Optimal Design of Cylindrical Shells

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.