Two-level optimization of prestressed structures

Some general considerations related to multilevel optimization of structures are discussed. The mathematical structure of the problem under consideration is presented, and a simplified formulation is introduced. A two-level design procedure for prestressed concrete structures is developed, where the prestressing force and the tendon coordinates are optimized at the first-level, while the concrete dimensions are selected at the second-level. It is shown that the first-level problem can be stated in a linear programming form, thereby allowing a simple and efficient solution. In addition, the minimum concrete dimensions can be determined by solving a simple explicit nonlinear programming problem. The design procedure presented involves solution of several simple subproblems. The main advantages of the solution process are: firstly, solution of each of the simplified problems presented involves only a single structural analysis. In addition, each problem can readily be solved by available computer programs. Secondly, useful results are obtained for various suboptimal and feasible designs. And finally, solution of the simplified problems is most efficient. (C) 1997 Elsevier Science Ltd.