Functionally graded plates with cutouts are common load-bearing structures in engineering, making the study of their dynamic behavior crucial. For plates with regularly shaped cutouts, the symplectic superposition method combined with subdomain decomposition technique can be used to establish a comprehensive analytical solution framework. However, when the research object is extended to plates with arbitrarily shaped cutouts, which have broader applications, the analytical solution faces significant challenges due to the increased complexity of the boundary conditions. While approximate or numerical methods exist, they may suffer from time-consuming computations and strong mesh dependency, often leading to insufficient accuracy in results. A novel solution framework that integrates the symplectic superposition method with the transfer learning technique is established. It leverages the analytically solvable natural frequencies of functionally graded rectangular plates with rectangular cutouts for knowledge transfer, thereby achieving efficient and highly accurate solutions for the free vibration problems of functionally graded plates with arbitrary quadrilateral cutouts. First, a multi-layer perceptron neural network is pre-trained on large-scale analytical solution dataset to extract the complex mapping relationships of geometric parameters between different shapes. Second, the pre-trained model is transferred based on few-shot finite element simulation data, effectively transferring knowledge from the natural frequency dataset of the rectangular plates with rectangular cutouts to the free vibration of plates with arbitrary quadrilateral cutouts. Finally, the accuracy and applicability of the proposed solution framework for predicting the natural frequencies of functionally graded plates with arbitrary quadrilateral cutouts are validated, using metrics such as mean squared error and coefficient of determination. The transfer learning technique is used to lever-age small-sample data and existing analytical solutions to efficiently and accurately solve free vibration problems of functionally graded with arbitrary quadrilateral plates cutouts. The proposed framework, adaptable to various working conditions through model parameter adjustments, offers a novel strategy for the mechanical analysis of complex-shaped plates.

The Digital Image Correlation (DIC) experimental system is widely used for mechanical performance evaluation of structures in high-temperature environments due to its ability to achieve non-contact precise measurements of full-field strain. However, experimental methods based on DIC measurement technology face challenges in directly characterizing the stress field of structures, particularly in high-temperature environments where material parameters are closely related to temperature, and the heavy reliance of the Finite Element Method (FEM) on these parameters leads to insufficient accuracy of stress outcomes. Therefore, it is of great significance to understand and evaluate the mechanical properties of structures by combining high-temperature DIC experiments and FEM to accurately characterize the full-field stress of structures. This paper proposes a data fusion-knowledge transfer method for stress characterization in high-temperature DIC experiments. A high-temperature DIC experimental system, a high-precision FEM model, and a transfer learning framework are developed for typical high-temperature titanium alloys in aerospace structures, achieving accurate characterization of stress fields based on small-sample experimental data. Firstly, a multi-layer perceptron neural network is employed to pre-train large-sample simulation data, capturing the mapping relationship between structural coordinates and stress in complex high-temperature environments. Secondly, based on small-sample high-temperature DIC test data, the pre-trained model is fine-tuned to characterize a structural stress field in high-temperature environments, and effectively transfer knowledge from the finite element model to the experimental data. Finally, the accuracy and applicability of the proposed method for predicting structural stress fields are verified using indicators such as the mean square error and the coefficient of determination, which provides a new approach for characterizing experimental stress fields in high-temperature environments.