Abstract: Using Modified method of mutiple scales,the nonlinear stability of a truncated shallow spherical shell of variable thickness with a nondeformable rigid body at the center under uniformly distributed loads is investigated in this paper. When the geometrical parameter k is large,the uniformly valid asymptotic solutions of this problem are obtained and the remainder terms are estimated.

Key words: Shallow shell of variable thickness, Nonlinear bucking, Singular perturbation