# 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

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topPeter 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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- [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. Zbl1197.49047

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