Buckling of reticulated shell structures

Buckling analyses of several reticulated shell structures are carried out using both an approximate equivalent shell analysis and a discrete analysis which is essentially exact. The structures considered are: an infinite reticulated beam under axial compression and resting at equally spaced intervals on elastic springs; a shallow section of a reticulated sphere with an equilateral triangle grid subject to normal loading; and an infinite reticulated cylindrical shell with an equilateral triangle grid subject to axial compression. The discrete analysis is used to evaluate the accuracy of the predictions of the equivalent shell analysis. The buckling load computed on the basis of the equivalent shell analysis is nonconservative when a characteristic wavelength of the buckling deformation is on the order of the member length or the axial load in a member at buckling is on the order of the Euler buckling load of a simply supported column. The effect on the buckling load of reducing the rigidity of the joints is investigated for both the beam-spring model and the reticulated spherical shell. Finally, the importance of the discrete analysis is illustrated by the determination of the optimum properties of a shallow section of a reticulated sphere subject to a prescribed normal loading and designed against buckling.