A Cross-Sectional Shape Multiplier Method for Two-Level Optimum Design of Frames

In this paper, a new method for optimum design of frame structures is presented. The method is based on a hierarchical decomposition of the structure into two-levels, namely, the bottom- and the top-level. The bottom-level consists of several subproblems each dealing with the cross-sectional sizing of a given frame-element. The top-level consists of one subproblem which is formulated for configuration design of the frame structure. Since there may be a large number of frame elements, a new shape multiplier method has been developed to simplify the formulation of the bottom-level subproblems. Furthermore, a two-level solution procedure has been developed which first solves the bottom-level subproblems based on their monotonicity analysis. It then solves the top-level subproblem as it coordinates, based on a linear approximation, the solutions to the bottom-level subproblems. Three examples with increasing degree of difficulty are presented to demonstrate the effectiveness of the method.