Shape Optimization of Spherical Networks

SUMMARY. Lattice shells are characterized by a significant number of different elements, whereas aesthetic, practical and economic considerations call for rendering each component (joints, bars, cladding panels) as uniform as possible. Regular subdivisions of the shell can generally be obtained by moving the joints on its middle surface until a global characteristic property of the network, expressed by some function defined on the set of nodal coordinates, reaches a relative extremum. In this paper, the geometry of single-layer spherical networks of given topology is optimized according to two criteria: the first is to minimize the sum of the bar lengths, the second to minimize their variance. The search for optimal shapes can be performed by studying the stable equilibrium configurations of a discrete set of points, movable without friction on a sphere and connected one to the other by linear elastic springs. First, the Lagrange multiplier method is used to solve both minimum prob...