STRUCTURAL OPTIMIZATION USING SINGLE-TERM POLYNOMIAL GEOMETRIC-PROGRAMMING

Due to its characteristics of finding global solutions, geometric programming (GP) in posynomial forms has attracted much attention in the optimization field. To solve structural optimization problems using GP, the constraints are approximated by single-term posynomials in this paper. Although the objective function may already be in the posynomial form it can still be condensed into a single-term posynomial. Two methods are proposed to solve the GP problem with all the objective functions and the constraints being single-term posynomials. One is to transform the GP problem directly into a standard linear programming formulation. The other is to transform it into the dual form. Both of these transformed problems are solved iteratively using linear programming techniques. The accuracies of the predictions of structural responses by using the single-term posynomial and the first-order Taylor's series are discussed. Numerical examples including the static displacement constraints or the natural frequency constraints prove the applicability of the proposed approaches.