Linear and nonlinear analysis of space trusses relative to cylindrical coordinates

Abstract

The element and system models for linear and nonlinear space trusses were formulated and implemented relative to cylindrical coordinates. Nonlinear equilibrium paths were traced using the modified Riks/Wempner method. Two radially symmetric reticulated domes which exhibit snap-through instability and which were subjected to radially symmetric loads were analyzed both linearly and nonlinearly. Along with the entire structures, "pie slices" of the structures were also analyzed. Accuracy was observed by comparison of element forces or of critical load values to those previously presented for these trusses. Reduction of computational effort from analysis of "pie slices" was studied, as were suppression and generation of bifurcation buckling modes. Structural models in cylindrical coordinates were found to greatly reduce computational effort by analysis of "pie slices" of radially symmetric structures with radially symmetric loads, and analysis of "pie slices" provided qualitative information regarding buckling mode geometries when techniques for branching onto bifurcation paths failed.