Optimal design of cylindrical shells

• Autorzy: Peter Nestler , Werner H. Schmidt
• Języki publikacji: EN

Abstrakty

EN

The present paper studies an optimization problem of dynamically loaded cylindrical tubes. This is a problem of linear elasticity theory. As we search for the optimal thickness of the tube which minimizes the displacement under forces, this is a problem of shape optimization. The mathematical model is given by a differential equation (ODE and PDE, respectively); the mechanical problem is described as an optimal control problem. We consider both the stationary (time independent) and the transient (time dependent) case. P. Nestler derives the model-equations from the Mindlin and Reissner hypotheses. Then, necessary optimality conditions for the optimal control problem are given. Numerical solutions are obtained by FEM, numerical examples are presented.

Słowa kluczowe

EN

linear elasticity; shell theory; cylindrical tube; optimal control; shape optimization

Kategorie tematyczne

• 49N90: Applications of optimal control and differential games
• 49K20: Problems involving partial differential equations
• 65N22: Solution of discretized equations
• 49M25: Discrete approximations
• 65M60: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods
• 74C99: None of the above, but in this section

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2010
• Tom: 30
• Numer: 2
• Strony: 253-267

Daty

wydano

2010

otrzymano

2009-12-07

Twórcy

autor

Peter Nestler

• Greifswald University, Germany

autor

Werner H. Schmidt

• Greifswald University, Germany

Bibliografia

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• [3] D. Braess, Finite Elemente (Springer Verlag, Berlin, Heidelberg, New York, 1997).
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• [5] J. Wloka, Partielle Differentialgleichungen (Teubner Verlag, Stuttgart, 1982). doi: 10.1007/978-3-322-96662-9
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• [8] G. Olenev, On optimal location of the additional support for an impulsively loaded rigid-plastic cylindrical shell, Trans. Tartu Univ. 772 (1987), 110-120.
• [9] Ü. Lepik and T. Lepikult, Automated calculation and optimal design of rigid-plastic beams under dynamic loading, Int. J. Impact Eng. 6 (1987), 87-99. doi: 10.1016/0734-743X(87)90012-1
• [10] J. Lellep, Optimization of inelastic cylindrical shells, Eng. Optimization 29 (1997), 359-375. doi: 10.1080/03052159708941002
• [11] T. Lepikult, W.H. Schmidt and H. Werner, Optimal design of rigid-plastic beams subjected to dynamical loading, Springer Verlag, Structural Optimization 18 (1999), 116-125. doi: 10.1007/BF01195986
• [12] J. Lellep, Optimal design of plastic reinforced cylindrical shells, Control-Theory and Advanced Technology 5 (2) (1989), 119-135.
• [13] P. Nestler, Calculation of deformation of a cylindrical shell, Preprint Mathematik 4/2008.
• [14] J. Sprekels and D. Tiba, Optimization problems for thin elastic structures, in 'Optimal Control of Coupled System of PDE', ISNM 158 Birkhaeuser (2009), 255-273.

Identyfikatory

DOI

10.7151/dmdico.1123