1 research outputs found
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.