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 nondeformable rigid body at the center under compound loads is investigated. When the geometrical parameter k is larger, the uniformly valid asymptotic solutions of this problem are obtained and the remainder terms are estimated.