The method of multiple scales applied to the nonlinear stability problem of a truncated shallow spherical shell of variable thickness with the large geometrical parameter

Using the modified method of multiple scales, the nonlinear stability of a truncated shallow spherical shell of variable thickness with a nondeformabl e rigid body at the center under compound loads is investigated. When the g eometrical parameter k is larger, the uniformly valid asymptotic solutions of this problem are obtained and the remainder terms are estimated.