Scaling the Dynamic Buckling Behavior of a Box Girder Based on the Finite Similitude Approach

In the design of small-scale test models for hull structures, the directional dimensional analysis method is commonly employed. However, conventional dimensional analysis based on elasticity theory may be insufficient to capture the nonlinear behaviors of structural materials under dynamic loading, which restricts its applicability in ultimate strength tests for small-scale hull structure models. This paper presents a scaling method grounded in the theory of finite similitude. Based on the finite similitude theory, this paper deduces similarity scaling criteria applicable to the static and dynamic responses of box girders and designs a series of trial models of box girders. The scaling criteria are verified and analyzed through numerical tests conducted under static and dynamic loads. On the basis of the numerical test results of dynamic responses, the dynamic response similarity criteria considering the similarity relationship of material constitutive parameters are modified and verified. By applying the static response scaling criteria in this paper to select appropriate materials, the prediction deviation of the box girder trial models under static loads is less than 2%. With the modified dynamic response scaling criteria proposed in this paper, the prediction deviations of each trial model under dynamic loads are less than 2% and 7%. A comprehensive analysis of material parameters was conducted to examine their impact on the nonlinear similarities observed in the processes. To validate the ultimate strength and nonlinear response scaling criterion based on the finite similitude approach, numerical experiments were performed to assess the ultimate strength and dynamic buckling response characteristics of the box girder across various scaling ratios and material parameters. The analysis demonstrated that the ultimate strength scaling criterion and the nonlinear response scaling criterion derived from the finite similitude approach effectively captured material nonlinearity. The results from the small-scale model provided accurate predictions of the ultimate strength of the full-scale model.