Inversion method for tire impact load characteristics based on Green's function

This study aims to indirectly identify tire impact loads and their distribution characteristics by analyzing structural responses, providing a basis for deck design and safety assessment. A load inversion method based on Green's function is proposed.

The study focuses on the stiffened plate of a ship deck. The impact load is represented as a superposition of unit impulse loads based on Green's function. The Green's function kernel matrix is derived through finite element simulations. An inversion model is formulated by combining the Tikhonov regularization method with the generalized cross-validation （GCV） criterion. For both single and multiple tire impact scenarios, the influence of multi-source loads on inversion accuracy is analyzed. The load distribution characteristics for three typical wheel load distribution forms—convex, saddle, and concave—are inverted by equivalently dividing the force application area and applying unit impulse loads.

The proposed method effectively identifies the time history and distribution characteristics of tire impact loads, with a relative error of less than 5%. Specifically, the inversion based on strain and displacement responses achieves higher accuracy, with errors below 2%. Even with 5% noise interference, the inversion results remain consistent with the actual loads.

The proposed method addresses the challenges such as short impact load duration, limited structural response range, and multi-source impact load interactions. It provides a novel approach for identifying wheel loads on real ships, with significant engineering applicability.