Optimal design of cylindrical shells

Peter Nestler; Werner H. Schmidt

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2010)

  • Volume: 30, Issue: 2, page 253-267
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Peter Nestler, and Werner H. Schmidt. "Optimal design of cylindrical shells." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 30.2 (2010): 253-267. <http://eudml.org/doc/271199>.

@article{PeterNestler2010,
abstract = {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.},
author = {Peter Nestler, Werner H. Schmidt},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {linear elasticity; shell theory; cylindrical tube; optimal control; shape optimization},
language = {eng},
number = {2},
pages = {253-267},
title = {Optimal design of cylindrical shells},
url = {http://eudml.org/doc/271199},
volume = {30},
year = {2010},
}

TY - JOUR
AU - Peter Nestler
AU - Werner H. Schmidt
TI - Optimal design of cylindrical shells
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2010
VL - 30
IS - 2
SP - 253
EP - 267
AB - 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.
LA - eng
KW - linear elasticity; shell theory; cylindrical tube; optimal control; shape optimization
UR - http://eudml.org/doc/271199
ER -

References

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  2. [2] F. Tröltzsch, Optimale Steuerung partieller Differentialgleichungen (Vieweg Verlag, Wiesbaden, 2005). 
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  8. [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. Zbl0664.73065
  9. [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. [10] J. Lellep, Optimization of inelastic cylindrical shells, Eng. Optimization 29 (1997), 359-375. doi: 10.1080/03052159708941002 
  11. [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. [12] J. Lellep, Optimal design of plastic reinforced cylindrical shells, Control-Theory and Advanced Technology 5 (2) (1989), 119-135. 
  13. [13] P. Nestler, Calculation of deformation of a cylindrical shell, Preprint Mathematik 4/2008. 
  14. [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. Zbl1197.49047

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