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Tytuł artykułu

Optimal design of cylindrical shells

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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.
Twórcy
  • Greifswald University, Germany
  • Greifswald University, Germany
Bibliografia
  • [1] V. Azhmyakov, J. Lellep and W. Schmidt, On the optimal design of elastic beams, Struct. Multidisc. Optim. 27 (2004), 80-88. doi: 10.1007/s00158-003-0352-1
  • [2] F. Tröltzsch, Optimale Steuerung partieller Differentialgleichungen (Vieweg Verlag, Wiesbaden, 2005).
  • [3] D. Braess, Finite Elemente (Springer Verlag, Berlin, Heidelberg, New York, 1997).
  • [4] D. Chapelle and K.J. Bathe, The Finite Element Analysis of Shells - Fundamentals (Springer Verlag, Berlin, Heidelberg, 2003). doi: 10.1007/978-3-662-05229-7
  • [5] J. Wloka, Partielle Differentialgleichungen (Teubner Verlag, Stuttgart, 1982). doi: 10.1007/978-3-322-96662-9
  • [6] St.P. Timoshenko, Schwingungsprobleme der Technik (J.-Springer-Verlag, 1932).
  • [7] R. Hill, The mathematical theory of plasticity (Oxford Clarendon Press, 1950).
  • [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.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1123
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