A comparison of minimum constrained weight and fully stressed design problems in discrete cross-section type bar structures

Abstract

The fully stressed design and the minimum constrained weight problems are frequently handled in the structural engineering field. Both are highly related problems and when applied in bar structures, even under certain circumstances they can share the design solution. In the case of the fully stressed design problem (FSD), see e.g. [1], we are handling an inverse problem [2] using the maximum admissible stresses of the bars of a structure as references, and aiming to be able to obtain the structure whose maximum stresses equal those considered references. In the case of the minimum constrained weight problem (MCW), see e.g. [3,4,5], the lightest structure (the one with lower cost in terms of raw material) which also does not violate certain constraints (which guarantee the right completion of the structural mission) is searched. Here, constraints in relation with limit stresses, limit displacements and limit slenderness are taken into account. When considering real engineering design of bar structures, where normalized cross section types belonging to national codes are required, the use of discrete variables in the search is needed. To solve the FSD and MCW problems is possible through the use of evolutionary algorithms [6]. They, as well as other metaheuristics, being population based search methods allow a global optimization without stagnating in local optima and they admit without constraints the use of discrete variables. Their use in structural engineering, particularly in discrete bar structural optimization has been still widely researched in the recent years (see e.g. [7,8]). Even very recently, they also started to be considered as useful tools for extracting design knowledge in engineering problems, as in [9]. Nevertheless, the optimization process of both problems, FSD and MCW, can present noticeable differences, resulting in different number of fitness evaluations required to obtain the best solution. This difference in behaviour is shown in this work. Several test cases of different search space size bar structures are handled. An example in a truss bar structure -bar structures with articulated nodes and only loaded on nodes; only normal effort in bars is expected-is handled here. Results indicate some interesting relationship among both types of problems (FSD and MCW), and the analysis of the evolutionary search through some statistical metrics evidences the difference of problem landscape through highly divergent behaviour of the evolutionary process until achieving the best design in each case.