New Approach for Discrete Structural Optimization

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Abstract
A new approach for selecting optimum members in steel frames from standard hot‐rolled sections is illustrated. The approach is applied to an example 8‐story, 3‐bay planar frame subjected to vertical and horizontal loads. In the example, optimum members are defined as those which minimize total frame weight while satisfying combined stress constraints under specified loading conditions. The approach computes the discrete optimum from the continuous optimum. It is implemented as a pre‐ and post‐processor to state‐of‐the‐art nonlinear continuous optimization algorithms. The approach is general, robust, and efficient in that a minimum number of structural analyses are required. The approach uses a convex hull generation algorithm, nonlinear programming algorithms, linearization, and a variation on the branch and bound method. The approach does not require the standard sections to be ordered in any way, nor does it require any approximate relationships between section properties.

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