Shaping of Curvilinear Steel Bar Structures for Variable Environmental Conditions Using Genetic Algorithms—Moving towards Sustainability

Abstract

The successful and effective shaping of curvilinear steel bar structures is becoming an increasingly complex and difficult task, due to the growing demands to satisfy both economic and environmental requirements. However, computer software for algorithmic-aided design makes it possible to take into account many aspects affecting structures, as early as the initial design stage. In this context, the paper presents an optimization method for shaping the curvilinear steel bar canopies of hyperbolic paraboloid and cylindroid shapes, in order to obtain effective structures adapted to external environmental conditions. The best structural solutions in terms of the structure’s shape, topology and support positions are obtained as the effects of multi-criteria optimizations with the application of genetic algorithms. The following are used as the optimization criteria: minimal structure mass and minimal deflections of the structure’s members, as well as their maximal utilization. Additionally, the best canopy locations in relation to the sides of the world are determined through analyzing their shadow casts for various locations, so the structures have the least impact on the surroundings. This research, with its interdisciplinary character, aims to present the possibility of applying generative shaping tools to obtain structurally effective and environment-adaptive curvilinear steel bar structures in the first phase of their design, which can support sustainable designing.

Algorithmic-Aided Approach for the Design and Evaluation of Curvilinear Steel Bar Structures of Unit Roofs

“…In this case, the form and topology significantly influence efficiency of the structure and the flow of forces in it [ 13 ]. As it has been shown in previous publications, the geometry of the base surface, which is divided during shaping, has a significant impact on the properties of the structure formed on its basis [ 14 ]. Ruled surfaces, which are the surfaces composed of straight lines, are especially advantageous due to their discretization [ 15 ].…”

Modeling of Curvilinear Steel Rod Structures Based on Minimal Surfaces

“…In the first method, in order to establish structure nodes' position, the coordinates of the point grid and directional vectors are used. However, in the second method, the polyhedral base solids can be used, which divide and fill a given space, or divisions of the so-called base surfaces can be applied [9]. Due to this fact, both the shape of the base surface and the kind of its division in order to establish structure's nodes are important.…”

“…This article is a continuation of the author's considerations on the shaping of effective steel rod structures, whose geometries were generated by division of the base surfaces using parametric design tools, which were presented in previous publications [9,[12][13][14][15]. There, as the base surfaces, the surfaces composed of straight lines have been used, that is, ruled surfaces such as cylindroid or hyperbolic paraboloid, which are advisable due to their easy discretization [9,[12][13][14][15].…”

“…The optimal structures in terms of their weights were obtained by genetic optimization methods. Namely, the multicriteria optimization method of shaping canopy roofs of hyperbolic paraboloid and cylindroid shapes using genetic algorithms is presented in [9,15], whereas a single criteria optimization method with the application of genetic algorithms is presented in [12][13][14].…”