In order to simplify the problem, former investigations ignored some nonlinear factors that may affect the response of anchored liquid storage tanks. Several researchers tried to refine the analysis by including the effects of these factors in the analysis. Sakai and Isoe ([234], [235]) investigated the nonlinearity due to partial sliding of the anchored tank base plate on its foundation. Huang [113] performed geometrically nonlinear analysis of tanks to investigate the large deflection effect. He stated that the beneficial effects of large deflections were most pronounced in plates having restraint against in-plane displacements. This restraint can be provided by adjoining plates in tank structures. Haroun and Mourad ([86], [88], [186], [187], [188], [189]) used experimental modal analysis techniques to assess the effects of out-of-roundness imperfections on the structure response. They also examined the buckling of the actual tanks. Costley et al ([41], [42]) presented a method to determine the critical buckling load of tanks using experimental modal analysis techniques. Rinne [231] developed a criterion for buckling of the shell due to lateral forces and defined a shell buckling resistance coefficient.
Uras et al [273] studied the influence of geometrical imperfections on the dynamic stability of liquid filled shells under horizontal ground excitations. He introduced a general imperfection pattern in the circumferential direction to analyze the geometrical stiffness term. Imperfection effects on buckling of liquid-filled shells were also discussed in ([4], [35], [266]).
Zhou et al [299] presented a method for analyzing the elephant-foot buckle failure of ground-supported broad cylindrical tanks under horizontal excitations. Peek ([217], [218]) reviewed buckling criteria and showed that the plastic collapse criteria developed by axisymmetric analyses were also approximately applicable when the loading was not axisymmetric. Chiba [33] presented a theoretical analysis for the dynamic stability of a cylindrical shell partially filled with a liquid, under periodic shearing forces. He used a dynamic version of the Donnell equations and the velocity potential theory to determine the instability boundaries. Other issues related to buckling of liquid storage tanks were also presented in ([133], [158], [159], [170], [181], [190]).