**Jolanta Dzwierzynska**

Department of Architectural Design and Engineering Graphics; Rzeszow University of Technology, 35-084 Rzeszow, Poland; joladz@prz.edu.pl

Received: 10 January 2020; Accepted: 24 February 2020; Published: 28 February 2020

**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.

**Keywords:** a curvilinear structure; a hyperbolic paraboloid; shaping structures; structural optimization; parametric design; genetic algorithms; multi-objective optimization; topology; Grasshopper; FEM
