In this study, a novel and efficient formula based on machine learning is developed for the first time to estimate the central deflection of thick functionally graded sandwich plates (TFGSPs). The mechanical behavior of TFGSPs is modeled using the Element-Free Galerkin (EFG) method within the framework of Reddy’s higher-order shear deformation theory (HSDT), which accurately captures both shear deformation and thickness stretching effects. The sandwich structure consists of functionally graded (FG) face sheets and a homogeneous core, with material properties varying through the thickness according to Reddy’s power-law distribution. To improve prediction efficiency, a machine learning model utilizing the logistic regression algorithm and three-dimensional sigmoid estimation functions is proposed. The accuracy and reliability of the proposed approach are validated through comparisons with conventional numerical solutions. Finally, a parametric study is conducted to examine the effects of key design variables including the material gradient of FG face sheets, aspect ratio, thickness-to-length ratio, and boundary conditions on the deflection and stress distribution of TFGSPs.

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