Similarity laws of geometric distortion for stiffened plate under low velocity impact loads

As a thin-walled structure, it is impractical or uneconomical to scale the thickness of stiffened plate with the same scale factor as the length, which leads to geometric distortion and the failure of traditional similarity laws. In this study, firstly, the common stiffened plate structure in engineering is selected as the object, and a reasonable equivalent technique for transforming stiffened plate into double-plate structure is proposed, which is named relative plastic capacity equivalence. Then, based on the ODLV system, the similarity law of geometric distortion for beam/plate structure is compared, and the Zhao's response number of stiffened plate is derived, from which the similarity law of co-direction geometric distortion for stiffened plate is obtained expanding the object of single thin-walled plates for the ODLV system. The similarity law of hetero-direction geometric distortion for the stiffened plate structure is derived under the premise that the relative plastic capacity K of stiffeners would be constant between the scaled model and the prototype. Satisfying this premise, the yield stress of the stiffener material and the number of stiffeners along x and y directions in the plane can both be adjusted. The similarity laws of co-direction and hetero-direction geometric distortion for stiffened plates are numerically validated through several mass-impacted stiffened plates. The results show that the similarity laws can enable the geometrically distorted stiffened plate model to predict the dynamic responses of the prototype structure, such as displacement, velocity, energy and impact force.