Design Considerations in the Optimization of Structural Topologies

Some design considerations related to the optimization of structural topologies are discussed. The basic difficulties involved in the solution process are first reviewed and the ground structure approach is discussed. Formulating the problem as a nonlinear programming problem, the computational effort involved in the solution process might become prohibitive and solutions with a singular optimal topology might be encountered. Neglecting the implicit compatibility equations, an explicit approximate problem is obtained. However, the approximate displacement constraints might be meaningless in cases where members are eliminated from the structure. If the latter constraints are neglected, the resulting problem can be stated as linear programming under certain assumptions. The difficulties involved in topological optimization suggest that a two-stage design procedure might be useful. Several such procedures, where an approximate solution is evaluated at the first stage and modified at the second stage, are presented. It is shown that the first-stage solution can be viewed as the final optimum if a set of control forces or displacements is applied. The latter can readily be determined at the second stage by solving a linear programming problem.