Deals with an approximate, but very simple, method of finding the minimum of structural weight under static loads. The design consists of assigning an appropriate rolled profile, from a given catalogue, to each structural member. The design is then formulated as a discrete structural optimization problem. The structure may be subjected to an arbitrary number of constraints imposed on stresses and structural material from members with the least stress. Presented examples are showing that the problems with k0 catalogue elements, and j0 structural members, including k0 to the power j0 combinations, can be solved with k0j0 analyses only. The knowledge needed to solve the problem is limited to structural analysis.
The potential of two distinct approaches applied to the truss discrete optimization problem is presented in the paper. The sequential discrete optimization method SDO (which is a deterministic procedure, using heuristics based on the idea of fully stressed truss design) and the genetic algorithm GA (a stochastic search method, inspired by the natural evolution model) are compared. The minimum weight design of truss structures subjected to stress and displacement constraints is investigated, including the case of multiple load conditions. The discrete design variables are areas of members, selected from a finite catalogue of available sections. Benchmark 2D and 3D problems are presented in numerical examples. The effectiveness of two approaches is discussed. The improvements of both algorithms and GA integrating the results of SDO method are proposed. They enable us to accelerate the convergence, diminish the number of structural analyses and guide to refined “near optimal” solutions.
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