Dynamic problems of shape optimal design for shallow curved plates

The problem of optimal structural design of shallow thin-walled elements such as curved rectangular plates are formulated and solved for dynamic conditions. The distribution of the initial curvature of shallow plates in a nonstrained state is taken as the control function. Dynamic compliance is considered as the minimized performance functional. Optimality conditions are derived for the distributed parameter system considered and applied for the construction of the analytical solution. The rigorous analysis of extremum conditions and behavioural equations shows that the initial optimization problem is decomposed into several problems of classical structural analysis, which can be successfully solved analytically. Some optimal designs obtained for rectangular plates under stretching and bending, and a plate lying on an elastic foundation and subjected to lateral forces are presented. Received: November 27, 1998