APPROXIMATE DISCRETE VARIABLE OPTIMIZATION OF FRAME STRUCTURES WITH DUAL METHODS

The purpose of this work is to present an efficient method for optimum design of frame structures, using approximation concepts. A dual stra tegy in which the design variables can be considered as discrete varia bles is used. A two-level approximation concept is used. In the first level, all the structural response quantities such as forces and displ acements are approximated as functions of some intermediate variables. Then the second level approximation is employed to convert the first- level approximation problem into a series of problems of separable for ms, which can be solved easily by dual methods with discrete variables . In the second-level approximation, the objective function and the ap proximate constraints are linearized. The objective of the first-level approximation is to reduce the number of structural analyses required in the optimization problem and the second level approximation reduce s the computational cost of the optimization technique. A portal frame and a single layer grid are used as design examples to demonstrate th e efficiency of the proposed method.