7–8), 391–402 (2006)
5. Kostin G.V., Saurin V.V.: Method of Integro-Differential Relation for Optimal
Beam Control. PAMM. Special Issue: GAMM Annual Meeting 2006 – Berlin.
6, (2006) (to print)