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The design of original gridshell forms has become an increasingly complex process, which aims to search for unique spatial systems which are also effective engineering solutionsboth architecturally as well as structurally. The search for synergistic solutions which combine the aesthetics of the form with structural logic is supported by modern bionic tendencies. They allow the reproduction of the organic shapes not only by means of proportions, but also by mimicking the biological developmental processes and by understanding the logic of the structural forms occurring in nature. The analogies between architectural design and morphogenesis of biological forms have increased the interest in bionic structures as a whole. The improvement of digital tools based on algorithmic codes has enabled architects to implement their bold designs based on the logic of Nature's technologies.One of the most interesting bionic methods of discretization of structural surfaces is Delaunay triangulation, a dual graph of the Voronoi Diagram, which describes the divisions of the plane and space found in nature. Examples can be found in the patterns of a dragonfly wing, giraffe's mottled skin or a turtle's shell. The Delaunay divisions are more and more often used in the design of architectural forms based on gridshells. Solutions for such systems are obtained through generative modeling, and the algorithm responsible for the surface discretization is incorporated into 3D modeling programs. A big advantage of using digital generators in the search for optimal architectural and structural solutions is the ability to model multiple-variants and to the easily modify them (the models result from iterations of the entered numerical data).The paper will present the trends in the development of spatial bionic gridshells based on Delaunay triangulation, as well as the results from own research on selected gridshells. The undertaken analyses compare material efficiency on two analyzed cases.

The search for the structural form of reticulated roofs is significant in interdisciplinary Architectural Design optimisation. Combining parametric design with structural logic influences the visual perception of the shape by choosing the most suitable technical solutions. Therefore, the divisions of reticulated structures should be determined to pursue structural, material and fabrication advancement. Structural divisions of free-formed canopies should simultaneously be solved in architectural and structural design at an early stage. Choosing a proper design becomes a complicated process, requiring the ability to select a type of production and rationalise technical solutions mainly due to the computer-aided design supported by algorithmic tools. Based on searching for optimal geometrical divisions, the case study investigates the differences between planar quadrilateral and triangular mesh panelisation. The study concludes the assets and flaws of both geometry shaping methods of reticulated structures based on minimal weight and fabrication aspects. The study concludes that implementing the manufacturing method of the chosen type of gridshells divisions into the architectural design optimisation enhances the resulting free-form structures at the early design stage.

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Bionics is an interdisciplinary field of science, the aim of which is to create models that map processes and principles of functioning of the living organisms that can be transferred to technology. The bionic design is an interesting trend in contemporary architecture, which is characterized by the search for spatial forms in analogy to living organisms. The analyses of the possibilities to describe natural patterns using mathematical models that enable the transfer of biological structures are of particular importance. The natural patterns open up new ways to look for effective structures and materials. Shaping the forms "adapted" to the conditions, the environment and the surroundings is an element of structural design optimized in terms of working loads, which exists in accordance with the idea of a sustainable development. The paper presents the results of the research on the possibility of using mathematical models in architecture that mimic the forms found in nature and the analysis of the efficiency of bionic and geometrical forms due to the minimum weight criterion.