This thesis, by Nanette South Clark, was presented to the Department of Civil Engineering at Idaho State University in December 2005. It features ten chapters, figures and tables discussing the history of thin-shell and Monolithic Domes, shell theory, finite element analysis, comparisons of shell theories and a buckling analysis.
Figure 9-14 from thesis: Controlling Buckling Eigenvalue λ = 141 for 101.5 ft. diameter hemisphere with 1' x 1' radial ribs 20' long at 30 degrees off 2' x 1' ring at top of dome around 12' diameter skylight. Two 1' x 1' transverse ribs are located at 10' and 20' from ring beam. Shell thickness = 5 in.
ABSTRACT:Read A finite element analysis of the Monolithic Dome in its entirety.
Four of the major influences in the history of thin-shell structures are discussed. David B. South and his brothers, Barry and Randy South, are presented as the inventors of the Monolithic Dome. Monolithic Domes are thin-shell structures constructed by applying polyurethane foam to the interior surface of an airform followed by attaching rebar to the foam. About three inches of shotcrete is then sprayed onto the interior surface. Basic stress resultants are developed from membrane theory as presented by David P. Billington. The finite element analysis process (FEA) is discussed as well as an introduction to NE/NASTRAN, a finite element analysis program. Comparisons of stress resultants between shell theory and FEA are made for a hemispherical dome, a truncated, hemispherical dome, and a non-hemispherical dome. Shell theory for domes, rings and wall interactions is introduced to facilitate a comparison between theory and FEA for the dome-ring-wall problem. Finally, a finite element buckling analysis is presented for a non-hemispherical, truncated dome with a tower. The current design practice utilizes shell theory. The finite element analysis process was found to be very accurate when compared with shell theory results and more powerful when complicated problems were presented.