Decomposition in Optimum Structural Design

A general method for optimal elastic design of indeterminate structures by decomposition of the structure into separate subproblems is proposed. Both stiffness and flexibility method formulations are presented. The iterative two-level approach that is mainly intended for large systems consists of dividing the structure into smaller substructures, optimized independently at a first level. Forces and displacements along the intersections of the substructures are held constant during the first-level solutions but are optimized at a second level. All intermediate solutions of the first-level problem are feasible and thus the optimization iteration can always be terminated with a feasible solution. In general, decomposition can be performed in different ways. Criteria for successful formulation are established, for which simple and efficient solutions are obtained. The method might prove useful in different optimal design problems of trusses, frames, and beams. Numerical examples demonstrate the application of the method to a variety of problems.