Elastic–Plastic Buckling of Scaled Model of Radial Ring-Stiffened Shallow Spherical Shells Based on Energy Method

Stiffened shallow spherical shell has the advantages including high strength and light weight, which allows it to be widely applied in areas including aerospace, submarine and civil engineering. For the design of scaled model for elastic–plastic buckling of a large radially–circumferentially stiffened shallow spherical shell under uniformly distributed pressure and for the purpose of similarity prediction, the similarity relation of the elastic–plastic buckling coefficient of the shell is derived; then by using the dense stiffening theory and considering the dual nonlinearity of geometry and materials, the energy increment formula for the structure under uniformly distributed external pressure is established; next, based on the similarity transformation of the energy increment of the structural system, the generalized similarity condition and similarity relation of elastic–plastic buckling of the structure under uniformly distributed external pressure are identified. Based on the scaling and equivalence of tensile–compressive stiffness and bending stiffness, the distortion scaled model for the prototype is designed. Through numerical simulation, the distortion similarity prediction for elastic–plastic buckling under uniformly distributed pressure of the radially–circumferentially stiffened shallow spherical shell that has square-shaped dimple defects has been conducted; based on the derived similarity relation of elastic–plastic buckling of stiffened plate, the similarity prediction for the elastic–plastic buckling of orthogonally stiffened plate in the plane under unidirectional uniformly distributed pressure has been conducted. The results indicate that the load–displacement curve, buckling load, and buckling mode of the distortion similarity scaled model, combined with the established radial displacement scaling factor expression, the scaling relation of tension–compression stiffness, and the similarity relation of buckling mode, can effectively predict the elastic–plastic buckling characteristics of its prototype structure. The research results can provide theoretical reference for the design and test of the scaled model with distortion of elastic–plastic buckling of similar stiffened large shell structures.