An introduction to structural optimization problems

The object of the research described in this thesis is to examine the possibilities of developing analytical and computational procedures for a class of structural optimization problems in the presence of behaviour and side constraints. These are essentially optimal control problems based on the maximum principle of Pontryagin and dynamic programming formalism of Bellman. They are characterised by inequality constraints on the state and control variables giving rise to systems of highly complex differential equations which present formidable difficulties both in the construction of the appropriate boundary conditions and subsequent development of solution procedures for these boundary value problems. Therefore an alternative approach is used whereby the problem is discretised leading to a non-linear programming approximation. The associated non-linear programs are characterised by non-analytic "black box" type representations for the behaviour constraints. The solutions are based on a "steepest descent–alternate step" mode of travel in design space. [Continues.]