Optimal control of a pre-stressed, orthotropic thin cylindrical shell subjected to a constant pressure at its interior wall

Abstract

The open loop optimal control of a pre-stressed, orthotropic thin cylindrical shell subjected to a constant pressure at its interior wall relative to a given index of performance is investigated. The optimal control function is obtained by using a calculus of variations approach on the basis of a thin-shell theory. The response and the hoop stress (circumferential stress) of the controlled shell are presented in graphical form and compared with those of an uncontrolled shell. Moreover, it is observed that the time required for the effectiveness of the control increases as the orthotropy coefficient increases. An interesting aspect of the investigation is the singularity of the mass matrix.