Geodesic
Optimal design of cylindrical shells
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 30 (2010) no. 2, pp. 253-267.

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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.
Keywords: linear elasticity, shell theory, cylindrical tube, optimal control, shape optimization 
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Nestler, Peter; Schmidt, Werner. Optimal design of cylindrical shells. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 30 (2010) no. 2, pp. 253-267. http://geodesic.mathdoc.fr/item/DMDICO_2010_30_2_a5/

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