Generative Design Process and Optimization of Geodesic Dome with Variable Frequency

A geodesic dome is a hemispherical thin-shell structure based on a geodesic polyhedron. The triangular elements of the hemisphere are structurally rigid and distribute the structural stress throughout the structure, making geodesic domes able to withstand heavy loads considering their size. After the first geodesic dome was built in Jena (Germany, 1922) on top of the Zeiss optics company as a projection surface for their planetarium projector, thanks to R. Buckminster Fuller, the geodesic domes have been explored far more thoroughly. As a result of their properties, these structures are used for many purposes: as residential modules, greenhouses, water reservoirs and as expositive pavilions. The present paper focuses on geodesic domes optimization, minimizing the overall volume of the frame structure and its connections. In the optimization phase, the base radius of the dome is considered constant, representing a shape constraint. The frequency variability allows for modification of the frame’s number, thus varying the structural topology while acting on the shape of the sections (shape optimization). In the case study, self-weight and asymmetric load actions are considered while including the construction aspects for the assembly of a geodesic dome. The optimization phase involves evolutionary genetic algorithms (EAs) exploiting the results of a Finite Element Analysis (FEA).