Optimization of Vibrating Thin-Walled Structures

Thin-walled structures play an important role in structural engineering. These structures — due to the thinness of the walls — are very sensitive to external excitation which can be caused either by harmonically fluctuating loading or by impact. The aim of the paper is to determine optimality criteria for vibrating thin-walled structures. In deriving these conditions, one must be very careful since thin-walled structures exhibit a different mechanical behaviour to solid sections. These special effects are the influence of shear deformations and of the deformation of the cross-section. Moreover, for special cross-sections there is a coupling of bending and torsion. In order to consider all these effects, a system of differential equations is introduced. Then, optimization problems are discussed and optimality conditions are derived, including some known and several new results.