Multi-Objective Optimizing Curvilinear Steel Bar Structures of Hyperbolic Paraboloid Canopy Roofs

Abstract

The paper concerns shaping curvilinear steel bar structures that are hyperbolic paraboloid canopy roofs by means of parametric design software Rhinoceros/Grasshopper and Karamba 3D. Hyperbolic paraboloid shape has found applications in various solutions of building roofs, mainly as reinforced concrete or steel coverings made of bent sheets. The hyperbolic paraboloid as a ruled surface can be a good base surface for forming bar grids. However, there are few studies on the effect of its division and the obtained topology of bar structures on their load-bearing capacity. In order to fill this gap, the aim of the presented research was to compare the effectiveness of various curvilinear steel bar structures of hyperbolic paraboloid canopy roofs covering the same plane, as well as defining both the most effective pattern of their structural grids and the optimal supporting system. This analysis was carried out thanks to the application of genetic algorithms enabling the free flow of information between geometrical and structural models, as well as thanks to the obtained result of multi-objective optimizations of the shaped structures for given boundary conditions. Minimal mass of the structure as well as minimal deflection of the structural members were assumed as the optimization criteria.

Architecture and Engineering: The Challenges—Trends—Achievements

“…The issue of parametric design, so attractive in recent years, is the centrepiece of the next article [7]. Rhinoceros, Grasshopper, and Karamba 3D software is commented and the calculations are supported by the finite element method (FEM).…”

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

“…A broad overview of the different kinds of spatial mesh structures, their improvement, and their applications, is presented in reference [ 18 ]. However, various analytical approaches to shaping double-layer trusses are shown in reference [ 19 ], whereas the method of shaping steel bar structures by locating their nodes on the so-called base surfaces is presented in reference [ 20 , 21 , 22 , 23 , 24 ]. Nowadays, thanks to advancements in technology, curvilinear steel bar structures with a great variety of geometries and technical solutions are being developed on a large scale.…”

“…Due to hyperbolic paraboloid’s positive static properties, they have found application in creating lightweight shell concrete structures with large spans, and have also been used to form complex multi-shell structures from single ones [ 26 , 27 ], which was pioneered by F. Candela. Despite the widespread application of the hyperbolic paraboloid surface for roof construction, there is still little research being done on the influence of its divisions, or the consequentially obtained grid patterns, on the load-bearing capacity of the steel bar structures being formed [ 22 ]. However, as far as the roofs of cylindroid shapes are concerned, they are not as popular as the hyperbolic paraboloid ones and they receive little attention in the literature.…”

“…Particularly, the article attempts to perform ESO (multi-objective evolutionary structural optimization) on the considered canopies with respect to structural requirements, which means obtaining effective structures, the reduction of steel consumption, and finding a sustainable design. A similar approach was presented in reference [ 22 ]; however, this study performed only two-objective evolutionary structural optimization, and the considered hyperbolic paraboloid structure was supported by four single columns. This research also aims to compare the efficiencies of curvilinear steel bar structures of hyperbolic paraboloid and cylindroid shapes, and aims to find the most effective and optimized structure.…”

“…The algorithmic-aided shaping of steel bar structures is a novel area of research. However, an attempt to design steel structures with the use of algorithms was undertaken in references [20][21][22][23], whereas a similar shaping of concrete shell structures was presented in reference [27].…”