Geometry optimization for geodesic dome with symmetric grid pattern

Abstract

The geometries, loading conditions, joint conditions, and geometrical imperfections of lattice domes affect their mechanical performance. Various optimization methods for lattice domes have been proposed. Some methods have been applied in actual buildings; however, they often create a new external dome shape, which may lose the aesthetic inner space intended by designers. This study conducted geometry optimization for geodesic domes using a precise mathematical expression. The symmetry of the grid pattern and the external shape of the initial dome were maintained during optimization. The optimization considered the member lengths on the meridian as design variables to reduce the number of iterations for the optimal solution. The proposed optimization scheme was applied to 64 geodesic domes using six objective functions. The optimization results were compared with those of the authors’ previous study on optimal domes, which considered the nodal coordinates on a spherical surface as the design variables. The previous and present optimal domes exhibited significant mechanical and geometric similarities when the objective function was considered as the standard deviation of the member length and minimum buckling safety factor. In addition, the computational complexity of the present optimization scheme for reaching the optimal solution was approximately 10–100 times lower than that of the previous optimization scheme. The proposed scheme can be used to optimize lattice domes with less computational complexity while ensuring their mechanical effectivity and retaining their intended inner space and external shape.