Multistage Optimization of Structures

The design optimization problem is formulated as a multistage decision system by decomposing the structure into a series of substructures. The adoption of indeterminate forces as the state variables in a dynamic programming formulation is shown to be an effective means to describe truss and frame structural systems. A set of decomposition principles are presented which relate static indeterminacy, the number and position of the external reactions, and the stability of the structures corresponding to each stage. Design constraints on the individual members are considered by the concept of constrained policy space for the force state variables. A discrete programming technique is developed for elastic frame optimization problems in which member sizes are restricted to standard structural shapes.