Direct similarity method for thickness distorted elastic-plastic thin plates under impact loading

Abstract

In practical engineering, thin plates or stiffened plates with too small thicknesses due to machining technology limits may not be scaled accurately. Therefore, independent scaling of thickness can be considered. To overcome the shortcoming of the traditional dimension systems that use a single geometric scaling factor to relate the prototype and scaled models, the DLT- L_z dimension basis is proposed, which reflects the effect of thickness on the similarity law by introducing the dimension L_z, and the similarity framework of thickness distorted thin plates in the elastic-plastic phase is established. Afterwards, we propose the loss function method based on the DLT- L_z basis to obtain optimal scaling factors directly. In order to verify the validity of the method, numerical simulations are carried out on the distorted circular thin plate and stiffened plate. With the responses of distorted models inverted by the proposed similarity law, for the circular thin plate under impulses, the displacement, stress and strain responses show good consistency with those of the prototype in the spatial and temporal fields. For the stiffened plate impacted by a hammer, distorted models are equally capable of predicting the responses of the prototype with high accuracy. The mechanism of the effect of stiffeners on temporal similarity is further revealed, and the applicability of the proposed method for thin-walled stiffened plates is demonstrated.