This paper introduces a novel application of the element-free Galerkin (EFG) technique for addressing the static bending behavior of thick power-law and exponential-law functionally graded plates (P-FGPs and E-FGPs). The main features of this approach include the elimination of predefined mesh requirements, high adaptability to real-world models, accuracy in stress calculation, and compliance with the C1 continuity requirements of the displacement field. The approximate effects of thickness stretching are captured by the higher-order shear deformation theory (HSDT). Additionally, this study introduces a technique to eliminate the shear-locking phenomenon through specific shape functions. The anisotropic mechanical properties, including Young’s modulus and Poisson’s ratio, exhibit continuous variation throughout the thickness of the dual-phase metalceramic membrane following power-law and exponential distributions. Moreover, this study proposes an innovative approach for estimating the central deflection of FGPs by employing the EFG method and sigmoid-cubic functions, introduced here as a novel contribution to the literature. This novel estimation function achieves excellent curve fitting, establishing itself as a highly efficient and robust solution for analyzing complex static bending behaviors of thick FG plates.

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