Geometric and material distortion similarity laws for the low-velocity impact response of stiffened plates considering elastic effects

It is well accepted that experiments employing scaled models for predicting the dynamic response of large engineering structures under impact loading can significantly reduce research time and costs. Although many studies have focused on similarity laws in distortion scaled models, elastic effects have often been neglected. To address this issue, the present study proposes impact similarity laws for the geometric distortion and material distortion of stiffened plates by considering elastic effects. Through discretizing the stiffened plate into a plate and stiffeners, similarity relationships for the plate and stiffeners are derived by adopting an equation analysis approach based on thin plate theory and Euler-Bernoulli beam theory. Furthermore, combining the displacement compatibility conditions between the plate and the stiffeners, a similarity correction technique is proposed to account for both the elastic and plastic phases, by correcting the elastic modulus and density of the stiffener material. Geometric and material distortion effects are compensated by correcting the initial impact velocity. A series of stiffened plates with different degrees of geometric distortion and based on different materials are established for numerical verification and in-depth discussion. In particular, attention focuses on the effect of the corrected velocity scaling factor on the resulting error and the validity of the similarity law under varying levels of elastic deformation. The results indicate that the proposed impact similarity law accurately predicts the dynamic response of a full-size stiffened plate prototype structure in terms of displacement, velocity, energy and impact force. The proposed similarity laws account for elastic effects, thereby expanding the applicability of existing similarity laws.