Abstract
The reduction of the large in-plane static deformation of a thin hyperelastic plate using control loads is considered. This problem has important applications in the control of flexible space structures. A mathematical model leads to an elliptic optimal control problem in nonlinear elasticity. A numerical optimal control method, based on Finite Element (FE) discretization and Sequential Quadratic Programming (SQP), is employed to minimize the deformation of the plate. Results are presented for a specific example.
Partial funding provided by the Adler Fund for Space Research managed by the Israel Academy of Sciences, and by the Fund for the Promotion of Research at the Technion.
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References
S.M. Joshi, Control of Large Flexible Space Structures, Springer-Verlag, Berlin, 1989.
A.K. Chatterjee, “Optimal Orbit Transfer Suitable for Large Flexible Structures,” J. Astro. Sci., 37, 261–280, 1989.
M.G. Safonov, R.Y. Chiang and H. Flashner, “H-infinity Robust Control Synthesis for a Large Space Structure,” J. Guidance, Control and Dynamics, 14, 513–520, 1991.
M.P. Kamat, ed., Optimization Issues in the Design and Control of Large Space Structures, ASCE publication, New York, 1985.
S.N. Atluri and A.K. Amos, eds., Large Space Structures: Dynamics and Control, Springer-Verlag, Berlin, 1988.
D. Givoli and O. Rand, “Minimization of the Thermoelastic Deformation in Space Structures Undergoing Periodic Motion,” AIAA J. of Spacecraft and Rockets, 32, 662–669, 1995.
R.V. Grandhi, A. Kumar and A. Chaudhary, “State-space Representation and Optimal Control of Non-linear Material Deformation using the Finite Element Method,” Int. J. Num. Meth. Engng, 36, 1967–1986, 1993.
L.S. Hou and J.C. Turner, “Finite Element Approximation of Optimal Control Problems for the Von Karman Equations,” Numer. Methods Partial Differ. Equations, 11, 111–125, 1995.
M. Brokate and M. Sprekels, “Existence and Optimal Control of Mechanical Processes with Hysteresis in Viscous Solids,” IMA J. Applied Math, 43, 219, 1989.
G.E. Stavroulakis, “Optimal Prestress of Cracked Unilateral Structures: Finite Element Analysis of an Optimal Control Problem for Variational Inequalities,” Comp. Meth. Applied Mech. Engng, 123, 231–246, 1995.
G. Knowles, An Introduction to Applied Optimal Control, Academic Press, New York, 1981.
D. Givoli, “A Direct Approach to the Finite Element Solution of Elliptic Optimal Control Problems,” Numer. Methods Partial Differ. Equations, 15, 371–388, 1999.
J. Bonet and R.D. Wood, Nonlinear Continuum Mechanics for Finite Element Analysis, Cambridge University Press, 1997.
D. Goldfarb and A. Idnani, “A Numerically Dual Method for Solving Strictly Convex Quadratic Programs,” Mathematical Programming, 27, 1–33, 1983.
D. Givoli and I. Patlashenko, “Solution of Static Optimal Control Problems in Nonlinear Elasticity via Quadratic Programming,” Commun. Numer. Meth. Engng., submitted.
P.E. Gill, W. Murray and M.H. Wright, Practical Optimization, Academic Press, New York, 1981.
D.G. Luenberger, Linear and Nonlinear Programming, Addison-Wesley, Reading, MA, 1984.
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© 2001 Kluwer Academic Publishers
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Givoli, D., Patlashenko, I. (2001). Static Optimal Control of the Large Deformation of a Hyperelastic Plate. In: Durban, D., Givoli, D., Simmonds, J.G. (eds) Advances in the Mechanics of Plates and Shells. Solid Mechanics and its Applications, vol 88. Springer, Dordrecht. https://doi.org/10.1007/0-306-46954-5_10
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DOI: https://doi.org/10.1007/0-306-46954-5_10
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